Session Q08: Quantum Gases in Low Dimensions II

Berezinskii-Kosterlitz-Thouless transitions of an easy-plane ferromagnetic spin-1 Bose gas

In two-dimensional Bose gases thermal fluctuations preclude the formation of long-range order. Consequently, the superfluid transition is of the Berezinskii-Kosterlitz-Thouless (BKT) type, characterized by the emergence of quasi-long-range order driven by the binding of vortex-antivortex pairs. Spinor Bose gases provide a unique platform to study BKT transitions, on account of their ability to simultaneously exhibit phase and spin ordering. Here we utilize a stochastic Gross-Pitaevskii model to investigate the BKT transitions in an easy-plane ferromagnetic spin-1 Bose gas. We find that in general two BKT transitions occur with decreasing temperature: first mass superfluidity is established, followed at a lower temperature by spin superfluidity. We demonstrate that these transitions are associated with the binding of mass and spin vortex-antivortex pairs respectively. Furthermore, we develop a phase diagram dependent on quadratic Zeeman energy, which demonstrates that the mass and spin superfluid transitions become indistinguishable in the isotropic ferromagnetic phase.   

Curvature-induced BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap

The spherical bubble traps in microgravity allows cold atoms to be confined on a spherical surface. By considering a two-component Fermi gas with attractive interactions, we derive and analyze the BCS-Leggett theory of atomic Fermi superfluid on a thin spherical shell. Despite the flat dispersion within each angular momentum number and jumps between adjacent levels of an ideal Fermi gas on a spherical shell, the properly normalized gap and chemical potential of Fermi superfluid exhibit universal behavior regardless of the geometries. The conventional BCS-BEC crossover induced by increasing the interactions occurs on a sphere. However, a curvature-induced BCS-BEC crossover emerges when the particle number and interaction strength are fixed but the sphere is shrinking. Different from a 3D Fermi superfluid, the pairing energy scale of a 2D Fermi superfluid is determined by the two-body binding energy. When placed on a 2D compact geometry like the spherical shell, an increase of the curvature leads to an increase of the Fermi energy and causes a reduction of the ratio between the pairing and kinetic energies. Therefore, the system is pushed towards the BCS limit as the sphere shrinks. The curvature-induced BCS-BEC crossover thus demonstrates the effects of compact geometries in low dimensions on many-body systems.     

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We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies, and for a radius much larger than the healing length, we express the contact interaction strength in terms of the s-wave scattering length. Adopting this relation, we are then able to regularize the zero-point energy of the spherical Bose gas and to obtain its equation of state, which includes the corrections due to the finite radius of the sphere, and that coincides with the flat-case result in the infinite-radius limit. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.   

Particle-Imbalanced Bose Mixtures in the Droplet Regime

We unravel the transition of the bound state behavior of attractively interacting two-component bosonic mixtures from particle balanced settings towards the impurity limit. A multitude of phases is found to occur depending on the interplay between the intercomponent attraction and the particle-imbalance. For weak attractions (droplet regime) and larger imbalances the flat-top density profile of the majority component becomes progressively localized and it is restricted within the spatial region where the minority one is located. In contrast, turning to stronger attractions, the highly localized soliton-like state of the majority species features a spatial delocalization and eventually exhibits a flattened background for sufficiently large particle imbalance. A depletion of the density profile accompanied by strong two-body correlations is evinced for increasing repulsion of the minority component. The aforementioned structural deformations are explained by constructing a suitable effective potential approach within the modified Gross-Pitaevskii model, while the few- to many-body crossover is probed through an ab-initio variational approach.   

Spin dynamics in low-dimensional quantum gases

Cooled to nano-Kelvin temperatures, ultracold dilute atomic gases manifest as macroscopic quantum systems. Observable in experiments, atomic quantum gases give direct access to the physics of low-dimensional quantum phenomena. Be it the simulators of condensed matter systems or components of novel quantum technologies, it is of imense value to know the transport properties of ultracold atomic quantum gases to a fine detail. In this talk, we shall discuss that thermal fluctuations in a two-dimensional spinor system, in particular binary Bose-Bose mixtures, are much more important than in three dimensions. Not only they inhibit true Bose-Einstein condensation, as already well known, but they also smoothen all sharp features in the spin properties at finite temperature.   

