Observation of first and second sound in a BKT superfluid

An efficient method to generate near-ideal hollow beams of different shapes for box potential of quantum gases

Ultracold quantum gases are usually prepared in conservative traps for quantum simulation experiments. The atomic density inhomogeneity, together with the consequent position-dependent energy and time scales of cold atoms in traditional harmonic traps, makes it difficult to manipulate and detect the sample at a higher level. These problems are partially solved by optical box traps made of blue-detuned hollow beams. However, generating a high-quality hollow beam with high light efficiency for the box trap is challenging. Here, we present a scheme that combines the fixed optics, including axicons and prisms, to pre-shape a Gaussian beam into a hollow beam with a digital micromirror device (DMD) to improve the quality of the hollow beam further, providing a nearly ideal optical potential of various shapes for preparing highly homogeneous cold atoms. The highest power-law exponent of potential walls can reach a value over 100, and the light efficiency from a Gaussian to a hollow beam is also improved compared to direct optical shaping by a mask or a DMD. Combined with a one-dimensional optical lattice, a nearly ideal two-dimensional uniform quantum gas with different geometrical boundaries can be prepared for exploring quantum many-body physics to an unprecedented level.

Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate

The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.

Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas

We numerically study the transport properties of a two-dimensional Fermi gas in a weakly and strongly interacting regimes, in the range of temperatures close to the transition to a superfluid phase. For that we excite sound waves in a fermionic mixture by using the phase imprinting technique, follow their evolution, and finally determine both their speed and attenuation. Our formalism, originated from a density-functional theory, incorporates thermal fluctuations via the grand canonical ensemble description and with the help of Metropolis algoritm. From numerical simulations we extract temperature dependence of the sound velocity and diffusivity as well as the dependence on the interaction strength. We emphasize the role of virtual vortex-antivortex pairs creation in the process of sound dissipation.

Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators

Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.

Thermography of the superfluid transition in a strongly interacting Fermi gas

Heat transport can serve as a fingerprint identifying different states of matter. In a normal liquid, a hotspot diffuses, whereas in a superfluid, heat propagates as a wave called "second sound." Direct imaging of heat transport is challenging, and one usually resorts to detecting secondary effects. In this study, we establish thermography of a strongly interacting atomic Fermi gas, whose radio-frequency spectrum provides spatially resolved thermometry with subnanokelvin resolution. The superfluid phase transition was directly observed as the sudden change from thermal diffusion to second-sound propagation and is accompanied by a peak in the second-sound diffusivity. This method yields the full heat and density response of the strongly interacting Fermi gas and therefore all defining properties of Landau's two-fluid hydrodynamics.

Effects of Quantum Fluctuations on the Low-Energy Collective Modes of Two-Dimensional Superfluid Fermi Gases from the BCS to the Bose Limit

We investigate the effects of quantum fluctuations on the low-energy collective modes of two-dimensional (2D) s-wave Fermi superfluids from the BCS to the Bose limit. We compare our results to recent Bragg scattering experiments in 2D box potentials, with very good agreement. We show that quantum fluctuations in the phase and modulus of the pairing order parameter are absolutely necessary to give physically acceptable chemical potential and dispersion relation of the low-energy collective mode throughout the BCS to Bose evolution. Furthermore, we demonstrate that the dispersion of the collective modes change from concave to convex as interactions are tuned from the BCS to the Bose regime, and never crosses the two-particle continuum, because arbitrarily small attractive interactions produce bound states in two dimensions.

Superfluid Fraction in an Interacting Spatially Modulated Bose-Einstein Condensate

At zero temperature, a Galilean-invariant Bose fluid is expected to be fully superfluid. Here we investigate theoretically and experimentally the quenching of the superfluid density of a dilute Bose-Einstein condensate due to the breaking of translational (and thus Galilean) invariance by an external 1D periodic potential. Both Leggett's bound fixed by the knowledge of the total density and the anisotropy of the sound velocity provide a consistent determination of the superfluid fraction. The use of a large-period lattice emphasizes the important role of two-body interactions on superfluidity.

Probing quantum phase transition point by tuning an external anti trap

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.

Fluctuation-Dissipation Relation for a Bose-Einstein Condensate of Photons

For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here, we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the thermal nature of the optical condensate and demonstrates the validity of the fluctuation-dissipation theorem for a Bose-Einstein condensate.

Emergence of Isotropy and Dynamic Scaling in 2D Wave Turbulence in a Homogeneous Bose Gas

We realize a turbulent cascade of wave excitations in a homogeneous 2D Bose gas and probe on all relevant time and length scales how it builds up from small to large momenta, until the system reaches a steady state with matching energy injection and dissipation. This all-scales view directly reveals the two theoretically expected cornerstones of turbulence formation-the emergence of statistical momentum-space isotropy under anisotropic forcing and the spatiotemporal scaling of the momentum distribution at times before any energy is dissipated.

First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the U(1) symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with 6Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime.

Spontaneous generation and active manipulation of real-space optical vortices

Optical vortices are beams of light that carry orbital angular momentum¹, which represents an extra degree of freedom that can be generated and manipulated for photonic applications^2-8. Unlike vortices in other physical entities, the generation of optical vortices requires structural singularities^9-12, but this affects their quasiparticle nature and hampers the possibility of altering their dynamics or making them interacting^13-17. Here we report a platform that allows the spontaneous generation and active manipulation of an optical vortex-antivortex pair using an external field. An aluminium/silicon dioxide/nickel/silicon dioxide multilayer structure realizes a gradient-thickness optical cavity, where the magneto-optic effects of the nickel layer affect the transition between a trivial and a non-trivial topological phase. Rather than a structural singularity, the vortex-antivortex pairs present in the light reflected by our device are generated through mathematical singularities in the generalized parameter space of the top and bottom silicon dioxide layers, which can be mapped onto real space and exhibit polarization-dependent and topology-dependent dynamics driven by external magnetic fields. We expect that the field-induced engineering of optical vortices that we report will facilitate the study of topological photonic interactions and inspire further efforts to bestow quasiparticle-like properties to various topological photonic textures such as toroidal vortices, polarization and vortex knots, and optical skyrmions.

First and Second Sound in a Compressible 3D Bose Fluid

The two-fluid model is fundamental for the description of superfluidity. In the nearly incompressible liquid regime, it successfully describes first and second sound, corresponding, respectively, to density and entropy waves, in both liquid helium and unitary Fermi gases. Here, we study the two sounds in the opposite regime of a highly compressible fluid, using an ultracold ^{39}K Bose gas in a three-dimensional box trap. We excite the longest-wavelength mode of our homogeneous gas, and observe two distinct resonant oscillations below the critical temperature, of which only one persists above it. In a microscopic mode-structure analysis, we find agreement with the hydrodynamic theory, where first and second sound involve density oscillations dominated by, respectively, thermal and condensed atoms. Varying the interaction strength, we explore the crossover from hydrodynamic to collisionless behavior in a normal gas.

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 property 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. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment was carried out in a nanostructured dye-filled optical microcavity. We observed signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.

Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid

Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.