Ultracold Bose Gas Research Articles

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at $$\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)$$ in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.

Path-integral Monte Carlo simulation of time-reversal noninvariant bulk systems with a case study of rotating Yukawa gases.

We elaborate on the methodology to simulate bulk systems in the absence of time-reversal symmetry by the phase-fixed path-integral Monte Carlo method under (possibly twisted) periodic boundary conditions. Such systems include two-dimensional electrons in the quantum Hall regime and rotating ultracold Bose and Fermi gases; time-reversal symmetry is broken by an external magnetic field and the Coriolis force, respectively. We provide closed-form expressions in terms of Jacobi elliptic functions for the thermal density matrix (or the Euclidean propagator) of a single particle on a flat torus under very general conditions. We then modify the multislice sampling method in order to sample paths by the magnitude of the complex-valued thermal density matrix. Finally, we demonstrate that these inventions let us study the vortex melting process of a two-dimensional Yukawa gas in terms of the de Boer interaction strength parameter, temperature, and rotation (Coriolis force). The bosonic case is relevant to ultracold Fermi-Fermi mixtures of widely different masses under rotation.

Quantum phases of a spin-1 ultracold Bose gas with three-body interactions

We study the effects of a three-body interaction potential on a spin-1 ultracold Bose gas using mean-field approach (MFA). For an antiferromagnetic (AF) interaction, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in the 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. Also the spin nematic (singlet) formation occurs for all the odd (even) MI lobes for the former, while there is neither any asymmetry, nor spin nematic (singlet) formation being observed for the latter case. The results are confirmed after carefully scrutinizing the spin eigenvalue and spin nematic order parameter for both the cases. We have compared our MFA results with the analytic phase diagrams obtained using a perturbation mean-field (PMFA) expansion.

Shortcuts to adiabaticity in the strongly coupled regime: Nonadiabatic control of a unitary Fermi gas

Coherent control of complex quantum systems is a fundamental requirement in quantum information processing and engineering. Recently developed notion of shortcut to adiabaticity (STA) has spawned intriguing prospects. So far, the most experimental investigations of STA are implemented in the ideal thermal gas or the weakly interacting ultracold Bose gases. Here we report the first demonstration of a many-body STA in a 3D anisotropically trapped unitary Fermi gas. A new dynamical scaling law is demonstrated on such a strongly interacting quantum gas. By simply engineering the frequency aspect ratio of a harmonic trap, the dynamics of the gas can be manipulated and the many-body state can be transferred adiabatically from one stationary state to another one in short time scale without the excitation. The universal scaling both for non-interacting and unitary Fermi gas is also verified. This could be very important for future many-body quantum engineering and the exploration of the fundamental law of the thermodynamics.

Solvable Hydrodynamics of Quantum Integrable Systems.

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Thermo-optical interactions in a dye-microcavity photon Bose–Einstein condensate

Superfluidity and Bose–Einstein condensation are usually considered as two closely related phenomena. Indeed, in most macroscopic quantum systems, like liquid helium, ultracold atomic Bose gases, and exciton-polaritons, condensation and superfluidity occur in parallel. In photon Bose–Einstein condensates realized in the dye microcavity system, thermalization does not occur by direct interaction of the condensate particles as in the above described systems, i.e. photon–photon interactions, but by absorption and re-emission processes on the dye molecules, which act as a heat reservoir. Currently, there is no experimental evidence for superfluidity in the dye microcavity system, though effective photon interactions have been observed from thermo-optic effects in the dye medium. In this work, we theoretically investigate the implications of effective thermo-optic photon interactions, a temporally delayed and spatially non-local effect, on the photon condensate, and derive the resulting Bogoliubov excitation spectrum. The calculations suggest a linear photon dispersion at low momenta, fulfilling the Landau’s criterion of superfluidity. We envision that the temporally delayed and long-range nature of the thermo-optic photon interaction offer perspectives for novel quantum fluid phenomena.

