%0 Journal Article %D 2023 %T Effect of non-unital noise on random circuit sampling %A Bill Fefferman %A Soumik Ghosh %A Michael Gullans %A Kohdai Kuroiwa %A Kunal Sharma %X

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates — meaning it is never too "flat" — regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

%8 6/28/2023 %G eng %U https://arxiv.org/abs/2306.16659 %0 Journal Article %D 2022 %T Clifford-deformed Surface Codes %A Dua, Arpit %A Kubica, Aleksander %A Jiang, Liang %A Flammia, Steven T. %A Michael Gullans %K Disordered Systems and Neural Networks (cond-mat.dis-nn) %K FOS: Physical sciences %K Mesoscale and Nanoscale Physics (cond-mat.mes-hall) %K Quantum Physics (quant-ph) %K Statistical Mechanics (cond-mat.stat-mech) %X

Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of single-qubit Clifford operators. We first analyze CDSCs on the 3×3 square lattice and find that depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSCs with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations at finite bias outperform the thresholds and subthreshold logical error rates of the best known translationally invariant codes.

%8 1/19/2022 %G eng %U https://arxiv.org/abs/2201.07802 %R 10.48550/ARXIV.2201.07802 %0 Journal Article %J Physical Review Letters %D 2022 %T Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions %A Aidan Zabalo %A Michael Gullans %A Justin H. Wilson %A Romain Vasseur %A Andreas W. W. Ludwig %A Sarang Gopalakrishnan %A David A. Huse %A J. H. Pixley %X

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

%B Physical Review Letters %V 128 %8 2/11/2022 %G eng %U https://arxiv.org/abs/2107.03393 %R 10.1103/physrevlett.128.050602 %0 Journal Article %J Phys. Rev. Research %D 2022 %T Universal scattering with general dispersion relations %A Wang, Yidan %A Michael Gullans %A Na, Xuesen %A Whitsitt, Seth %A Alexey V. Gorshkov %K FOS: Physical sciences %K Mathematical Physics (math-ph) %K Quantum Physics (quant-ph) %X

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension D≥1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=±|d|km, where m≥2 is an integer. For a large class of these problems for any positive integer m, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson's theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D≥1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.

%B Phys. Rev. Research %V 4 %8 4/6/2022 %G eng %U https://arxiv.org/abs/2103.09830 %& 023014 %R https://doi.org/10.1103/PhysRevResearch.4.023014 %0 Journal Article %J Phys. Rev. Res. %D 2022 %T Universality in one-dimensional scattering with general dispersion relations %A Yidan Wang %A Michael Gullans %A Xuesen Na %A Alexey V. Gorshkov %X

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in one dimension when the dispersion relation is ϵ(k)=±|d|km, where m≥2 is an integer. We study impurity scattering problems in which a single-particle in a one-dimensional waveguide scatters off of an inhomogeneous, discrete set of sites locally coupled to the waveguide. For a large class of these problems, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson's theorem -- which relates the scattering phases to the number of bound states -- to impurity scattering for these more general dispersion relations.

%B Phys. Rev. Res. %V 4 %8 3/17/2021 %G eng %U https://arxiv.org/abs/2103.09830 %& 023014 %R https://doi.org/10.48550/arXiv.2103.09830 %0 Journal Article %D 2021 %T Chiral transport of hot carriers in graphene in the quantum Hall regime %A Bin Cao %A Tobias Grass %A Olivier Gazzano %A Kishan Ashokbhai Patel %A Jiuning Hu %A Markus Müller %A Tobias Huber %A Luca Anzi %A Kenji Watanabe %A Takashi Taniguchi %A David Newell %A Michael Gullans %A Roman Sordan %A Mohammad Hafezi %A Glenn Solomon %X

Photocurrent (PC) measurements can reveal the relaxation dynamics of photo-excited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. In graphene subject to a magnetic field, PC measurements are able to probe the existence of Landau levels with different edge chiralities which is exclusive to relativistic electron systems. Here, we report the accurate measurement of PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples' edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs' power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical- phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication. 