Exploring quantum dynamics in homogeneous two-dimensional quantum gases

Realization of a homogeneous quantum gas loaded in an arbitrarily painted box potential could unveil intricate quantum many-body dynamics inaccessible using samples localized in conventional harmonic traps. In equilibrium, trap uniformity permits realization of many-body phases that may only exist in a narrow parameter space. Moreover, inducing non-equilibrium quantum dynamics via interaction quenches in a painted box trap could control or inhibit global mass transport and disentangle its effect from the spreading of quantum correlations across a sample. In this talk, we discuss realizations of novel quantum dynamics in tunable cesium atomic quantum gases confined in a two-dimensional (2D) box trap. In the first example, we perform interaction quenches to attractive values and observe for the first time 2D matter-wave Townes solitons that form from a modulational instability exhibiting universal scaling behaviors in its early time quantum dynamics. Using a homogeneous gas loaded in a 2D optical lattice, in the second example we discuss how by employing control of local chemical potential and interaction parameters to investigate the elusive quantum critical dynamics across a superfluid-Mott insulator quantum critical point.

    

Strongly-interacting bosons at 2D-1D dimensional crossover

Quantum gases at dimensional crossover exhibit fruitful physics which reflects special properties of non-integer dimensions. While various fascinating researches have been carried out in the tight-binding limit [1-3], the smooth dimensional crossover for strongly-interacting bosons in continuous lattice, which is beyond mean-field theory and strongly adapted to current generation of experiments, is rarely studied. In this talk, I will present our study about strongly-interacting bosons under continuous potential at 2D-1D dimensional crossover [4]. Using exact quantum Monte Carlo calculations, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fractions as well as the superfluid correlation as a function of temperature, interactions and potential. We find the special behavior of longitudinal superfluidity at the crossover which signatures the interplay of dimensionalities. Moreover, we show the correlation function evolves from a Berezinskii-Kosterlitz-Thouless (BKT) to Tomonaga-Luttinger liquid (TLL) type, with the coexistence of 2D and 1D behaviors appearing at the dimensional crossover. In the end, I will discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.    

Probing sine-Gordon dynamics in coupled spin chains

The recent progress in the control and manipulation of synthetic quantum matter has sparked a large interest in the realization of effective theories that form a low-energy description of a wide class of systems. A very prominent example of such an effective theory is the quantum sine-Gordon field theory, which naturally describes many one-dimensional quantum systems at low temperatures.

With the uprising interest in non-equilibrium dynamics of many-body quantum systems, testing the validity of these realizations far from the ground state is of utmost importance.

We investigate the emergence of the sine-Gordon theory as the low-energy description of a one-dimensional spin ladder. We use matrix-product state techniques to numerically characterize its low-energy sector and probe the validity of the effective dynamics deeply in the quantum regime.

Then, we probe the integrability of the sine-Gordon dynamics by realizing wave-packet scattering events. We introduce experimentally relevant probes of the sine-Gordon field theory in the described setup. Our results can be readily verified with currently available ultracold atom quantum simulators.   

Compressibility and the Equation of State of an Optical Quantum Gas in a Box

The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental quantity determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. In the quantum degenerate ideal Bose gas in two dimensions, however, a peculiar prediction so far has remained unseen: the compressibility of the gas is expected to become infinitely large. Here we demonstrate a measurement of the equation of state as well as the compressibility of a homogeneously trapped two-dimensional quantum gas of light inside a nanostructured dye-filled optical microcavity. Upon reaching quantum degeneracy we observe signatures of Bose-Einstein condensation in the finite-size system, causing a sharp increase of the density response to an external force, hiniting at the infinite compressibility of the uniform two-dimensional Bose gas.   

Excitonic Tonks-Girardeau and charge-density-wave phases in monolayer semiconductors

Excitons in two-dimensional semiconductors provide a novel platform for fundamental studies of many-body interactions. In particular, dipolar interactions between spatially indirect excitons may give rise to strongly correlated phases of matter that so far have been out of reach of experiments in ultracold gases. Here, we show that excitonic few-body systems in atomically thin transition-metal dichalcogenides confined to a one-dimensional geometry undergo a crossover from a Tonks-Girardeau to a charge-density-wave regime. To this end, we take into account realistic system parameters and predict the effective exciton-exciton interaction potential. We find that the pair correlation function of excitons contains key signatures of the many-body crossover already at small exciton numbers and show that photoluminescence spectra provide readily accessible experimental fingerprints of these strongly correlated quantum many-body states. We then study the system within the Luttinger Liquid theory that agrees remarkably well with few-body exact calculations in predicting spatial correlation functions and blueshifting of the photoluminescence spectra for an increasing number of excitons. Finally, we predict the excitation spectrum of the system for all densities in the many-body limit and study the temporal-spatial pair-correlation functions of emitted photons. Our findings showcase TMDs as an alternative platform for many-body dipolar physics in low-dimensions that may outperform most alternative experimental settings in different tasks and that may complement studies using ultracold molecules that have yet to reach the required densities and control to realize their full potential.