We report exact numerical calculation of chemical potential, condensate fraction and specific heat of $N$ non-interacting bosons confined in an isotropic harmonic oscillator trap in one, two and three dimensions, as also for interacting bosons in a 3D trap. Quasi phase transitions are observed in all these cases, including one-dimension, as shown by a rapid change of all the thermodynamic quantities at the transition point. The change becomes more rapid as $N$ increases in 2D and 3D cases. However with increase in $N$, the sudden change in the nature of specific heat, gets gradually wiped out in 1D, while it becomes more drastic in 2D and 3D. The sudden change in the nature of condensate fraction and chemical potential as $N$ increases becomes more drastic even in 1D. Defining transition exponents, which characterize the nature of a thermodynamic quantity at the transition point of a quasi phase transition, we evaluate them by careful numerical calculation very near the transition temperature. These exponents are found to be independent of the size of the system and whether the bosons are interacting or not, demonstrating their universality property.
We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.
In this work we investigate the unique properties of ultracold Bose gases in one and two dimensions. In two dimensions, we present simulations of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the projected Gross-Pitaevskii equation formalism. We confirm the presence of the BKT phase by observing algebraic decay in the first-order correlation function, unbinding of vortex pairs, and behaviour of the superfluid fraction. In one dimension we use a transverse Gaussian ansatz and the Lagrangian approach to derive an effective equation of motion for the one dimensional Bose gas at…
We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) that makes the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero termparture. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.
The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the Schrödinger equation. In the present study we employ different Monte Carlo methods, that are stochastic techniques that allow to find numerical solutions to it.
We propose an experimental scheme for studying the Fermi-Pasta-Ulam (FPU) phenomenon in a quantum mechanical regime using ultracold atoms. Specifically, we suggest and analyze a setup of one-dimensional Bose gases confined into an optical lattice. The strength of quantum fluctuations is controlled by tuning the number of atoms per lattice sites (filling factor). By simulating the real-time dynamics of the Bose-Hubbard model by means of the exact numerical method of time-evolving block decimation, we investigate the effects of quantum fluctuations on the FPU recurrence and show that strong quan…
In this paper, the condensate fraction and the critical atom number and its corresponding critical temperature of condensate ultracold boson atoms trapped in optical box traps, are investigated. The semiclassical approximation is employed in this study. The boxes traps are modeled by a general power-law potential. The deviation of the boxes traps from an ideal boxes traps are discussed. The out come results furnish useful quantitative theoretical results for the future BEC experiments in such traps
We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source which models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock-Bogoliubov approximation. We apply this method to study the transport of dilute Bose gase…
We study the Bose-Einstein condensate phase transition of three-dimensional ultracold bosons with isotropic Rashba spin-orbit coupling. Investigating the structure of Ginzburg-Landau free energy as a function of the condensate density, we show, within the Bogoliubov approximation, that the condensate phase transition is first order with a jump in the condensate density. We calculate the transition temperature and the jump in the condensate density at the transition for large spin-orbit coupling, where the transition temperature depends linearly on the density of particles. Finally, we discuss …
We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multi-band spectroscopy for fermionic atoms we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to self-trapping of the atoms.
