Gutzwiller projection for bosons

Collective Excitations of a Strongly Correlated Nonequilibrium Photon Fluid across the Insulator-Superfluid Phase Transition

We develop a Gutzwiller theory for the nonequilibrium steady states of a strongly interacting photon fluid driven by a non-Markovian incoherent pump. In particular, we explore the collective modes of the system across the out-of-equilibrium insulator-superfluid transition of the system, characterizing the diffusive Goldstone mode in the superfluid phase and the excitation of particles and holes in the insulating one. Observable features in the pump-and-probe optical response of the system are highlighted. Our predictions are experimentally accessible to state-of-the-art circuit-QED devices and open the way for the study of novel driven-dissipative many-body scenarios with no counterparts at equilibrium.

Fine-grained domain counting and percolation analysis in two-dimensional lattice systems with linked lists

We present a fine-grained approach to identify clusters and perform percolation analysis in a two-dimensional (2D) lattice system. In our approach, we develop an algorithm based on the linked-list data structure whereby the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from the Mott insulator to the superfluid phase of bosons in 2D square optical lattices. The results obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute the correlation length using definitions based on percolation theory and use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we compute the critical exponent ν which quantify the divergence of the correlation length ξ across the phase transition and the fractal dimension of the hulls of the superfluid clusters.

Lattice Polarons across the Superfluid to Mott Insulator Transition

We study the physics of a mobile impurity confined in a two-dimensional lattice, moving within a Bose-Hubbard bath at zero temperature. Exploiting the quantum Gutzwiller formalism, we develop a beyond-Fröhlich model of the bath-impurity interaction to describe the properties of the polaronic quasiparticle formed by the dressing of the impurity by quantum fluctuations of the bath. We find a stable and well-defined polaron throughout the entire phase diagram of the bath, except for the very low tunneling limit of the hard-core superfluid. The polaron properties are highly sensitive to the different universality classes of the quantum phase transition between the superfluid and Mott insulating phases, providing an unambiguous probe of correlations and collective modes in a quantum critical many-body environment.

Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss, and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body SU(1,1) pair-coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.

Ultracold Bosons on a Regular Spherical Mesh

Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.

Nonequilibrium Fixed Points of Coupled Ising Models

Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) ℤ 2 symmetry. However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a ℤ 2 × ℤ 2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

Observation of the Mott insulator to superfluid crossover of a driven-dissipative Bose-Hubbard system

Dissipation is ubiquitous in nature and plays a crucial role in quantum systems such as causing decoherence of quantum states. Recently, much attention has been paid to an intriguing possibility of dissipation as an efficient tool for the preparation and manipulation of quantum states. We report the realization of successful demonstration of a novel role of dissipation in a quantum phase transition using cold atoms. We realize an engineered dissipative Bose-Hubbard system by introducing a controllable strength of two-body inelastic collision via photoassociation for ultracold bosons in a three-dimensional optical lattice. In the dynamics subjected to a slow ramp-down of the optical lattice, we find that strong on-site dissipation favors the Mott insulating state: The melting of the Mott insulator is delayed, and the growth of the phase coherence is suppressed. The controllability of the dissipation is highlighted by quenching the dissipation, providing a novel method for investigating a quantum many-body state and its nonequilibrium dynamics.

Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases

We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a novel universality class, with critical exponents associated with the divergence of the correlation length ν ≈ 2 / 3 and the order parameter susceptibility γ ≈ 1 / 2 . We solve the effective spin model exactly using the density matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

Motivated by recent optical lattice experiments [J.-y. Choi et al., Science 352, 1547 (2016)SCIEAS0036-807510.1126/science.aaf8834], we study the dynamics of strongly interacting bosons in the presence of disorder in two dimensions. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.

Collective phases of strongly interacting cavity photons

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin- 1 2 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 trajectory 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.

Ultracold lattice gases with periodically modulated interactions

We show that a time-dependent magnetic field inducing a periodically modulated scattering length may lead to interesting novel scenarios for cold gases in optical lattices, characterized by a nonlinear hopping depending on the number difference at neighboring sites. We discuss the rich physics introduced by this hopping, including pair superfluidity, exactly defect-free Mott-insulator states for finite hopping, and pure holon and doublon superfluids. We also address experimental detection, showing that the introduced nonlinear hopping may lead in harmonically trapped gases to abrupt drops in the density profile marking the interface between different superfluid regions.

First-order phase transitions in optical lattices with tunable three-body onsite interaction

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean-field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for a sufficiently attractive three-body interaction, the n=2 Mott lobe disappears and the system displays first-order phase transitions separating the n=1 from the n=3 lobes and the n=1 and n=3 Mott insulator from the superfluid. We also analyze the effect of finite temperature and find that transitions are still of first order at temperatures T~J, where J is the hopping matrix element.