%8 10/3/2021 %G eng %U https://arxiv.org/abs/2110.01079 %0 Journal Article %D 2021 %T Constructing quantum many-body scar Hamiltonians from Floquet automata %A Pierre-Gabriel Rozon %A Michael Gullans %A Kartiek Agarwal %X

We provide a systematic approach for constructing approximate quantum many-body scars(QMBS) starting from two-layer Floquet automaton circuits that exhibit trivial many-body revivals. We do so by applying successively more restrictions that force local gates of the automaton circuit to commute concomitantly more accurately when acting on select scar states. With these rules in place, an effective local, Floquet Hamiltonian is seen to capture dynamics of the automata over a long prethermal window, and neglected terms can be used to estimate the relaxation of revivals. We provide numerical evidence for such a picture and use our construction to derive several QMBS models, including the celebrated PXP model.

%8 12/22/2021 %G eng %U https://arxiv.org/abs/2112.12153 %0 Journal Article %J Phys. Rev. Lett., in press %D 2021 %T Entanglement and purification transitions in non-Hermitian quantum mechanics %A Sarang Gopalakrishnan %A Michael Gullans %X

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.

%B Phys. Rev. Lett., in press %8 12/2/2020 %G eng %U https://arxiv.org/abs/2012.01435 %0 Journal Article %J Physical Review X %D 2021 %T Entanglement Phase Transitions in Measurement-Only Dynamics %A Ippoliti, Matteo %A Michael Gullans %A Gopalakrishnan, Sarang %A Huse, David A. %A Khemani, Vedika %X

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the "scrambling" and "un-scrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators. We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.

%B Physical Review X %V 11 %8 1/2/2021 %G eng %U https://arxiv.org/abs/2004.09560 %N 1 %! Phys. Rev. X %R 10.1103/PhysRevX.11.011030 %0 Journal Article %J Physical Review X %D 2021 %T Maximum Refractive Index of an Atomic Medium %A Andreoli, Francesco %A Michael Gullans %A High, Alexander A. %A Browaeys, Antoine %A Chang, Darrick E. %X

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single, isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density, but rather reaches a limiting value n≈1.7. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

%B Physical Review X %V 11 %8 2/18/2021 %G eng %U https://arxiv.org/abs/2006.01680 %N 1 %! Phys. Rev. X %R 10.1103/PhysRevX.11.011026 %0 Journal Article %D 2021 %T Observation of measurement-induced quantum phases in a trapped-ion quantum computer %A Crystal Noel %A Pradeep Niroula %A Daiwei Zhu %A Andrew Risinger %A Laird Egan %A Debopriyo Biswas %A Marko Cetina %A Alexey V. Gorshkov %A Michael Gullans %A David A. Huse %A Christopher Monroe %X

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

%8 6/10/2021 %G eng %U https://arxiv.org/abs/2106.05881 %0 Journal Article %D 2021 %T Singularities in nearly-uniform 1D condensates due to quantum diffusion %A Christopher L. Baldwin %A P. Bienias %A Alexey V. Gorshkov %A Michael Gullans %A M. Maghrebi %X

Dissipative systems can often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k2 (k being the wavevector) and vanishing at long wavelengths as k→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensate -- a dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation -- which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

%8 3/10/2021 %G eng %U https://arxiv.org/abs/2103.06293 %0 Journal Article %D 2021 %T Tight bounds on the convergence of noisy random circuits to uniform %A Abhinav Deshpande %A Bill Fefferman %A Alexey V. Gorshkov %A Michael Gullans %A Pradeep Niroula %A Oles Shtanko %X

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work. 