We analyze theoretically the transport properties of a weakly-interacting ultracold Bose gas enclosed in two reservoirs connected by a constriction. We assume that the transport of the superfluid part is hydrodynamic, and we describe the ballistic transport of the normal part using the Landauer-Buttiker formalism. Modeling the coupled evolution of the phase, atom number, and temperature mismatches between the reservoirs, we predict that Helmholtz (plasma) oscillations, induced by an initial imbalance in atom numbers, can be observed at non-zero temperatures below Tc. We show that, because of i…
We report on the experimental implementation of tunable occupation-dependent tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic modulation of the on-site interaction energy. The tunneling rate is inferred from a time-resolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated many-body system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lat…
We study the dynamics of a two-dimensional Bose gas after an instantaneous quench of an initially ultracold thermal atomic gas across the Berezinskii-Kosterlitz-Thouless phase transition, confirming via stochastic simulations that the system undergoes phase ordering kinetics and fulfills dynamical scaling hypothesis at late-time dynamics. Specifically, we find in that regime the vortex number decaying in time as $\langle N_v \propto t^{-1}\rangle$, consistent with a dynamical critical exponent $z \approx 2$ for both temperature and interaction quenches. Focusing on finite-size box-like geometr…
The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg landscape, with corresponding spectra that differ fundamentally from the homonuclear case. A semi-analytical treatment of the three-body recombination predicts an unusual spectra with intertwined resonance peaks and minima, and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the patterns of the Efimov-Stückelberg landscape are shown to depend inherently on the degree of diabaticity of the three-body collisions, which strongl…
We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excita…
Under certain circumstances, three or more interacting particles may form bound states. While the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associat…
We study theoretically some effects produced by a propagation of the charged particles in dilute gases of alkali-metal atoms in the state with Bose-Einstein condensates. The energy change of the high-speed (relativistic) particle that corresponds to the Cherenkov effect in the condensate is investigated. We show that in the studied cases the particle can both loose and receive the energy from a gas. We find the necessary conditions for the particle acceleration in the multi-component condensate. It is shown that the Cherenkov effect in Bose-Einstein condensates can be used also for defining th…
Quantum droplets have intrigued much attention recently in view of their successful observations in the ultracold homonuclear atoms. In this work, we demonstrate a new mechanism for the formation of quantum droplet in heteronuclear atomic systems, i.e., by applying the synthetic spin-orbit coupling(SOC). Take the Bose-Fermi mixture for example, we show that by imposing a Rashba SOC between the spin states of fermions, the greatly suppressed Fermi pressure can enable the formation of Bose-Fermi droplets even for very weak boson-fermion attractions, which are insufficient to bound a droplet if w…
We discuss the finite-temperature phase diagram in the three-dimensional Bose-Hubbard (BH) model in the strong correlation regime, relevant for Bose-Einstein condensates in optical lattices, by employing a quantum rotor approach. In systems with strong on site repulsive interactions, the rotor U(1) phase variable dual to the local boson density emerges as an important collective field. After establishing the connection between the rotor construction and the the on--site interaction in the BH model the robust effective action formalism is developed which allows us to study the superfluid phase …
In this letter, by the use of the generalized effective potential theory, with the help of process-chain approach under the framework of Kato formulation of perturbation expansion, we calculate out the quantum phase diagram up to 8-th order for an ultracold Bose system in a square optical superlattice. Base on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are gotten, which are in excellent agreement with recent Monte-Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion,…
We study a two-component Bose gas with artificial spin-orbit coupling (SOC) which couples the center-of-mass momentum of atom to its internal states. We show that in this system resonance can be induced by tuning SOC strength. With a two-dimensional SOC, resonances in two scattering channels can be induced by tuning the aspect ratio of SOC strengths. With a three-dimensional SOC, resonance in all scattering channels can be induced by tuning the appropriate SOC strength. Similarly, we also find that in a Fermi gas with two- or three-dimensional SOC resonance can be induced by tuning SOC strengt…
We study the superfluidity of a pure spin current that is a spin current without mass current. We examine two types of pure spin currents, planar and circular, in spin-1 Bose gas. For the planar current, it is usually unstable, but can be stabilized by the quadratic Zeeman effect. The circular current can be generated with spin-orbit coupling. When the spin-orbit coupling strength is weak, we find that the circular pure spin current is the ground state of the system and thus a super-flow. We discuss the experimental schemes to realize and detect a pure spin current.
The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an a…
We reveal that the p-wave superfluid can be realized in a mixture of fermionic and F=1 bosonic gases. We derive a general set of the gap equations for gaps in the s- and p-channels. It is found that the spin-spin bose-fermi interactions favor the p-wave pairing and naturally suppress the pairing in the s-channel. The gap equations for the polar phase of p-wave superfluid fermions are numerically solved. It is shown that a pure p-wave superfluid can be observed in a well-controlled environment of atomic physics.
We investigate the stability of supercurrents in a Bose-Einstein condensate with one-dimensional spin-orbit and Raman couplings. The consequence of the lack of Galilean invariance is explicitly discussed. We show that in the plane-wave phase, characterized by a uniform density, the supercurrent state can become dynamically unstable, the instability being associated with the occurrence of a complex sound velocity, in a region where the effective mass is negative. We also discuss the emergence of energetic instability in these supercurrent states. We argue that both the dynamical and the energet…
We show that arbitrarily high-order exceptional points (EPs) can be achieved in a repulsively interacting two-species Bose gas in one dimension. By exactly solving the non-Hermitian two-boson problem, we demonstrate the existence of third-order EPs when the system is driven across the parity-time symmetry breaking transition. We further address the fourth-order EPs with three bosons and generalize the results to $N$-body system, where the EP order can be as high as $N+1$. Physically, such high order originates from the intrinsic ferromagnetic correlation in spinor bosons, which renders the ent…
We study the dynamics of counterflowing bosonic and fermionic lithium atoms. First, by tuning the interaction strength we measure the critical velocity vc of the system in the BEC-BCS crossover in the low temperature regime and we compare it to the recent prediction of Castin et al., Comptes Rendus Physique, 16, 241 (2015). Second, raising the temperature of the mixture slightly above the superfluid transitions reveals an unexpected phase-locking of the oscillations of the clouds. We interpret this observation as resulting from a Zeno-like effect induced by dissipation.
