We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. Within a generalized Gutzwiller approach which includes the description of mixed state density matrices, we characterize the complete phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.
We study a circularly moving impurity in an atomic condensate for the realisation of superradiance phenomena in tabletop experiments. The impurity is coupled to the density fluctuations of the condensate and, in a quantum field theory language, it serves as an analog of a detector for the quantum phonon field. For sufficiently large rotation speeds, the zero-point fluctuations of the phonon field induce a sizeable excitation rate of the detector even when the condensate is initially at rest in its ground state. For spatially confined condensates and harmonic detectors, such a superradiant emis…
Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly, and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-pa…
Large clouds of cold atoms prepared in a magneto-optical trap are known to present spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears similarities with trapped plasmas where the role of the Coulomb interaction is played by the exchange of scattered photons, and astrophysical objects such as stars whose size is dependent on radiative forces. We present in this paper a study of the phase-space of such instabilities, and reveal different dynamical regimes. Three dimensional simulations of the highly nonlinear atomic d…
We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body theory with density-density interactions. A variety of correlations and structures arise as the inter- and intra- species interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of select…
Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible---thanks to tremendous progress in cooling, trapping, and manipulating ultracold samples---to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two part…
Tunability of effective two body interactions near Feshbach resonances is a powerful experimental tool in systems of ultracold atoms. It has been used to explore a variety of intriguing phenomena in recent experiments. However not all of the many-body properties of such systems can be understood in terms of effective models with contact interaction given by the scattering length of the two particles in vacuum. For example, when a two component Fermi mixture is quenched to the BEC side of the Feshbach resonance, a positive scattering length suggests that interactions are repulsive and thus coll…
We propose a novel type of a Bose-Hubbard ladder model based on an open quantum-gas--cavity-QED setup to study the physics of dynamical gauge potentials. Atomic tunneling along opposite directions in the two legs of the ladder is mediated by photon scattering from transverse pump lasers to two distinct cavity modes. The resulting interplay between cavity photon dissipation and the optomechanical atomic back-action then induces an average-density-dependent dynamical gauge field. The dissipation-stabilized steady-state atomic motion along the legs of the ladder leads either to a pure chiral curr…
Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and inter-particle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet-engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabiliti…
Large three-body losses in a three-component Fermi gas confined in an optical lattice can prevent the occupation of a lattice site by three atoms. This effective constraint not only gives rise to a suppression of actual three-body loss, but stabilises BCS pairing phases by suppressing the formation of trions. We study the effects of the constraint using bosonisation and density matrix renormalisation group techniques (DMRG). We discuss the case of lithium experiments, and study the dissipative dynamics including loss using time-dependent DMRG with quantum trajectories methods.
We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transp…
A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with delta-function interactions. We report on measurements of the contact, using RF spectroscopy, for an $^{85}$Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short timescales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In i…
We study the physics of a three-component Fermi gas in an optical lattice, in the presence of a strong three-body constraint arising due to three-body loss. Using analytical and numerical techniques, we show that an atomic color superfluid phase is formed in this system and undergoes phase separation between unpaired fermions and superfluid pairs. This phase separation survives well above the critical temperature, giving a clear experimental signature of the three-body constraint.
We consider the ground states of binary atomic boson-boson and fermion-fermion mixtures confined in one-dimensional box potentials by simulating the systems using few-body models with delta-function interactions and many-body models with density-density interactions. For boson-boson mixtures, both models show signatures of phase separation in the strong repulsion regime and sandwiched structures emerge in the presence of mass imbalance. The structural difference between equal-mass and mass-imbalanced systems is due to the minimization of the interaction energy and the kinetic energies from the…
We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF type experiment.
We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO coupling strength. Nevertheless, these trimers exhibit a new kind of discrete scaling law incorporating the…
We theoretically investigate superradiance effects in quantum field theories in curved space-times by proposing an analogue model based on Bose--Einstein condensates subject to a synthetic vector potential. The breaking of the irrotationality constraint of superfluids allows to study superradiance in simple planar geometries and obtain intuitive insight in the amplified scattering processes at ergosurfaces. When boundary conditions are modified allowing for reflections, dynamical instabilities are found, similar to the ones of ergoregions in rotating space-times. Their stabilization by horizon…
Recent experimental advances in the field of cold-atom cavity QED provide a powerful tool for exploring non-equilibrium correlated quantum phenomena beyond conventional condensed-matter scenarios. We present the dynamical phase diagram of a driven Bose-Einstein condensate coupled with the light field of a cavity, with a transverse driving field red-detuned from atomic resonance. We identify regions in parameter space showing dynamical instabilities in the form of limit cycles, which evolve into chaotic behavior in the strong driving limit. Such limit cycles originate from the interplay between…
Suppressing Parametric Instabilities in Driven Bosonic Lattices through Multi-tone Control
University of Strathclyde（斯特拉斯克莱德大学）；University of Birmingham（伯明翰大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；ETH Zürich（苏黎世联邦理工学院）；Collège de France（法兰西公学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎文理研究大学）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）；Université Libre de Bruxelles（布鲁塞尔自由大学）
The simplest model for itinerant ferromagnetism, the Stoner model, has so far eluded experimental observation in repulsive ultracold fermions due to rapid three-body recombination at large scattering lengths. Here we show that a ferromagnetic phase can be stabilised by imposing a moderate optical lattice. The reduced kinetic energy drop upon formation of a polarized phase in an optical lattice extends the ferromagnetic phase to smaller scattering lengths where three-body recombination is small enough to permit experimental detection of the phase. We also show, using time dependent density func…
