We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark soliton significantly depends on whether its phase kink is located at a lattice site or a link of two neighboring sites. It has also shown that the dark soliton is unstable in a regime of strong quantum fluctuations regardless of the phase-kink position. To bridge the gap between the classical and strongly quantum regimes, we investigate the dynamical stability of the dark soliton in a regime of weak quantum fluctuations. We find that the position dependence of the dynamical stability gradually diminishes and eventually vanishes as the strength of quantum fluctuations increases. This classical-to-quantum crossover of the soliton stability remains even in the presence of a parabolic trapping potential. We suggest that the crossover behavior can be used for experimentally diagnosing whether the instability of a dark soliton is due to quantum fluctuations or classical dynamical instability.
We consider a mixture of two bosonic species with tunable interspecies interaction in a periodic potential and discuss the advantages of low filling factors on the detection of the pair-superfluid phase. We show how the emergence of such a phase can be put dramatically into evidence by looking at the interference pictures and density correlations after expansion and by changing the interspecies interaction from attractive to repulsive.
We report the observation of many-body interaction effects for a homonuclear bosonic mixture in a three-dimensional optical lattice with variable state dependence along one axis. Near the superfluid-to-Mott insulator transition for one component, we find that the presence of a second component can reduce the apparent superfluid coherence, most significantly when it either experiences a strongly localizing lattice potential or none at all. We examine this effect by varying the relative populations and lattice depths, and discuss the observed behavior in view of recent proposals for scattering f…
We use optical images of a superfluid consisting of a weakly interacting Bose-Einstein condensate of sodium atoms to investigate the structure of quantized three-dimensional vortex filaments. We find that the measured optical contrast and the width of the vortex core quantitatively agree with the predictions of the Gross-Pitaevskii equation.
The superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of $^{87}$Rb atoms are in good agreement with both t…
Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bo…
In this paper we address the ratio of the shear viscosity to entropy density $η/s$ in bosonic and fermionic superfluids. A small $η/s$ is associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low temperature transport associated with the quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. …
We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model focusing on the strong-coupling regime. Other than analytic calculations we apply two methods: variational Monte Carlo based on the Baeriswyl wave function and exact diagonalization. The former gives zero superfluid response at integer filling, while the latter gives a superfluid response at finite hopping. From the polarization amplitude we derive the variance and the associated size scaling exponent. Again, the variational study does not produce a finite superfluid weight at intege…
We study the response of trapped two dimensional cold bosons to time dependent lattices. We find that in lattice ramps from 11 (superfluid, $\hbar/U_{\text{i}} = 3$ms, $\hbar/J_{\text{i}} = 45$ms) to 16 recoils (Mott, $\hbar/U_{\text{f}} = 2$ms, $\hbar/J_{\text{f}} = 130$ms) the local number fluctuations remains at their equilibrium values if ramps are slower than 3 ms. Global transport, however, is much slower (1s), especially in the presence of Mott shells. This separation of timescales has practical implications for cold atom experiments and cooling protocols.
Kinetic energy driven phase transitions in Bose superfluids occur at low values of the repulsion when the values of the next-to-nearest and next-to-next-to-nearest hopping term attain certain critical values, resulting in alterations in the wave vector of the condensate. We map out the space of possible phases allowed by particular forms of the single-particle energy dispersion in the superfluid state, noting the appearance of a new phase, and examine in more detail the effects of additional repulsive terms on the form of the condensate wavefunction. We also examine the effect of these additio…
We review our theoretical results about the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the $U(1)$ symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii-Kosterlitz-Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate c…
We present a microscopic theory of heat and particle transport of an interacting, low temperature Bose-Einstein condensate in a quantum point contact. We show that, in contrast to charged, fermionic superconductors, bosonic systems feature tunneling processes of condensate elements, leading to the presence of odd-order harmonics in the AC Josephson current. A crucial role is played by an anomalous tunneling process where condensate elements are coherently converted into phonon excitations, leading to even-order harmonics in the AC currents as well as a DC contribution. At low bias, we find dis…
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, consideri…
We study a bosonic gas of hard spheres by using of the exact zero-temperature Path-Integral Ground-State (PIGS) Monte Carlo method and the equations of superfluid hydrodynamics. The PIGS method is implemented to calculate for the bulk system the energy per particle and the condensate fraction through a large range of the gas parameter $na^3$ (with $n$ the number density and $a$ the s--wave scattering length), going from the dilute gas into the solid phase. The Maxwell construction is then adopted to determine the freezing at $na^3=0.278\pm 0.001$ and the melting at $na^3=0.286\pm 0.001$. In th…