%8 12/1/2021 %G eng %U https://arxiv.org/abs/2112.00716 %0 Journal Article %J Phys. Rev. Lett., in press %D 2021 %T Tunable three-body loss in a nonlinear Rydberg medium %A Dalia P. Ornelas Huerta %A Przemyslaw Bienias %A Alexander N. Craddock %A Michael Gullans %A Andrew J. Hachtel %A Marcin Kalinowski %A Mary E. Lyon %A Alexey V. Gorshkov %A Steven L. Rolston %A J. V. Porto %X

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential to generate novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study a three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wavefunction and analytical estimates based on Fermi's Golden Rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

%B Phys. Rev. Lett., in press %8 9/28/2020 %G eng %U https://arxiv.org/abs/2009.13599 %0 Journal Article %J Physical Review B %D 2020 %T Coherent transport of spin by adiabatic passage in quantum dot arrays %A Michael Gullans %A Petta, J. R. %X

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

%B Physical Review B %V 102 %8 9/17/2020 %G eng %U https://arxiv.org/abs/2007.10582 %N 15 %! Phys. Rev. B %R 10.1103/PhysRevB.102.155404 %0 Journal Article %J Phys. Rev. B %D 2020 %T Coherent transport of spin by adiabatic passage in quantum dot arrays %A Michael Gullans %A J. R. Petta %X

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

%B Phys. Rev. B %V 102 %8 9/17/2020 %G eng %U https://arxiv.org/abs/2007.10582 %N 155404 %R https://doi.org/10.1103/PhysRevB.102.155404 %0 Journal Article %J Physical Review X %D 2020 %T Dynamical Purification Phase Transition Induced by Quantum Measurements %A Michael Gullans %A Huse, David A. %X

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate, and (ii) a "mixed" phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace where quantum information is reliably encoded against the future non-unitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal tradeoffs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The mutual information of an initially completely-mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error protected subspace. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of non-equilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

%B Physical Review X %V 10 %8 7/30/2020 %G eng %U https://arxiv.org/abs/1905.05195 %N 4 %! Phys. Rev. X %R 10.1103/PhysRevX.10.041020 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Exotic photonic molecules via Lennard-Jones-like potentials %A Przemyslaw Bienias %A Michael Gullans %A Marcin Kalinowski %A Alexander N. Craddock %A Dalia P. Ornelas-Huerta %A Steven L. Rolston %A J. V. Porto %A Alexey V. Gorshkov %X

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{ö}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

%B Phys. Rev. Lett. %V 125 %8 9/19/2020 %G eng %U https://arxiv.org/abs/2003.07864 %N 093601 %R https://doi.org/10.1103/PhysRevLett.125.093601 %0 Journal Article %D 2020 %T Quantum coding with low-depth random circuits %A Michael Gullans %A Stefan Krastanov %A David A. Huse %A Liang Jiang %A Steven T. Flammia %X

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D≥1 spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N1/D) depth suffices or that O(log3N) depth suffices for all-to-all connectivity (D→∞). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(logN) only for dimensions D≥2, and that random circuits require O(N−−√) depth for D=1. Finally, we introduce an "expurgation" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D≥2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications. 

%8 10/19/2020 %G eng %U https://arxiv.org/abs/2010.09775 %0 Journal Article %D 2020 %T Resonant enhancement of three-body loss between strongly interacting photons %A Marcin Kalinowski %A Yidan Wang %A Przemyslaw Bienias %A Michael Gullans %A Dalia P. Ornelas-Huerta %A Alexander N. Craddock %A Steven L. Rolston %A J. V. Porto %A Hans Peter Büchler %A Alexey V. Gorshkov %X

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schrödinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

%8 10/19/2020 %G eng %U https://arxiv.org/abs/2010.09772 %0 Journal Article %D 2018 %T Bose Condensation of Photons Thermalized via Laser Cooling of Atoms %A Chiao-Hsuan Wang %A Michael Gullans %A J. V. Porto %A William D. Phillips %A J. M. Taylor %X

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number-conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. Here we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.

