We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $|x|<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1} < R <ξ$ (here $n$ is the average density and $ξ$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.
We study large deviations in interacting quantum liquids with the polytropic equation of state $P(ρ)\sim ρ^γ$, where $ρ$ is density and $P$ is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes $γ$ and the result can be analytically continued to any value of $γ\ge 1$. Our findings agree with (and significantly expand on) …
We have studied the collective excitation of Bose-Einstein condensate of short range weak interacting atoms with spin-orbit coupling (SOC) in two dimension in liquid phase. In our study, we have included Rashba, Dresselhaus SOC as well as Raman SOC. The study of Bogoliubov excitation shows that in small interaction case only phonon modes are present and for higher interactions roton modes start to appear. Energy spectra contain two roton modes in the system relatively strong interacting atomic system.
We study the low-temperature thermodynamics of weakly-interacting uniform liquids in one-dimensional attractive Bose-Bose mixtures.~The Bogoliubov approach is used to simultaneously describe quantum and thermal fluctuations. First, we investigate in detail two different thermal mechanisms driving the liquid-to-gas transition, the dynamical instability and the evaporation, and we draw the phase diagram. Then, we compute the main thermodynamic quantities of the liquid, such as the chemical potential, the Tan's contact, the adiabatic sound velocity and the specific heat at constant volume. The st…
We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at $T=0$. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the $s$-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enoug…
In this paper we study the low temperature behaviors of a system of Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram approximation, we show that at nonzero temperatures $T\rightarrow0$ the fermions exhibit non-fermi liquid behavior. We propose that this is a general feature of Bose-Fermi mixtures at two dimensions. An experimental signature of this new state is proposed.
By using exact quantum Monte-Carlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid…
A comparative study is done of the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates in Gross-Pitaevskii and logarithmic models, by means of the Thomas-Fermi approximation. It is shown that in the linear regime the propagation of small density fluctuations is essentially one-dimensional in both models, in the direction perpendicular to the cross section of a liquid's lump. Under these approximations, it is shown that the speed of sound scales as a square root of particle density in the case of the Gross-Pitaevskii liquid/condensate, but it is constant in a cas…
We study wave propagation in interacting Bose liquid, where the short range part of the interaction between atoms is of a hard core type, and its long range part scales with a distance as a power law. The cases of Coulomb, dipole-dipole and Van der Waals interaction are considered. We employ a hydrodynamic approach, based on the exact solution of Lieb-Liniger model, and study the evolution of a density pulse instantly released from a potential trap. We analyze semi-classical Euler and continuity equations and construct the corresponding Riemann invariants. We supplement our analysis with numer…
Quantum droplets are small clusters of atoms self-bound by the balance of attractive and repulsive forces. Here we report on the observation of a novel type of droplets, solely stabilized by contact interactions in a mixture of two Bose-Einstein condensates. We demonstrate that they are several orders of magnitude more dilute than liquid helium by directly measuring their size and density via in situ imaging. Moreover, by comparison to a single-component condensate, we show that quantum many-body effects stabilize them against collapse. We observe that droplets require a minimum atom number to…
We present a full set of wave equations describing a dense Bose fluid, applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in liquid 4He is found and the fraction of condensed particles is calculated at zero temperature for a wide range of densities. The theory also yields the ground-state energy for the quantum liquid 4He in agreement to high accuracy with Monte Carlo simulations and experimental data at low pressure. We also present the derivation of a generalized Hartree-Fock equation describing roton clusters in low temperature liquid 4He, allowing us to confirm that…
We present a theory describing the lambda transition and the Bose-Einstein condensation (BEC) in a liquid ${\rm ^4He}$ based on the diatomic quasiparticle concept. It is shown that in liquid ${\rm ^4He}$ for the temperature region $1~{\rm K}\leq{\rm T}\leq {\rm T}_λ$ the diatomic quasiparticles macroscopically populate the ground state which leads to BEC in liquid ${\rm ^4He}$. The approach yields the lambda transition temperature as ${\rm T}_λ=2.16~{\rm K}$ which is in excellent agreement with the experimental lambda temperature ${\rm T}_λ=2.17~{\rm K}$. The concept of diatomic quasiparticles…
We present a thorough study of the thermodynamics of a one-dimensional repulsive Bose gas, focusing in particular on corrections beyond the Luttinger-liquid description. We compute the chemical potential, the pressure and the contact, as a function of temperature and gas parameter with exact thermal Bethe-Ansatz. In addition, we provide interpretations of the main features in the analytically tractable regimes, based on a variety of approaches (Bogoliubov, hard-core, Sommerfeld and virial). The beyond Luttinger-liquid thermodynamic effects are found to be non-monotonic as a function of gas par…
We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the …