The energy spectrum of a system of Bose atoms in the superfluid phase in an optical lattice of the graphene type has been studied. The dispersion laws for the energy bands and the single particle spectral densities are calculated in the random phase approximation and in the framework of the hard-core boson formalism, and their changes at the transition from the normal phase to the superfluid one are described. As a result of this transformation, the number of subbands doubles. In the case of the subband energetic equivalence, the Dirac points in the spectrum survive, and their number becomes t…
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a $p$-band Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [X. Wang et al., https://www.nature.com/articles/s41586-021-03702-0 Nature (London) 596, 227 (2021)]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real exp…
We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group veloc…
We study a two-dimensional bosonic Hubbard model with two hard-core species away from half filling using Quantum Monte Carlo simulations. The model includes a repulsive interspecies interaction and different nearest-neighbor hopping terms for the two species. By varying the filling we find a total of five distinct phases, including a normal liquid phase at higher temperature, and four different phases at lower temperature. We find an anti-ferromagnetically ordered Mott insulator and a region of coexistent anti-ferromagnetic and superfluid phases near half filling. Further away from half fillin…
We study the topological properties of elementary excitations in a staggered $p_x \pm i p_y$ Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous $p_x+ ip_y$ momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with $π$ Berry flux. Remarkably, if we induce a population imbalance between the $p_x+ip_y$ and $p_x-ip_y$ condensate components, a gap opens up in the excitation spectrum resulting …
We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intra-species interactions provided they are balanced by comparable attractive inter-species interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one- and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases and a Mott-insula…
We consider the standard double well setup extended with a laser beam in the center to create a "triple well" potential. The beam in the center is much more narrow than the barrier, and it creates a tunable depth well which can support a localized state in the middle. We show that the presence of the localized state in the central well changes the sign of tunneling between the left and right wells and therefore controls the fixed point dynamics of the bosonic Josephson junction.
Competition between pair and single-particle superfluidity in bosonic quasi-flat bands: A Gaussian state approach
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；International Solvay Institutes（国际索尔维研究所）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（巴黎文理研究大学卡斯勒布罗塞尔实验室）
We consider quasi-stationary scattering of interacting bosonic matter waves in one-dimensional waveguides, as they arise in guided atom lasers. We show how the truncated Wigner (tW) method, which corresponds to the semiclassical description of the bosonic many-body system on the level of the diagonal approximation, can be utilized in order to describe such many-body bosonic scattering processes. Special emphasis is put on the discretization of space at the exact quantum level, in order to properly implement the semiclassical approximation and the tW method, as well as on the discussion of the …
Quantum phase slips, i.e the primary excitations in one-dimensional superfluids at low temperature, have been well characterized in most condensed-matter systems, with the notable exception of ultracold quantum gases. Here we present our experimental investigation of the dissipation in onedimensional Bose superfluids flowing along a periodic potential, which show signatures of the presence of quantum phase slips. In particular, by controlling the velocity of the superfluid and the interaction between the bosons we are apparently able to drive a crossover from a regime of thermal phase slips in…
Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two Lithium isotopes, 6Li and 7Li. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high precis…
We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.
While quantum fluctuations in binary mixtures of bosonic atoms with short-range interactions can lead to the formation of a self-bound droplet, for equal intra-component interactions but an unequal number of atoms in the two components, there is an excess part that cannot bind to the droplet. Imposing confinement, as here through periodic boundary conditions in a one-dimensional setting, the droplet becomes amalgamated with a residual condensate. The rotational properties of this compound system reveal simultaneous rigid-body and superfluid behavior in the ground state and uncover that the res…
We analyze the dynamical and energetic instabilities of spin currents in a system of two-component bosons in an optical lattice, with a particular focus on the Neel state. We consider both the weakly interacting superfluid and the strongly interacting Mott insulating limits as well as the regime near the superfluid-insulator transition and establish the criteria for the onset of these instabilities. We use Bogoliubov theory to treat the weakly interacting superfluid regime. Near the Mott transition, we calculate the stability phase diagram within a variational Gutzwiller wavefunction approach.…
We study, using quantum Monte-Carlo simulations, the bosonic Kondo-Hubbard model in a two dimensional square lattice. We explore the phase diagram and analyse the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight binding Hamiltonians can be realized in optical lattice experiments, whi…
We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.