Truncated Wigner dynamics and conservation laws

Ultracold Bose gases can be used to experimentally test many-body theory predictions. Here we point out that both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional Bose gas, and these provide an important validation of methods. We show that the first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics. Center-of-mass position variance is also exactly calculable. This is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as ${N}^{\ensuremath{-}3/2}$ as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ with fixed momentum cutoff. Examples of this are calculated in experimentally relevant, mesoscopic cases.

Observation of Efimov Molecules Created from a Resonantly Interacting Bose Gas

We convert a strongly interacting ultracold Bose gas into a mixture of atoms and molecules by sweeping the interactions from resonant to weak. By analyzing the decay dynamics of the molecular gas, we show that in addition to Feshbach dimers it contains Efimov trimers. Typically around 8% of the total atomic population is bound into trimers, identified by their density-independent lifetime of about 100 μs. The lifetime of the Feshbach dimers shows a density dependence due to inelastic atom-dimer collisions, in agreement with theoretical calculations. We also vary the density of the gas across a factor of 250 and investigate the corresponding atom loss rate at the interaction resonance.

Continuum of classical-field ensembles in Bose gases from canonical to grand canonical and the onset of their equivalence

The canonical and grand-canonical ensembles are two usual marginal cases for ultracold Bose gases, but real collections of experimental runs commonly have intermediate properties. Here we study the continuum of intermediate cases and look into the appearance of ensemble equivalence as interaction rises for mesoscopic $1d$ systems. We demonstrate how at sufficient interaction strength the distributions of condensate and excited atoms become practically identical, regardless of the ensemble used. Importantly, we find that features that are fragile in the ideal gas and appear only in a strict canonical ensemble can become robust in all ensembles when interactions become strong. As evidence, the steep cliff in the distribution of the number of excited atoms is preserved. To make this study, a straightforward approach for generating canonical and intermediate classical field ensembles using a modified stochastic Gross-Pitaevskii equation is developed.

Optical lattices as a tool to study defect-induced superfluidity

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior, which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides an extremely well-controlled model for studying defect-induced superfluidity.

Onset of nanoscale dissipation in superfluid He4 at zero temperature: Role of vortex shedding and cavitation

Two-dimensional flow past an infinitely long cylinder of nanoscopic radius in superfluid He-4 at zero temperature is studied by time-dependent density functional theory. The calculations reveal two distinct critical phenomena for the onset of dissipation: 1) vortex-antivortex pair shedding from the periphery of the moving cylinder and 2) appearance of cavitation in the wake, which possesses similar geometry as observed experimentally for fast moving micrometer-scale particles in superfluid He-4. Vortex pairs with the same circulation are occasionally emitted in the form of dimers, which constitute the building blocks for the Benard-von Karman vortex street structure observed in classical turbulent fluids and Bose-Einstein condensates. The cavitation induced dissipation mechanism should be common to all superfluids that are self-bound and have a finite surface tension, which include the recently discovered self-bound droplets in ultracold Bose gases.

Two-Dimensional Talbot Effect with Atomic Density Gratings**Supported by the State Key Development Program for Basic Research of China under Grant No 2016YFA0301501, and the National Natural Science Foundation of China under Grant Nos 11504328, 61475007, 11334001 and 91336103.

We report the experimental observation of two-dimensional Talbot effect when a resonance plane wave interacts with a two-dimensional atomic density grating generated by standing wave manipulation of ultracold Bose gases. Clear self-images of the grating and sub-images with reversed phase or fractal patterns are observed. By calculating the autocorrelation functions of the images, the behavior of periodic Talbot images is studied. The Talbot effect with two-dimensional atomic density grating expands the applications of the Talbot effect in a wide variety of research fields.

Inflationary preheating dynamics with two-species condensates

We discuss the amplification of loop corrections in quantum many-body systems through dynamical instabilities. As an example, we investigate both analytically and numerically a two-component ultracold atom system in one spatial dimension. The model features a tachyonic instability, which incorporates characteristic aspects of the mechanisms for particle production in early-universe inflaton models. We establish a direct correspondence between measureable macroscopic growth rates for occupation numbers of the ultracold Bose gas and the underlying microscopic processes in terms of Feynman loop diagrams. We analyze several existing ultracold atom setups featuring dynamical instabilities and propose optimized protocols for their experimental realization. We demonstrate that relevant dynamical processes can be enhanced using a seeding procedure for unstable modes and clarify the role of initial quantum fluctuations and the generation of a non-linear secondary stage for the amplification of modes.

