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 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 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 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 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 %0 Journal Article %J Nature Physics %D 2008 %T High-sensitivity diamond magnetometer with nanoscale resolution %A J. M. Taylor %A P. Cappellaro %A L. Childress %A L. Jiang %A D. Budker %A P. R. Hemmer %A A. Yacoby %A R. Walsworth %A M. D. Lukin %X We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$. %B Nature Physics %V 4 %P 810 - 816 %8 2008/9/14 %G eng %U http://arxiv.org/abs/0805.1367v1 %N 10 %! Nat Phys %R 10.1038/nphys1075 %0 Journal Article %J Physical Review A %D 2007 %T A fast and robust approach to long-distance quantum communication with atomic ensembles %A L. Jiang %A J. M. Taylor %A M. D. Lukin %X Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality. %B Physical Review A %V 76 %8 2007/7/2 %G eng %U http://arxiv.org/abs/quant-ph/0609236v3 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.76.012301 %0 Journal Article %J Physical Review B %D 2007 %T Relaxation, dephasing, and quantum control of electron spins in double quantum dots %A J. M. Taylor %A J. R. Petta %A A. C. Johnson %A A. Yacoby %A C. M. Marcus %A M. D. Lukin %X Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. %B Physical Review B %V 76 %8 2007/7/13 %G eng %U http://arxiv.org/abs/cond-mat/0602470v2 %N 3 %! Phys. Rev. B %R 10.1103/PhysRevB.76.035315 %0 Journal Article %D 2006 %T Cavity quantum electrodynamics with semiconductor double-dot molecules on a chip %A J. M. Taylor %A M. D. Lukin %X We describe a coherent control technique for coupling electron spin states associated with semiconductor double-dot molecule to a microwave stripline resonator on a chip. We identify a novel regime of operation in which strong interaction between a molecule and a resonator can be achieved with minimal decoherence, reaching the so-called strong coupling regime of cavity QED. We describe potential applications of such a system, including low-noise coherent electrical control, fast QND measurements of spin states, and long-range spin coupling. %8 2006/05/05 %G eng %U http://arxiv.org/abs/cond-mat/0605144v1 %0 Journal Article %J Physical Review Letters %D 2006 %T Fault-tolerant Quantum Communication with Minimal Physical Requirements %A L. Childress %A J. M. Taylor %A A. S. Sorensen %A M. D. Lukin %X We describe a novel protocol for a quantum repeater which enables long distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits. %B Physical Review Letters %V 96 %8 2006/2/23 %G eng %U http://arxiv.org/abs/quant-ph/0410123v3 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.96.070504 %0 Journal Article %D 2005 %T Dephasing of quantum bits by a quasi-static mesoscopic environment %A J. M. Taylor %A M. D. Lukin %X We examine coherent processes in a two-state quantum system that is strongly coupled to a mesoscopic spin bath and weakly coupled to other environmental degrees of freedom. Our analysis is specifically aimed at understanding the quantum dynamics of solid-state quantum bits such as electron spins in semiconductor structures and superconducting islands. The role of mesoscopic degrees of freedom with long correlation times (local degrees of freedom such as nuclear spins and charge traps) in qubit-related dephasing is discussed in terms of a quasi-static bath. A mathemat- ical framework simultaneously describing coupling to the slow mesoscopic bath and a Markovian environment is developed and the dephasing and decoherence properties of the total system are investigated. The model is applied to several specific examples with direct relevance to current ex- periments. Comparisons to experiments suggests that such quasi-static degrees of freedom play an important role in current qubit implementations. Several methods of mitigating the bath-induced error are considered. %8 2005/12/07 %G eng %U http://arxiv.org/abs/quant-ph/0512059v2 %0 Journal Article %J Physical Review A %D 2005 %T Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters %A L. I. Childress %A J. M. Taylor %A A. S. Sorensen %A M. D. Lukin %X We analyze a novel method that uses fixed, minimal physical resources to achieve generation and nested purification of quantum entanglement for quantum communication over arbitrarily long distances, and discuss its implementation using realistic photon emitters and photonic channels. In this method, we use single photon emitters with two internal degrees of freedom formed by an electron spin and a nuclear spin to build intermediate nodes in a quantum channel. State-selective fluorescence is used for probabilistic entanglement generation between electron spins in adjacent nodes. We analyze in detail several approaches which are applicable to realistic, homogeneously broadened single photon emitters. Furthermore, the coupled electron and nuclear spins can be used to efficiently implement entanglement swapping and purification. We show that these techniques can be combined to generate high-fidelity entanglement over arbitrarily long distances. We present a specific protocol that functions in polynomial time and tolerates percent-level errors in entanglement fidelity and local operations. The scheme has the lowest requirements on physical resources of any current scheme for fully fault-tolerant quantum repeaters. %B Physical Review A %V 72 %8 2005/11/28 %G eng %U http://arxiv.org/abs/quant-ph/0502112v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.72.052330 %0 Journal Article %J Physical Review Letters %D 2005 %T Solid-state circuit for spin entanglement generation and purification %A J. M. Taylor %A W. Dür %A P. Zoller %A A. Yacoby %A C. M. Marcus %A M. D. Lukin %X We show how realistic charge manipulation and measurement techniques, combined with the exchange interaction, allow for the robust generation and purification of four-particle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherence-free subspace; all additional errors are corrected by a purification protocol. This approach may find application in quantum computation, communication, and metrology. %B Physical Review Letters %V 94 %8 2005/6/15 %G eng %U http://arxiv.org/abs/cond-mat/0503255v2 %N 23 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.94.236803 %0 Journal Article %D 2004 %T Quantum information processing using localized ensembles of nuclear spins %A J. M. Taylor %A G. Giedke %A H. Christ %A B. Paredes %A J. I. Cirac %A P. Zoller %A M. D. Lukin %A A. Imamoglu %X We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. %8 2004/07/23 %G eng %U http://arxiv.org/abs/cond-mat/0407640v2 %0 Journal Article %J Physical Review Letters %D 2003 %T Controlling a mesoscopic spin environment by quantum bit manipulation %A J. M. Taylor %A A. Imamoglu %A M. D. Lukin %X We present a unified description of cooling and manipulation of a mesoscopic bath of nuclear spins via coupling to a single quantum system of electronic spin (quantum bit). We show that a bath cooled by the quantum bit rapidly saturates. Although the resulting saturated states of the spin bath (``dark states'') generally have low degrees of polarization and purity, their symmetry properties make them a valuable resource for the coherent manipulation of quantum bits. Specifically, we demonstrate that the dark states of nuclear ensembles can be used to coherently control the system-bath interaction and to provide a robust, long-lived quantum memory for qubit states. %B Physical Review Letters %V 91 %8 2003/12/10 %G eng %U http://arxiv.org/abs/cond-mat/0308459v1 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.91.246802 %0 Journal Article %J Physical Review Letters %D 2003 %T Long-lived memory for mesoscopic quantum bits %A J. M. Taylor %A C. M. Marcus %A M. D. Lukin %X We describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for ``engineering'' entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system. %B Physical Review Letters %V 90 %8 2003/5/20 %G eng %U http://arxiv.org/abs/cond-mat/0301323v1 %N 20 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.90.206803