We present a detailed derivation of a multi-site mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a non-trivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for …
We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining $U(1) \times \mathbb{Z}_2$ symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and anti-vortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. …
We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures th…
Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations, and show that …
We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the super…
A two-component two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure fact…
We demonstrate many-body multifractality of the Bose-Hubbard Hamiltonian's ground state in Fock space, for arbitrary values of the interparticle interaction. Generalized fractal dimensions unambiguously signal, even for small system sizes, the emergence of a Mott insulator, that cannot, however, be naively identified with a localized phase in Fock space. We show that the scaling of the derivative of any generalized fractal dimension with respect to the interaction strength encodes the critical point of the superfluid to Mott insulator transition, and provides an efficient way to accurately est…
Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles a…
We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg-de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability o…
We report on the production of a stable mixture of bosonic and fermionic superfluids composed of the elements $^{174}$Yb and $^6$Li which feature a strong mismatch in mass and distinct electronic properties. We demonstrate elastic coupling between the superfluids by observing the shift in dipole oscillation frequency of the bosonic component due to the presence of the fermions. The measured magnitude of the shift is consistent with a mean-field model and its direction determines the previously unknown sign of the interspecies scattering length to be positive. We also observe the exchange of an…
We study the impact of the non-analytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may be also observable in clean superconducting films.
We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. F…
We study the occurrence of non-classical rotational inertia (NCRI) arising from superfluidity along grain boundaries in a two-dimensional bosonic system. We make use of a standard mapping between the zero-temperature properties of this system and the statistical mechanics of interacting vortex lines in the mixed phase of a type-II superconductor. In the mapping, the liquid phase of the vortex system corresponds to the superfluid bosonic phase. We consider numerically obtained polycrystalline configurations of the vortex lines in which the microcrystals are separated by liquid-like grain bounda…
Entanglement entropy (EE), a fundamental conception in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, for the first time, in the framework of a cluster MF treatment, we extract the signature of EE in the bosonic superfluid-insulator transitions. We consider a trimerized Kagome lattice of interacting bosons, in which each trimer is treated as a cluster, and implemen…
Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattic…
Properties of bosonic atoms in small systems with a periodic quasi one-dimensional circular toroidal lattice potential subjected to rotation are examined by performing exact diagonalization in a truncated many body space. The expansion of the many-body Hamiltonian is considered in terms of the first band Bloch functions, and no assumption regarding restriction to nearest-neighbor hopping (tight-binding approximation) is involved. A finite size version of the zero temperature phase diagrams of Fisher et al. \cite{Fisher} is obtained and the results, in remarkable quantitative correspondence wit…
We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field dynamics takes place on a deformed version of the Bloch sphere, a teardrop shaped surface with a cusp singularity. We analyse the mean-field and many-particle correspondence, which shows typical features of quantum-classical correspondence. We demonstrate that semiclassical methods can be employed to recover full many-particle features from the me…
We determine and analyze collective normal modes of a finite disk-shaped two-dimensional vortex crystal formed in a compressible bosonic superfluid in an artificial magnetic field. Using the microscopic Gross-Pitaevskii theory in the lowest Landau level approximation, we generate vortex crystal ground states and solve the Bogoliubov-de Gennes equations for small amplitude collective oscillations. We find chiral surface waves that propagate at frequencies larger than those of the bulk Tkachenko modes. Furthermore, we study low frequency bulk excitations and identify a torsional Ruderman mode, w…
Since the discovery of superfluidity in He4 and Landau's phenomenological theory, the relationship between Bose condensation and superfluidity has been intensely debated. He4 is known by now to be both superfluid and condensed at low temperature, and more generally, in dimension D\geq2, all superfluid bosonic models realized in experiments are condensed in their ground-state, the most recent example being provided by ultracold bosonic atoms trapped in an optical lattice. In this paper, it is shown that a 2D gas of bosons which is not condensed at T=0 can be achieved by populating a layer throu…
Recent experiments in ultracold atoms and photonic analogs have reported the implementation of artificial gauge fields in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate the Haldane honeycomb lattice tight-binding model, for bosons with local interactions at the average filling of one boson per site. We analyze the ground state phase diagram and uncover three distinct phases: a uniform superfluid (SF), a chiral superfluid (CSF) and a plaquette Mott insulator with local current loops (PMI). Nearest-neighbor and next-nearest neighbo…
We study the one-dimensional hard-core Bose-Hubbard model with three-body interactions. In previous work[1], the two-thirds filling solid with both bond-wave order (BOW) and charge-density wave order (CDW) is found and it undergoes a second order phase transition to the superfluid phase. However, in recent work[2], we found the BOW not independent with CDW order. Thus, by utilizing the density matrix renormalization group, we make use of both entanglement entropy and fidelity susceptibility to detect the phase transition. In two-thirds filling, the extreme point of the entanglement entropy als…
We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ an hydrodynamic parametrization of the bosonic field to calculate the superfluid equations of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the finite-range interaction, are regularized with an improved dimensional regularization technique.