%G eng %U https://arxiv.org/abs/1809.07777 %0 Journal Article %D 2018 %T Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal %A Tobias Graß %A Przemyslaw Bienias %A Michael Gullans %A Rex Lundgren %A Joseph Maciejko %A Alexey V. Gorshkov %X

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

%G eng %U https://arxiv.org/abs/1809.04493 %0 Journal Article %J Science %D 2018 %T Observation of three-photon bound states in a quantum nonlinear medium %A Qi-Yu Liang %A Aditya V. Venkatramani %A Sergio H. Cantu %A Travis L. Nicholson %A Michael Gullans %A Alexey V. Gorshkov %A Jeff D. Thompson %A Cheng Chin %A Mikhail D. Lukin %A Vladan Vuletic %X

Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

%B Science %V 359 %P 783-786 %8 2018/02/16 %G eng %U http://science.sciencemag.org/content/359/6377/783 %N 6377 %R 10.1126/science.aao7293 %0 Journal Article %D 2018 %T Photon propagation through dissipative Rydberg media at large input rates %A Przemyslaw Bienias %A James Douglas %A Asaf Paris-Mandoki %A Paraj Titum %A Ivan Mirgorodskiy %A Christoph Tresp %A Emil Zeuthen %A Michael Gullans %A Marco Manzoni %A Sebastian Hofferberth %A Darrick Chang %A Alexey V. Gorshkov %X

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions. 

%G eng %U https://arxiv.org/abs/1807.07586 %0 Journal Article %J Phys. Rev. A 98, 013834 %D 2018 %T Photon thermalization via laser cooling of atoms %A Chiao-Hsuan Wang %A Michael Gullans %A J. V. Porto %A William D. Phillips %A J. M. Taylor %X

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.

%B Phys. Rev. A 98, 013834 %8 2018 %G eng %U https://arxiv.org/abs/1712.08643 %R https://doi.org/10.1103/PhysRevA.98.013834 %0 Journal Article %J Physical Review B %D 2018 %T Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X

Electron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

%B Physical Review B %V 97 %P 035305 %8 2018/01/16 %G eng %U https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305 %N 3 %R 10.1103/PhysRevB.97.035305 %0 Journal Article %D 2018 %T Single-photon bound states in atomic ensembles %A Yidan Wang %A Michael Gullans %A Antoine Browaeys %A J. V. Porto %A Darrick E. Chang %A Alexey V. Gorshkov %X

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

%G eng %U https://arxiv.org/abs/1809.01147 %0 Journal Article %J Physical Review Letters %D 2017 %T Correlated Photon Dynamics in Dissipative Rydberg Media %A Emil Zeuthen %A Michael Gullans %A Mohammad F. Maghrebi %A Alexey V. Gorshkov %X

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

%B Physical Review Letters %V 119 %P 043602 %8 2017/07/26 %G eng %U https://arxiv.org/abs/1608.06068 %N 4 %R 10.1103/PhysRevLett.119.043602 %0 Journal Article %J Physical Review Letters %D 2017 %T Efimov States of Strongly Interacting Photons %A Michael Gullans %A S. Diehl %A S. T. Rittenhouse %A B. P. Ruzic %A J. P. D'Incao %A P. Julienne %A Alexey V. Gorshkov %A J. M. Taylor %X

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

%B Physical Review Letters %V 119 %P 233601 %8 2017/12/04 %G eng %U https://arxiv.org/abs/1709.01955 %N 23 %R 10.1103/PhysRevLett.119.233601 %0 Journal Article %J Physical Review B %D 2017 %T High-Order Multipole Radiation from Quantum Hall States in Dirac Materials %A Michael Gullans %A J. M. Taylor %A Atac Imamoglu %A Pouyan Ghaemi %A Mohammad Hafezi %X

Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

%B Physical Review B %V 95 %P 235439 %8 2017/06/30 %G eng %U https://arxiv.org/abs/1701.03464 %N 23 %R 10.1103/PhysRevB.95.235439 %0 Journal Article %J Physical Review Letters %D 2017 %T Light-induced fractional quantum Hall phases in graphene %A Areg Ghazaryan %A Tobias Graß %A Michael Gullans %A Pouyan Ghaemi %A Mohammad Hafezi %X

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

%B Physical Review Letters %V 119 %P 247403 %8 2017/12/15 %G eng %U https://arxiv.org/abs/1612.08748 %N 24 %R 10.1103/PhysRevLett.119.247403 %0 Journal Article %J Physical Review Letters %D 2017 %T Threshold Dynamics of a Semiconductor Single Atom Maser %A Liu, Y.-Y. %A Stehlik, J. %A Eichler, C. %A Mi, X. %A Hartke, T. R. %A Michael Gullans %A J. M. Taylor %A Petta, J. R. %X

