Andreev-Bashkin effect in superfluid cold gases mixture

We study a mixture of two superfluids with density-density and current-current (Andreev-Bashkin) interspecies interactions. The Andreev-Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl-Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.Comment: 12 pages, 4 figure

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures $T$, we demonstrate that the coefficient in $T^2$ expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly-interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-{\it ansatz} equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in details. At $T=0$ we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.Comment: 14 pages, 16 figure

Gapped spectrum in pair-superfluid bosons

We study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum on both sides of this transition by using two microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both the density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value.Postprint (author's final draft

Superexchange liquefaction of strongly correlated lattice dipolar bosons

Optical lattices with dipolar bosons provide a unique platform for fundamental studies of the extended Bose-Hubbard model. The interplay between anisotropic long-range interaction, strong on-site repulsion and periodic confinement give rise to unexpected phases of matter that have not been explored so far in experiments. We propose a mechanism that stabilizes quantum liquids in strongly interacting dipolar gases in a one-dimensional optical lattice. The mechanism is based on the enhanced role of the superexchange processes close to a self-bound Mott insulator state. To support this finding, we contrast our perturbative calculations with full density-matrix renormalization group simulations and characterize the properties of different phases of the system. Finally, we analyze the speed of sound of the model that exhibits a non-trivial behavior owing to the breaking of Galilean invariance. We argue that an experimental detection of this unknown quantum liquid could provide a fingerprint of the superexchange process and open intriguing possibilities of investigating non-Galilean invariant liquids.Comment: 6+5 pages, 4+4 figure

Quantum droplets of bosonic mixtures in a one-dimensional optical lattice

We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intraspecies interactions provided they are balanced by comparable attractive interspecies 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-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a nontrivial dependence on the number of particles

The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State

Ground-state properties of bosons interacting via inverse square potential (three dimensional Calogero-Sutherland model) are analyzed. A number of quantities scale with the density and can be naturally expressed in units of the Fermi energy and Fermi momentum multiplied by a dimensionless constant (Bertsch parameter). Two analytical approaches are developed: the Bogoliubov theory for weak and the harmonic approximation (HA) for strong interactions. Diffusion Monte Carlo method is used to obtain the ground-state properties in a non-perturbative manner. We report the dependence of the Bertsch parameter on the interaction strength and construct a Padé approximant which fits the numerical data and reproduces correctly the asymptotic limits of weak and strong interactions. We find good agreement with beyond-mean field theory for the energy and the condensate fraction. The pair distribution function and the static structure factor are reported for a number of characteristic interactions. We demonstrate that the system experiences a gas-solid phase transition as a function of the dimensionless interaction strength. A peculiarity of the system is that by changing the density it is not possible to induce the phase transition. We show that the low-lying excitation spectrum contains plasmons in both phases, in agreement with the Bogoliubov and HA theories. Finally, we argue that this model can be interpreted as a realization of the unitary limit of a Bose system with the advantage that the system stays in the genuine ground state contrarily to the metastable state realized in experiments with short-range Bose gases

Quantum phase transition of a two-dimensional quadrupolar system

Ensembles with long-range interactions between particles are promising for revealing strong quantum collective effects and many-body phenomena. Here we study the ground-state phase diagram of a two-dimensional Bose system with quadrupolar interactions using a diffusion Monte Carlo technique. We predict a quantum phase transition from a gas to a solid phase. The Lindemann ratio and the condensate fraction at the transition point are ¿=0.269(4) and n0/n=0.031(4), correspondingly. We observe the strong rotonization of the collective excitation branch in the vicinity of the phase transition point. Our results can be probed using state-of-the-art experimental systems of various nature, such as quasi-two-dimensional systems of quadrupolar excitons in transition metal dichalcogenide trilayers, quadrupolar molecules, and excitons or Rydberg atoms with quadrupole moments induced by strong magnetic fields.Postprint (author's final draft

Correlation properties of a one-dimensional repulsive Bose gas at finite temperature

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms

Composite boson description of a low-density gas of excitons

Ground-state properties of a fermionic Coulomb gas are calculated using the fixed-node diffusion Monte Carlo method. The validity of the composite boson description is tested for different densities. We extract the exciton–exciton s-wave scattering length by solving the four-body problem in a harmonic trap and mapping the energy to that of two trapped bosons. The equation of state is consistent with the Bogoliubov theory for composite bosons interacting with the obtained s-wave scattering length. The perturbative expansion at low density has contributions physically coming from (a) exciton binding energy, (b) mean-field Gross–Pitaevskii interaction between excitons, and (c) quantum depletion of the excitonic condensate (Lee–Huang–Yang terms for composite bosons). In addition, for low densities we find a good agreement with the Bogoliubov bosonic theory for the condensate fraction of excitons. The equation of state in the opposite limit of large density is found to be well described by the perturbative theory including (a) mixture of two ideal Fermi gases and (b) exchange energy. We find that for low densities both energetic and coherent properties are correctly described by the picture of composite bosons (excitons)