Recent experiments on $p$-orbital atomic bosons have suggested the emergence of a spectacular ultracold superfluid with staggered orbital currents in optical lattices. This raises fundamental questions like the effects of collective thermal fluctuations, and how to directly observe such chiral order. Here, we show via Monte Carlo simulations that thermal fluctuations destroy this superfluid in an unexpected two-step process, unveiling an intermediate normal phase with spontaneously broken time-reversal symmetry, dubbed "chiral Bose liquid". For integer fillings ($n\geq 2$) in the chiral Mott r…
Spin-incoherent Luttinger liquid (SILL) is a different universal class from the Luttinger liquid.\ This difference results from the spin incoherence of the system when the thermal energy of the system is higher than the spin excitation energy.\ We consider one-dimensional spin-$1$ Bose gas in the SILL regime and investigate its spin-dependent many-body properties.\ In Tonks-Girardeau limit, we are able to write down the general wave functions in a harmonic trap.\ We numerically calculate the spin-dependent (spin-plus, minus, and $0$) momentum distributions in the sector of zero magnetization w…
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributi…
We investigate spin-incoherent Luttinger liquid of a one-dimensional spin-1 Bose gas in a harmonic trap. In this regime highly degenerate spin configurations emerge since the spin exchange energy is much less than the thermal energy of the system, while the temperature is low enough that the lowest energetic orbitals are occupied. As an example we numerically study the momentum distribution of a one-dimensional spin-1 Bose gas in Tonks- Girardeau gas limit and in the sector of zero magnetization.We find that the momentum distributions broaden as the number of atoms increase due to the averagin…
We use entanglement to investigate the transition from vortex liquid phase to vortex lattice phase in weakly interacting rotating Bose-Einstein condensate (BEC). Ground state entanglement spectrum is analyzed to distinguish these two different phases. For the torus geometry, the low-lying part of ground state entanglement spectrum, as well as the behavior of its lowest level change clearly when the transition occurs. For the sphere geometry, the disappearance of entanglement gap in the conformal limit (CL) can indicate this transition. We also show that the decrease of entanglement between par…
Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid in the presence of a local velocity field $v(x)$, local Galilei transformations are used to derive formulas for the spatial distribution of superfluidity. The local formulation is shown to subsume several descriptions of superfluidity, from Landau's free quasiparticle picture of the normal fluid to the fully microscopic winding number formula for superfluid density. We derive the superfluid distribution of generic pure states of 1-d bosonic systems by using the continuum analog of matrix product states. With a view t…
We study in detail the properties of pi-fluxes embedded in a state with a finite density of anyons that form either a Fermi liquid or a Bose-Einstein condensate. By employing a recently developed exact lattice bosonization in 2D, we demonstrate that such pi-flux remains a fully deconfined quasiparticle with a finite energy cost in a Fermi liquid of emergent fermions coupled to a Z2 gauge field. This pi-flux is accompanied by a screening cloud of fermions, which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8 of a fermionic hole. In addition there is a long-ranged power…
Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and agains…
Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behavior of thermodynamic quantities. For liquid Helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example for ultracold atomic Bose gases. Here we examine the thermodynamic behavior of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of…
In two-dimensional incompressible quantum spin liquids, a large enough magnetic field generically induces "doping" of polarized S=1 triplons or S=1/2 spinons. We review a number of cases such as spin-3/2 AKLT or spin-1/2 Resonating Valence Bond (RVB) liquids where the Projected Entangled Pair States (PEPS) framework provides very simple and comprehensive pictures. On the bipartite honeycomb lattice, simple PEPS can describe Bose condensed triplons (AKLT) or spinons (RVB) superfluids with transverse staggered (Néel) magnetic order. On the Kagome lattice, doping the RVB state with deconfined spi…
We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Due …
We study the properties of self-bound liquid droplets of three-dimensional Bose mixtures in a weak random potential with Gaussian correlation function at both zero and finite temperatures. Using the Bogoliubov theory, we derive useful formulas for the ground-state energy, the equilibrium density, the depletion, and the anomalous density of the droplet. The quantum fluctuation induced by the disorder known as the glassy fraction is also systematically computed. At finite temperature, we calculate the free energy, the thermal equilibrium density, and the critical temperature in terms of the diso…
The Landau-Zener model of a quantum mechanical two-level system driven with a linearly time dependent detuning has served over decades as a textbook paradigm of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2, 46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dyna…
Using quantum Monte Carlo methods we have studied dilute Bose-Bose mixtures with attractive interspecies interaction in the limit of zero temperature. The calculations are exact within some statistical noise and thus go beyond previous perturbative estimations. By tuning the intensity of the attraction, we observe the evolution of an $N$-particle system from a gas to a self-bound liquid drop. This observation agrees with recent experimental findings and allows for the study of an ultradilute liquid never observed before in Nature.