We investigate the dimensionally induced phase transition from the normal to the Bose-Einstein-condensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding is in agreement with the dominant role of quantum fluctuations in lower dimensions, as they are explic…
Recent measurements of Efimov resonances in a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of $^{40}$K and $^{87}$Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between $^{40}$K$^{87}$Rb Feshbach molecules and $^{87}$Rb atoms. However, we do not observe any Efimov-related res…
We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature. We compare our equation of state with an equation of state measured by the Tokyo group, that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well describe…
We present a study of interspecies Feshbach resonances in ultracold $^{7}$Li-$^{133}$Cs Bose-Bose mixtures. We locate ten interspecies resonances in three different spin-state combinations. By comparing to coupled-channel calculations, we assign six of the resonances to $s$-wave channels and the rest to $p$-wave channels. We use the $s$-wave resonances to refine the ground-state potentials of LiCs in the coupled-channel calculations and then obtain an accurate characterization of the scattering and bound-state properties of the mixtures. Our results will be useful for future experiments with u…
Anderson localization was first investigated in the context of electrons in solids. One of the successes was in explaining the puzzle of negative magneto-resistance - as early as the 1940s it had been observed that electron diffusion rates in some materials can increase with the application of a magnetic field. Anderson localization has now been demonstrated in ultra-cold atomic gases. We present a theoretical study of the two-dimensional ultra-cold Bose gas in the presence of disorder, to which we apply a synthetic magnetic field. We demonstrate that, in the ballistic transport regime this le…
We present two Diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a discrete spin generalization of the T- moves spin-orbit DMC, which provides an upper bound to the fixed-phase energy. The second is a spin-integrated DMC method which recovers the fixed-phase property by avoiding the definition of the effective Hamiltonian involved in the T-moves approach. The latter is a more accurate method but it is restricted to spin-independent two-body interactions. We report a comparison between both algorithms for …
Both mixtures of atomic Bose-Einstein condensates and systems with atoms trapped in optical lattices have been intensely explored theoretically, mainly due to the exceptional developments on the experimental side. We investigate the properties of ultracold atomic impurities (bosons) immersed in a vortex lattice of a second Bose-condensed species. In contrast to the static optical-lattice configuration, the vortex lattice presents intrinsic dynamics given by its Tkachenko modes. These excitations induce additional correlations between the impurities, which consist in a long-range attractive pot…
The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady state of the system. We propose, as a variational ansatz, a condensate wave function for a weakly trapped system which behaves similarly to the striped state near the center, but does not have particle flow at the boundaries. This state has a line of unquantized coreless vortices. We show, by minimizing the total energy, that our modified stri…
We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit coupling in three dimensions against quantum and thermal fluctuations. The ground state depletion of the plane-wave condensate due to quantum fluctuations is, as we show, finite, and therefore the condensate is stable. We also calculate the corresponding shift of the ground state energy. Although the system cannot condense in the absence of interparticle interactions, we show by estimating the number of excited particles that interactions stabilize the condensate even at non-zero temperature. Unlike in the usual Bose…
Bose-Fermi mixtures have been recently realized and invesitigated in ultracold atomic experiments. We formulate quantum Monte Carlo simulation of Bose-Fermi mixtures on the (3+1)-dimensional lattice. As its first application, we analyze the boson-fermion pair correlation and the phase diagram of the Bose-Einstein condensation.
We study the universality of the three-body parameters for systems relevant for ultracold quantum gases with positive $s$-wave two-body scattering lengths. Our results account for finite-range effects and their universality is tested by changing the number of deeply bound diatomic states supported by our interaction model. We find that the physics controlling the values of the three-body parameters associated with the ground and excited Efimov states is constrained by a variational principle and can be strongly affected by $d$-wave interactions that prevent both trimer states from merging into…
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is c…
We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfne ground state manifold of atoms in a dilute ultracold gas. Our analysis is based upon recent developments and application of Floquet theory to periodically driven quantum systems. The simulation results show the non-Abelian gauge transformation and the non-commuting property of the SU(2) transformation operators. Based on these results, we propose a possible experimental implementation with an ultracold dilute Bose gas.