A recent experiment has provided the first evidence for itinerant ferromagnetism in an ultracold atomic gas of fermions with repulsive interactions. However, the gas in this regime is also subject to significant three-body loss. We adopt an extended Hertz-Millis theory to account for the effect of loss on the transition and on the ferromagnetic state. We find that the losses damp quantum fluctuations and thereby significantly increase the critical interaction strength needed to induce ferromagnetism. This effect may resolve a discrepancy between the experiment and previous theoretical predicti…
We report on three-body recombination of a single trapped Rb^+ ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K_3 depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is…
We use an effective-field-theory framework to analyze the Efimov effect in heteronuclear three-body systems consisting of two species of atoms with a large interspecies scattering length. In the leading-order description of this theory, various three-body observables in heteronuclear mixtures can be universally parameterized by one three-body parameter. We present the next-to-leading corrections, which include the effects of the finite interspecies effective range and the finite intraspecies scattering length, to various three-body observables. We show that only one additional three-body param…
In Efimov physics, a three-body parameter (3BP), previously regarded as nonuniversal, uniquely defines bound and scattering properties of three particles. A universal 3BP, however, have been recently shown in experiments and theory in ultracold homonuclear gases. Our present study further predicts a universal 3BP for heteronuclear atomic systems near broad Feshbach resonances, and provides physical interpretations for its origin. We show that for a system composed of two light and one heavy atoms, the physical origin of the universal 3BP is similar to the homonuclear case while for systems com…
Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. Here we investigate the strong coupling between atomic internal ("spin") degrees of freedom and motion, which arises from spin-dependent forces associated with the exchange of guided photons. We show that this system can realize a remarkable and extreme limit of quantum spin-orbital systems, where both the direct spin exchange between neighboring sites and the kinetic energy of the orbital motion vanish. We find that this previously unexplored system has a rich phase diagram of emer…
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its non-equilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. As hallmarks of the many-body localized phase we confirm, furthermore, a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size a…
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long-range, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio …
Topologically-ordered matter is a novel quantum state of matter observed only in a small number of physical systems, notably two-dimensional electron systems exhibiting fractional quantum Hall effects. It was recently proposed that a simple form of topological matter may be created in interacting systems of rotating ultra-cold atoms. We describe ensemble measurements on small, rotating clusters of interacting bosonic atoms, demonstrating that they can be induced into quantum ground states closely analogous to topological states of electronic systems. We report measurements of inter-particle co…
We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature and superfluid transition temperature $T_c$ and superfluid density in a manner consistent with the standard ground state equations, and thereby present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for $T_c$, or by low $T$ instabilities. At unitarity the polarized state is an ``intermediate temperature superfluid".
Three-body recombination is a prime example of the fundamental interaction between three particles. Due to the complexity of this process it has resisted a comprehensive description. Experimental investigations have mainly focussed on the observation of corresponding loss rates without revealing information on the reaction products. Here, we provide the first general experimental study on the population distribution of molecular quantum states after three-body recombination in a non-resonant regime. We have developed a highly sensitive detection scheme which combines photoionization of the mol…
Collective excitations (spinwaves) of long-lived atomic hyperfine states can be synthesized into a Bose-Hubbard model in momentum space. We explore many-body ground states and dynamics of a two-leg momentum-space lattice formed by two coupled hyperfine states. Essential ingredients of this setting are a staggered artificial magnetic field engineered by lasers that couple the spinwave states, and a state-dependent long-range interaction, which is induced by laser-dressing a hyperfine state to a Rydberg state. The Rydberg dressed two-body interaction gives rise to a state-dependent blockade in m…
Systems of three particles show a surprising feature in their bound state spectrum: a series of geometrically scaled states, known as Efimov states. These states have not yet been observed directly, but many recent experiments show indirect evidence of their existence via the so-called recombination process. The theories that predict the Efimov states also predicts either resonant enhancement of the recombination process or suppression by destructive interference, depending on the sign of the interaction between the particles. The theories predict universal features for the Efimov states, for …
We address the microscopic origin of the universal three-body parameter that fixes the spectrum of three-atom systems in the Efimov regime. We identify it with the van der Waals two-body correlation, which causes the three-atom system to deform when the three atoms come within the distance of the van der Waals length, effectively preventing them from coming closer due to the kinetic-energy cost associated with this three-body deformation. This deformation mechanism explains the universal ratio of the scattering length at the triatomic resonance to the van der Waals length observed in several e…
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting p…
We benchmark three standard approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. These configuration-interaction calculations used up to $2 \times 10^8$ uncoupled basis states, equivalent to $ 10^7$ coupled basis states (configuration state functions.) Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approx…
We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $γ$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $κ$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty…
Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper-Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external time-periodi…
We propose an experiment to probe ferromagnetic phenomena in an ultracold Fermi gas, while alleviating the sensitivity to three-body loss and competing many-body instabilities. The system is initialized in a small pitch spin spiral, which becomes unstable in the presence of repulsive interactions. To linear order the exponentially growing collective modes exhibit critical slowing down close to the Stoner transition point. Also, to this order, the dynamics are identical on the paramagnetic and ferromagnetic sides of the transition. However, we show that scattering off the exponentially growing …
We consider three-body recombination into deep dimers in a mass-imbalanced two-component atomic gas. We use an optical model where a phenomenological imaginary potential is added to the lowest adiabatic hyper-spherical potential. The consequent imaginary part of the energy eigenvalue corresponds to the decay rate or recombination probability of the three-body system. The method is formulated in details and the relevant qualitative features are discussed as functions of scattering lengths and masses. We use zero-range model in analyses of recent recombination data. The dominating scattering len…
Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterise these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunabl…
