Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.

%8 04/02/2019 %G eng %U https://arxiv.org/abs/1904.00016 %0 Journal Article %J J. Phys. B: At. Mol. Opt. Phys. %D 2018 %T Machine learning assisted readout of trapped-ion qubits %A Alireza Seif %A Kevin A. Landsman %A Norbert M. Linke %A Caroline Figgatt %A C. Monroe %A Mohammad Hafezi %XWe reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

%B J. Phys. B: At. Mol. Opt. Phys. %V 51 %8 2018/05/01 %G eng %U https://arxiv.org/abs/1804.07718 %& 174006 %R https://doi.org/10.1088/1361-6455/aad62b %0 Journal Article %J Physical Review A %D 2017 %T Emergent equilibrium in many-body optical bistability %A Michael Foss-Feig %A Pradeep Niroula %A Jeremy T. Young %A Mohammad Hafezi %A Alexey V. Gorshkov %A Ryan M. Wilson %A Mohammad F. Maghrebi %XMany-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

%B Physical Review A %V 95 %P 043826 %8 2017/04/17 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826 %R doi.org/10.1103/PhysRevA.95.043826 %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 Jacob M. Taylor %A Atac Imamoglu %A Pouyan Ghaemi %A Mohammad Hafezi %XTopological 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 J. Gullans %A Pouyan Ghaemi %A Mohammad Hafezi %XWe 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 A %D 2016 %T Collective phases of strongly interacting cavity photons %A Ryan M. Wilson %A Khan W. Mahmud %A Anzi Hu %A Alexey V. Gorshkov %A Mohammad Hafezi %A Michael Foss-Feig %XWe study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

%B Physical Review A %V 94 %P 033801 %8 2016/09/01 %G eng %U http://arxiv.org/abs/1601.06857 %N 3 %R http://dx.doi.org/10.1103/PhysRevA.94.033801 %0 Journal Article %J Physical Review A %D 2015 %T Fractional Quantum Hall States of Rydberg Polaritons %A Mohammad F. Maghrebi %A Norman Y. Yao %A Mohammad Hafezi %A Thomas Pohl %A Ofer Firstenberg %A Alexey V. Gorshkov %X We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. %B Physical Review A %V 91 %P 033838 %8 2015/03/31 %G eng %U http://arxiv.org/abs/1411.6624v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.91.033838 %0 Journal Article %J Nature Physics %D 2008 %T Anyonic interferometry and protected memories in atomic spin lattices %A Liang Jiang %A Gavin K. Brennen %A Alexey V. Gorshkov %A Klemens Hammerer %A Mohammad Hafezi %A Eugene Demler %A Mikhail D. Lukin %A Peter Zoller %X Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. %B Nature Physics %V 4 %P 482 - 488 %8 2008/4/20 %G eng %U http://arxiv.org/abs/0711.1365v1 %N 6 %! Nat Phys %R 10.1038/nphys943