We 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 B %D 2016 %T Kaleidoscope of quantum phases in a long-range interacting spin-1 chain %A Zhe-Xuan Gong %A Mohammad F. Maghrebi %A Anzi Hu %A Michael Foss-Feig %A Philip Richerme %A Christopher Monroe %A Alexey V. Gorshkov %X Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. %B Physical Review B %V 93 %P 205115 %8 2016/05/11 %G eng %U http://arxiv.org/abs/1510.02108 %N 20 %R http://dx.doi.org/10.1103/PhysRevB.93.205115 %0 Journal Article %J Physical Review B %D 2016 %T Topological phases with long-range interactions %A Zhe-Xuan Gong %A Mohammad F. Maghrebi %A Anzi Hu %A Michael L. Wall %A Michael Foss-Feig %A Alexey V. Gorshkov %X Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. %B Physical Review B %V 93 %P 041102 %8 2016/01/08 %G eng %U http://arxiv.org/abs/1505.03146 %N 4 %R 10.1103/PhysRevB.93.041102 %0 Journal Article %J Physical Review A %D 2011 %T Detecting paired and counterflow superfluidity via dipole oscillations %A Anzi Hu %A L. Mathey %A Eite Tiesinga %A Ippei Danshita %A Carl J. Williams %A Charles W. Clark %X We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. %B Physical Review A %V 84 %8 2011/10/27 %G eng %U http://arxiv.org/abs/1103.3513v3 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.84.041609 %0 Journal Article %J Physical Review A %D 2010 %T Noise correlations of one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Carl J. Williams %A Charles W. Clark %X We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. %B Physical Review A %V 81 %8 2010/6/2 %G eng %U http://arxiv.org/abs/1002.4918v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.063602 %0 Journal Article %J Physical Review A %D 2009 %T Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Ippei Danshita %A Eite Tiesinga %A Carl J. Williams %A Charles W. Clark %X We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. %B Physical Review A %V 80 %8 2009/8/24 %G eng %U http://arxiv.org/abs/0906.2150v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.80.023619