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

%B Physical Review Letters %V 119 %P 097702 %8 2017/08/31 %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.097702 %N 9 %R 10.1103/PhysRevLett.119.097702 %0 Journal Article %J Physical Review B %D 2017 %T Valley Blockade in a Silicon Double Quantum Dot %A Justin K. Perron %A Michael Gullans %A J. M. Taylor %A M. D. Stewart, Jr. %A Neil M. Zimmerman %X

Electrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots' carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

%B Physical Review B %V 96 %P 205302 %8 2017/11/13 %G eng %U https://arxiv.org/abs/1607.06107 %N 20 %R 10.1103/PhysRevB.96.205302 %0 Journal Article %J Physical Review X %D 2016 %T Double Quantum Dot Floquet Gain Medium %A J. Stehlik %A Y.-Y. Liu %A C. Eichler %A T. R. Hartke %A X. Mi %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X

Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a "Floquet gain medium," where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

%B Physical Review X %V 6 %P 041027 %8 2016/11/07 %G eng %U http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027 %R 10.1103/PhysRevX.6.041027 %0 Journal Article %J Physical Review Letters %D 2016 %T Effective Field Theory for Rydberg Polaritons %A Michael Gullans %A J. D. Thompson %A Y. Wang %A Q. -Y. Liang %A V. Vuletic %A M. D. Lukin %A Alexey V. Gorshkov %X

We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

%B Physical Review Letters %V 117 %P 113601 %8 2016/09/09 %G eng %U http://arxiv.org/abs/1605.05651 %N 11 %R http://dx.doi.org/10.1103/PhysRevLett.117.113601 %0 Journal Article %J Physical Review Letters %D 2016 %T Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot %A Michael Gullans %A J. Stehlik %A Y. -Y. Liu %A J. R. Petta %A J. M. Taylor %X