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate-like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly-interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a $^{87}$Rb condensate in a 2D lattice potential. The dynamical structure factor of the system …
We study weakly interacting mixtures of ultracold atoms composed of bosonic and fermionic species in 2D and 1D. When interactions between particles are appropriately tuned, self-bound quantum liquids can be formed. We show that while formation of these droplets in 2D is due to the higher order correction terms contributing to the total energy and originating in quantum fluctuations, in 1D geometry the quantum fluctuations have a negligible role on formation of the self-bound systems. The leading mean-field interactions are then sufficient for droplet formation in 1D. We analyse stability condi…
We study excitations in a normal Fermi liquid with a local scalar interaction. Spectrum of bosonic scalar-mode excitations is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations (a Pomeranchuk instability). An effective Lagrangian for the scalar ex…
A quantum liquid in a heterogeneous mixture of $^{41}$K and $^{87}$Rb atoms is studied using the diffusion Monte Carlo method and Density Functional Theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals (MF+LHY) are presented. Using Density Functional Theory, a systematic comparison between different functionals is performed, focusing on th…
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here, we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low…
Quantum spin ice in pyrochlore lattice exemplifies three dimensional frustrated spin systems.In existing studies, Bose-Einstein condensation of bosonic spinons gives rise to magnetically ordered ground state.A truly liquid quantum spin superfluid state that manifests a deconfined Higgs condensate of spinons is demonstrated.This state is shown to occur in the fully antiferromagnetic case of the non-Kramers quantum spin ice with a fluctuations-induced first-order quantum phase transition from the $U(1)$ spin liquid to the spin superfluid.The spin superfluid density jump is obtained analytically.
Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective oscillations and stability, including the metastability and macroscopic tunneling phenomena, both the variational approach and the Vakhitov-Kolokolov criterion are employed, calculations are done for condensates of an arbitrary spatial dimension. It is determined that that the trapless condensate described by the logarithmic wave equation is essentially stable, regardless of its dimensionality, while the t…
Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations. An effective Lagrangian for the scalar excitation modes is derived after performing a boson…
We examine a spinor Bose gas confined by an elongated trap. Since a spin-independent energy is much higher than a spin-dependent energy in alkali species, the system exhibits different properties by changing a radial confinement. We show that if a spin-dependent coupling is positive, a spin-liquid condensate, which breaks the charge U(1) symmetry but preserves the spin rotational symmetry, can be realized in an intermediate confinement regime. Properties of the spin-liquid condensate are visible if a temperature is lower than a spin gap to characterize the spin-disorder property. If a temperat…
We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid …
We study a liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under a variable confinement introduced along one or two spatial dimensions. Despite the atom-atom scattering has a three-dimensional character, discreetness of the available modes in the reduced dimension(s) strongly influences the zero-point energy -- the Lee-Huang-Yang term. In a weakly interaction limit, it is the leading correction to the mean-field energy at the crossover from three to two dimensions, or from three to one dimension. We analyze the properties of the droplets at the dimensional cross…
The field of quantum turbulence is related to the manifestation of turbulence in quantum fluids, such as liquid helium and ultracold gases. The concept of turbulence in quantum systems was conceived more than 70 years ago by Onsager and Feynman, but the study of turbulent ultracold gases is very recent. Although it is a young field, it already provides new approaches to the problem of turbulence. We review the advances and present status, of both theory and experiments, concerning atomic Bose-Einstein condensates (BECs). We present the difficulties of characterizing turbulence in trapped BECs,…
The Gross-Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose-Einstein condensates (BEC). However, in many physical situations, such as higher densities, this approximation unlikely suffices hence one might need models which would account for long-range correlations and multi-body interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the self-sustainability property: while the free GP condensate tends to spill all over the available volume the logarithmic…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose system…
We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $σ=\uparrow$, $\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow\uparrow}/|g_{\uparrow\downarrow}|$ and $g_{\downarrow\downarrow}/|g_{\uparrow\downarrow}|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{σσ}$ (or smaller $|g_{\uparrow…
The collective modes of a quantum liquid shape and impact its properties profoundly, including its emergent phenomena such as superfluidity. Here we present how a two-dimensional Bose gas responds to a moving lattice potential. In particular we discuss how the induced heating rate depends on the interaction strength and the temperature. This study is motivated by the recent measurements of Sobirey {\it et al.} arXiv:2005.07607 (2020), for which we provide a quantitative understanding. Going beyond the existing measurements, we demonstrate that this probing method allows to identify first and s…
In this paper, we present evidence for a liquid-like phase in systems of many interacting Bosons at intermediate densities. The interacting Bose gas has been studied extensively in the low and high density regimes, in which interactions do not play a physically significant role, and the system behaves similarly to the ideal quantum gas. Instead, we will turn our attention to the intermediate density regime, and report evidence that the system enters a strongly correlated phase where its behavior is markedly different from that of the ideal quantum gas. To do so, we use the Simplified approach …
We investigate the self-bound states of dipolar Dy condensates with the Gaussian-state ansatz which improves the conventional coherent-state ansatz with multimode squeezed coherent states. We show that the self-bound states consist of the experimentally observed self-bound liquid phase and the unobserved self-bound gas phase. The numerically obtained gas-liquid boundary is in good agreement with experimental data. Our theory also allows one to extract the real part of the three-body coupling constant of the Dy atoms from the particle number distribution of the condensates. In particular, we re…
A century of the Bose-Einstein condensation concept and half a century of the JINR experiments for observation of condensate in the superfluid 4He (He II)