Bosonic superfluid-insulator transition in continuous space

We investigate the zero-temperature phase diagram of interacting Bose gases in the presence of a simple cubic optical lattice, going beyond the regime where the mapping to the single-band Bose-Hubbard model is reliable. Our computational approach is a new hybrid quantum Monte Carlo method which combines algorithms used to simulate homogeneous quantum fluids in continuous space with those used for discrete lattice models of strongly correlated systems. We determine the critical interaction strength and optical lattice intensity where the superfluid-to-insulator transition takes place, considering also the regime of shallow optical lattices and strong interatomic interactions. The implications of our findings for the supersolid state of matter are discussed.

Counting atoms using interaction blockade in an optical superlattice

We report on the observation of an interaction blockade effect for ultracold atoms in optical lattices, analogous to the Coulomb blockade observed in mesoscopic solid state systems. When the lattice sites are converted into biased double wells, we detect a discrete set of steps in the well population for increasing bias potentials. These correspond to tunneling resonances where the atom number on each side of the barrier changes one by one. This allows us to count and control the number of atoms within a given well. By evaluating the amplitude of the different plateaus, we can fully determine the number distribution of the atoms in the lattice, which we demonstrate for the case of a superfluid and Mott insulating regime of 87Rb.

Supersolid bose-fermi mixtures in optical lattices

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.

Boson Mott insulators at finite temperatures

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where Mott insulator features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression.

Superfluid to Mott-insulator transition in Bose-Hubbard models

We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidence that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of preformed Mott-Hubbard sidebands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

Edge transport in 2D cold atom optical lattices

We theoretically study the observable response of edge currents in two-dimensional cold atom optical lattices. As an example, we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of the Chern number using edge currents of a topologically ordered optical lattice insulator.

Quantum phases of the extended Bose-Hubbard hamiltonian: possibility of a supersolid state of cold atoms in optical lattices

Cold atom optical lattices typically simulate zero-range Hubbard models. We discuss the theoretical possibility of using excited states of optical lattices to generate extended range Hubbard models. We find that bosons confined to higher bands of optical lattices allow for a rich phase diagram, including the supersolid phase. Using Gutzwiller, mean-field theory we establish the parameter regime necessary to maintain metastable states generated by an extended Bose-Hubbard model.

Superfluid-insulator transition in a moving system of interacting bosons

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.

Possibility of a first-order superfluid-Mott-insulator transition of spinor bosons in an optical lattice

We study the superfluid-Mott-insulator transition of antiferromagnetic spin-1 bosons in an optical lattice described by a Bose-Hubbard model. Our variational study with the Gutzwiller variational wave function determines that the superfluid-Mott-insulator transition is a first-order one at a part of the phase boundary curve, contrary to the spinless case.

Excitations of a superfluid in a three-dimensional optical lattice

We prepare a Bose-Einstein condensed gas in a three-dimensional optical lattice and study the excitation spectrum of the superfluid phase for different interaction strengths. We probe the response of the system by modulating the depth of the optical lattice along one axis. The interactions can be controlled independently by varying the tunnel coupling along the other two lattice axes. In the weakly interacting regime we observe a small susceptibility of the superfluid to excitations, while for stronger interactions an unexpected resonance appears in the excitation spectrum. In addition we measure the coherent fraction of the atomic gas, which determines the depletion of the condensate.

Oscillating superfluidity of bosons in optical lattices

Following a suggestion by Orzel et al. [Science 291, 2386 (2001)]], we analyze bosons in an optical lattice undergoing a sudden parameter change from the Mott to superfluid phase. We introduce a modified coherent states path integral to describe both phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. We calculate its damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.

Collapse and revival of the matter wave field of a Bose-Einstein condensate

A Bose-Einstein condensate represents the most 'classical' form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Nevertheless, the matter wave field has a quantized structure owing to the granularity of the discrete underlying atoms. Although such a field is usually assumed to be intrinsically stable (apart from incoherent loss processes), this is no longer true when the condensate is in a coherent superposition of different atom number states. For example, in a Bose-Einstein condensate confined by a three-dimensional optical lattice, each potential well can be prepared in a coherent superposition of different atom number states, with constant relative phases between neighbouring lattice sites. It is then natural to ask how the individual matter wave fields and their relative phases evolve. Here we use such a set-up to investigate these questions experimentally, observing that the matter wave field of the Bose-Einstein condensate undergoes a periodic series of collapses and revivals; this behaviour is directly demonstrated in the dynamical evolution of the multiple matter wave interference pattern. We attribute the oscillations to the quantized structure of the matter wave field and the collisions between individual atoms.