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

%B Physical Review Letters %V 117 %P 056801 %8 2016/07/25 %G eng %U http://arxiv.org/abs/1512.01248 %N 5 %R http://dx.doi.org/10.1103/PhysRevLett.117.056801 %0 Journal Article %J Physical Review Letters %D 2015 %T Coulomb bound states of strongly interacting photons %A Mohammad F. Maghrebi %A Michael Gullans %A P. Bienias %A S. Choi %A I. Martin %A O. Firstenberg %A M. D. Lukin %A H. P. Büchler %A Alexey V. Gorshkov %X We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. %B Physical Review Letters %V 115 %P 123601 %8 2015/09/16 %G eng %U http://arxiv.org/abs/1505.03859v1 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.115.123601 %0 Journal Article %J Physical Review A %D 2015 %T Injection Locking of a Semiconductor Double Quantum Dot Micromaser %A Y. -Y. Liu %A J. Stehlik %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. %B Physical Review A %V 92 %P 053802 %8 2015/11/02 %G eng %U http://arxiv.org/abs/1508.04147 %N 5 %R 10.1103/PhysRevA.92.053802 %0 Journal Article %J Physical Review B %D 2015 %T Optical Control of Donor Spin Qubits in Silicon %A Michael Gullans %A J. M. Taylor %X We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon $\Lambda$-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective $\Lambda$-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons. %B Physical Review B %V 92 %P 195411 %8 2015/11/11 %G eng %U http://arxiv.org/abs/1507.07929 %N 19 %R 10.1103/PhysRevB.92.195411 %0 Journal Article %J Physical Review Letters %D 2015 %T Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser %A Michael Gullans %A Y. -Y. Liu %A J. Stehlik %A J. R. Petta %A J. M. Taylor %X We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. %B Physical Review Letters %V 114 %P 196802 %8 2015/05/13 %G eng %U http://arxiv.org/abs/1501.03499v3 %N 19 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.196802 %0 Journal Article %J Physical Review A %D 2015 %T Quantum Nonlinear Optics Near Optomechanical Instabilities %A Xunnong Xu %A Michael Gullans %A J. M. Taylor %X Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons. %B Physical Review A %V 91 %P 013818 %8 2015/01/09 %G eng %U http://arxiv.org/abs/1404.3726v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.91.013818 %0 Journal Article %J Science %D 2015 %T Semiconductor double quantum dot micromaser %A Y. -Y. Liu %A J. Stehlik %A C. Eichler %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. %B Science %V 347 %P 285 - 287 %8 2015/01/15 %G eng %U http://arxiv.org/abs/1507.06359v1 %N 6219 %! Science %R 10.1126/science.aaa2501 %0 Journal Article %D 2014 %T A Quantum Network of Silicon Qubits using Mid-Infrared Graphene Plasmons %A Michael Gullans %A J. M. Taylor %X We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods. %8 2014/07/25 %G eng %U http://arxiv.org/abs/1407.7035v1 %0 Journal Article %J Physical Review A %D 2014 %T Scattering resonances and bound states for strongly interacting Rydberg polaritons %A P. Bienias %A S. Choi %A O. Firstenberg %A Mohammad F. Maghrebi %A Michael Gullans %A M. D. Lukin %A Alexey V. Gorshkov %A H. P. Büchler %X We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. %B Physical Review A %V 90 %8 2014/11/3 %G eng %U http://arxiv.org/abs/1402.7333v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.90.053804 %0 Journal Article %J Science %D 2013 %T All-Optical Switch and Transistor Gated by One Stored Photon %A Wenlan Chen %A Kristin M. Beck %A Robert Bücker %A Michael Gullans %A Mikhail D. Lukin %A Haruka Tanji-Suzuki %A Vladan Vuletic %X The realization of an all-optical transistor where one 'gate' photon controls a 'source' light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. %B Science %V 341 %P 768 - 770 %8 2013/07/04 %G eng %U http://arxiv.org/abs/1401.3194v1 %N 6147 %! Science %R 10.1126/science.1238169 %0 Journal Article %J Physical Review B %D 2013 %T Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots %A Michael Gullans %A J. J. Krich %A J. M. Taylor %A B. I. Halperin %A M. D. Lukin %X We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. %B Physical Review B %V 88 %8 2013/7/15 %G eng %U http://arxiv.org/abs/1212.6953v3 %N 3 %! Phys. Rev. B %R 10.1103/PhysRevB.88.035309 %0 Journal Article %J Physical Review Letters %D 2013 %T Single-photon nonlinear optics with graphene plasmons %A Michael Gullans %A D. E. Chang %A F. H. L. Koppens %A F. J. García de Abajo %A M. D. Lukin %X We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. %B Physical Review Letters %V 111 %8 2013/12/11 %G eng %U http://arxiv.org/abs/1309.2651v3 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.247401 %0 Journal Article %J Physical Review Letters %D 2012 %T Nanoplasmonic Lattices for Ultracold atoms %A Michael Gullans %A T. Tiecke %A D. E. Chang %A J. Feist %A J. D. Thompson %A J. I. Cirac %A P. Zoller %A M. D. Lukin %X We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. %B Physical Review Letters %V 109 %8 2012/12/6 %G eng %U http://arxiv.org/abs/1208.6293v3 %N 23 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.109.235309 %0 Journal Article %J Physical Review A %D 2010 %T Adiabatic preparation of many-body states in optical lattices %A Anders S. Sorensen %A Ehud Altman %A Michael Gullans %A J. V. Porto %A Mikhail D. Lukin %A Eugene Demler %X We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions. %B Physical Review A %V 81 %8 2010/6/22 %G eng %U http://arxiv.org/abs/0906.2567v3 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.061603 %0 Journal Article %J Physical Review Letters %D 2010 %T Dynamic Nuclear Polarization in Double Quantum Dots %A Michael Gullans %A J. J. Krich %A J. M. Taylor %A H. Bluhm %A B. I. Halperin %A C. M. Marcus %A M. Stopa %A A. Yacoby %A M. D. Lukin %X We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. %B Physical Review Letters %V 104 %8 2010/6/4 %G eng %U http://arxiv.org/abs/1003.4508v2 %N 22 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.104.226807