We study a single impurity driven by a constant force through a 1D Bose gas using a Lieb-Liniger based approach. Our calculaton is exact in the interaction amongst the particles in the Bose gas, and is perturbative in the interaction between the gas and the impurity. In contrast to previous studies of this problem, we are able to handle arbitrary interaction strength for the Bose gas. We find very good agreement with recent experiments [Phys. Rev. Lett. 103, 150601 (2009)].
In this paper, we present a generalized Green's function method which can be used to investigate the quantum phase transitions analytically in a systematic way for ultracold Bose systems in bipartite optical lattices. As an example, to the lowest order, we calculate the quantum phase boundaries of the localized states (Mott insulator or charge density wave) of an ultracold Bose system in a $d$-dimensional hypercubic optical lattice with nearest-neighbor repulsive interactions. Due to the inhomogeneity of the system, in the generalized Green's function method, cumuants on different sublattices …
Rabi-coupling-induced three-component quantum droplet in ultracold Bose gases
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）
We study the effects of both a repulsive and an attractive three body interaction potential on a spin-1 ultracold Bose gas using mean field approach (MFA). For an antiferromagnetic (AF) inter- action, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in presence of both the repulsive two and three body interactions. In case of a purely three body repulsive interaction, the higher order MI lobes stabilize against the superfluid phase. However, the spin nematic (singlet) formation is restricted upto the first (second) MI lobes for the former one, while there…
We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynami…
We study the spin orbit coupled ultra cold Bose-Einstein condensate placed in a single mode Fabry-Pérot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized extended Bose Hubbard model whose zero temperature phase diagram can be controlled by tuning the cavity parameters. In the non-interacting limit, where the atom-atom interaction is set to zero, the resulting atomic dispersion shows interesting features such as bosonic analogue of Dirac points, cavity controlled Hofstadter spectrum which bea…
We perform detailed analytical and numerical studies of a recently proposed method for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Previous theoretical work is extended by explicitly including the effects of non-zero temperature and interactions, and assessing the quantitative accuracy of the proposed measurement for a one-component Bose gas. We show that for suitably chosen experimental parameters the method yields an experimentally detectable signal and a sufficiently accurate measure…
We study three-body collisions within ultracold mixtures with resonant interspecies $p$-wave interactions. Our results for the three-body effective interaction strength and decay rate are crucial towards understanding the stability and lifetime of these dilute quantum fluids. On resonance, we find that a class of universal scattering pathways emerges, regardless of the details of the short-range interactions. This gives rise quite generally to a remarkable regime where three-body effective interactions dominate over both inelastic decay and two-body effective interactions. Additionally, we fin…
A model of two 1D ideal Bose gases A and B with strong AB attractions induced by a p-wave AB Feshbach resonance is studied. The model is solved exactly by a Bose-Bose duality mapping, and it is shown that there is no A-component or B-component Bose-Einstein condensation and no AB-pair off-diagonal long-range order (ODLRO), but both AA-pair and BB-pair ODLRO. After generalization by adding even-wave AA and BB repulsion and reducing the strength of the odd-wave AB attraction by Feshbach resonance detuning, a quantum phase transition occurs between a phase with AB contact nodes and one with no su…
Borromean ring refers to a peculiar structure where three rings are linked together while any two of them are unlinked. Here we propose the realization of its quantum mechanical analog in a many-body system of three-component ultracold bosons. Namely, we identify the {\it Borromean droplet}, where only the ternary bosons can form a self-bound droplet while any binary subsystems cannot. Its formation is facilitated by an additional attractive force induced by the density fluctuation of a third component, which enlarges the mean-field collapse region in comparison to the binary case and renders …
We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-li…
Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate (BEC), offers various aspects of advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, …
We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can b…
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…
We study experimentally the critical correlation in an ultra-cold Bose gas with a temporal Talbot-Lau (TL) interferometer. Near the critical temperature, we observe a bi-modal density distribution in an ultra-cold Bose gas after the application of the TL interferometer. The measured fraction of the narrower peak in the density distribution displays a clear peak within the critical regime. The peak position agrees with the critical temperature calculated with the finite-size and interaction corrections. The critical exponents are extracted from the peak and they agree with the critical exponent…