Low-lying Collective Modes of a 1D Dipolar Quantum Gas in an Anharmonic Trap

The low-lying collective modes of an anharmonically confined one-dimensional ultracold dipolar Bose gas are investigated by using time-dependent variational method. The frequencies of dipole mode and breathing mode are obtained analytically in the full crossover regime from a Tonks-Girardeau gas to a dipolar density wave state. We find that the frequency shifts caused by quartic distortion of the potential can be amplified by interparticle interaction and the collapse and revival of the collective excitations can be observed in the anharmonic trap.

Structural and quantum properties of van der Waals cluster near the unitary regime

We study the structural and several quantum properties of three-dimensional bosonic cluster interacting through van der Waals potential at large scattering length. We use Faddeev-type decomposition of the many-body wave function which includes all possible two-body correlations. At large scattering length, we observe spatially extended states which exhibit the exponential dependence on the state number. The cluster ground state energy shows universal nature at large negative scattering length. We also find the existence of generalized Tjon lines for N-body clusters. Signature of universal behaviour of weakly bound clusters can be observed in experiments of ultracold Bose gases. We also study the spectral statistics of the system. We calculate both the short-range fluctuation and long-range correlation and observe semi-Poisson distribution which interpolates the Gaussian Orthogonal Ensemble (GOE) and Poisson statistics of random matrix theory. It indicates that the van der Waal cluster near the unitary becomes highly complex and correlated. However additional study of P(r) distribution (without unfolding of energy spectrum) reveals the possibility of chaos for larger cluster.

Dimensionally induced one-dimensional to three-dimensional phase transition of the weakly interacting ultracold Bose gas

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 originates from an important correction due to quantum fluctuations, which are enhanced in lower dimensions. Furthermore, we determine for the one-dimensional to three-dimensional transition the power-law exponent of the critical temperature for two different noninteracting Bose gas models yielding the same value of 1/2, which indicates that they belong to the same universality class. For the weakly interacting Bose gas we find for both models that this exponent is robust with respect to finite interaction strengths.

Matter wave interference of dilute Bose gases in the critical regime**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504328, 11274024, and 11334001) and the National Basic Research Program of China (Grants Nos. 2013CB921903 and 2012CB921300).

Ultra-cold atomic gases provide a new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science 315 1556 (2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.

Thermal field theory of bosonic gases with finite-range effective interaction

We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical partition function we derive beyond-mean-field analytical results which depend on both scattering length and effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.

Optical Talbot carpet with atomic density gratings obtained by standing-wave manipulation

We report a method of generating atomic density gratings by standing-wave manipulation of ultracold Bose gases. By illuminating the gratings with a beam of homogeneous light, we observe one- and two-dimensional Talbot carpets. We further measure the autocorrelation function of the images, which varies with image plane position caused by Talbot effect. Periodically repeated self-images and subimages of the atomic density gratings are observed clearly. Our theoretical calculations and experimental results agree well with each other. The atomic density gratings hold promise for substituting for traditional gratings in many applications.

Condensate of excitations in moving superfluids

A possibility of the condensation of excitations with a non-zero momentum in rectilinearly moving and rotating superfluid bosonic and fermionic (with Cooper pairing) media is considered in terms of a phenomenological order-parameter functional at zero and non-zero temperature. The results might be applicable to the description of bosonic systems like superfluid $^4$He, ultracold atomic Bose gases, charged pion and kaon condensates in rotating neutron stars, and various superconducting fermionic systems with pairing, like proton and color-superconducting components in compact stars, metallic superconductors, and neutral fermionic systems with pairing, like the neutron component in compact stars and ultracold atomic Fermi gases. Order parameters of the "mother" condensate in the superfluid and the new condensate of excitations, corresponding energy gains, critical temperatures and critical velocities are found.