Quantum Depletion of a Homogeneous Bose-Einstein Condensate

Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation

We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with other theoretical schemes. Differently from the superfluid fraction, we find that at finite temperature the condensate fraction is a non-monotonic function of the interaction strength, presenting a global maximum at a characteristic value of the gas parameter, which grows as the temperature increases. This non-monotonic behavior has not yet been observed, but could be tested with the available experimental setups of ultracold bosonic atoms confined in a box potential. We clearly identify the region of parameter space that is of experimental interest to look for this behavior and provide explicit expressions for the relevant observables. Finite size effects are also discussed within a semiclassical approximation.

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.

Fermionic Correlation Functions from Randomized Measurements in Programmable Atomic Quantum Devices

We provide an efficient randomized measurement protocol to estimate two- and four-point fermionic correlations in ultracold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.

Photonic transistor based on a coupled-cavity system with polaritons

We investigate the transmission of probe fields in a coupled-cavity system with polaritons and propose a theoretical schema for realizing a polariton-based photonic transistor. When probe light passes through such a hybrid optomechanical device, its resonant point with Stokes or anti-Stokes scattered effects, intensity with amplification or attenuation effects, as well as group velocity with slow or fast light effects can be effectively controlled by another pump light. This controlling depends on the exciton-photon coupling and single-photon coupling. We also discover an asymmetric Fano resonance in transparency windows under the strong exciton-photon coupling, which is different from general symmetric optomechanically induced transparency. Our results open up exciting possibilities for designing photonic transistors, which may be useful for implementing polariton integrated circuits.

Observation of 1/k^{4}-Tails after Expansion of Bose-Einstein Condensates with Impurities

We measure the momentum density in a Bose-Einstein condensate (BEC) with dilute spin impurities after an expansion in the presence of interactions. We observe tails decaying as 1/k^{4} at large momentum k in the condensate and in the impurity cloud. These algebraic tails originate from the impurity-BEC interaction, but their amplitudes greatly exceed those expected from two-body contact interactions at equilibrium in the trap. Furthermore, in the absence of impurities, such algebraic tails are not found in the BEC density measured after the interaction-driven expansion. These results highlight the key role played by impurities when present, a possibility that had not been considered in our previous work [Chang et al., Phys. Rev. Lett. 117, 235303 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.235303]. Our measurements suggest that these unexpected algebraic tails originate from the nontrivial dynamics of the expansion in the presence of impurity-bath interactions.

Testing universality of Feynman-Tan relation in interacting Bose gases using high-order Bragg spectra

The Feynman-Tan relation, obtained by combining the Feynman energy relation with the Tan's two-body contact, can explain the excitation spectra of strongly interacting ³⁹K Bose-Einstein condensate (BEC). Since the shift of excitation resonance in the Feynman-Tan relation is inversely proportional to atomic mass, the test of whether this relation is universal for other atomic systems is significant for describing the effect of interaction in strongly correlated Bose gases. Here we measure the high-momentum excitation spectra of ¹³³Cs BEC with widely tunable interactions by using the second- and third-order Bragg spectra. We observe the backbending of frequency shift of excitation resonance with increasing interaction, and even the shift changes its sign under the strong interactions in the high-order Bragg spectra. Our finding shows good agreement with the prediction based on the Feynman-Tan relation. Our results provide significant insights for understanding the profound properties of strongly interacting Bose gases.

Multi-Qubit Bose-Einstein Condensate Trap for Atomic Boson Sampling

We propose a multi-qubit Bose-Einstein-condensate (BEC) trap as a platform for studies of quantum statistical phenomena in many-body interacting systems. In particular, it could facilitate testing atomic boson sampling of the excited-state occupations and its quantum advantage over classical computing in a full, controllable and clear way. Contrary to a linear interferometer enabling Gaussian boson sampling of non-interacting non-equilibrium photons, the BEC trap platform pertains to an interacting equilibrium many-body system of atoms. We discuss a basic model and the main features of such a multi-qubit BEC trap.

Unpredictable condensate-depletion dynamics in one-dimensional power-law traps

The dynamic depletion of a trapped one-dimensional Bose-Einstein condensate (BEC) that is driven by laser stirring is numerically explored using beyond mean-field methods. For this purpose, the multi-configurational time-dependent Hartree method for bosons (Alonet al2008Phys. Rev.A77033613) is applied. In order to induce the depletion, the BEC is excited by a negative Gaussian potential (dimple) whose depth is modulated with time. The BEC is examined in various trapping geometries, with different interactions, and the condensate depletion is recorded as a function of time. A general power-law trap is considered that can be experimentally generated and shaped by the holographic methods of Bruceet al(2011Phys. Rev.A84053410). The chief goal is to explore the interplay between trapping geometry and interactions in defining the depletion dynamics. It is chiefly found, that the details of these depletion dynamics are unpredictable and determined by a combination of the principle dimple depth, trap, and interactions. One significant feature of this work is that quite a number of plateaus is reached in the aforementioned dynamics.

High-Resolution Coherent Probe Spectroscopy of a Polariton Quantum Fluid

Characterizing elementary excitations in quantum fluids is essential to study their collective effects. We present an original angle-resolved coherent probe spectroscopy technique to study the dispersion of these excitation modes in a fluid of polaritons under resonant pumping. Thanks to the unprecedented spectral and spatial resolution, we observe directly the low-energy phononic behavior and detect the negative-energy modes, i.e., the ghost branch, of the dispersion relation. In addition, we reveal narrow spectral features precursory of dynamical instabilities due to the intrinsic out-of-equilibrium nature of the system. This technique provides the missing tool for the quantitative study of quantum hydrodynamics in polariton fluids.

On the survival of the quantum depletion of a condensate after release from a magnetic trap

We present observations of the high momentum tail in expanding Bose–Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.

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.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N−1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate

We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency Ω, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling ∝n^{5/2} to an expansion in integer powers of density, where, in addition to a two-body BMF term ∝n^{2}sqrt[Ω], there emerges a repulsive three-body contribution ∝n^{3}/sqrt[Ω]. We experimentally evidence these two contributions, thanks to their different scaling with Ω, in the expansion of a Rabi-coupled two-component ^{39}K condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.

Hanbury Brown and Twiss Bunching of Phonons and of the Quantum Depletion in an Interacting Bose Gas

We report the realization of a Hanbury Brown and Twiss (HBT)-like experiment with a gas of interacting bosons at low temperatures. The low-temperature regime is reached in a three-dimensional optical lattice and atom-atom correlations are extracted from the detection of individual metastable helium atoms after a long free fall. We observe, in the noncondensed fraction of the gas, a HBT bunching whose properties strongly deviate from the HBT signals expected for noninteracting bosons. In addition, we show that the measured correlations reflect the peculiar quantum statistics of atoms belonging to the quantum depletion and of the Bogoliubov phonons, i.e., of collective excitations of the many-body quantum state. Our results demonstrate that atom-atom correlations provide information about the quantum state of interacting particles, extending the interest of HBT-like experiments beyond the case of noninteracting particles.

All-optical negative differential transporter of Bose-Einstein condensates in cavity

We present a new and interesting physical phenomenon of optical negative differential transmission (ONDT, whose output intensity decreases with the increasing of input field intensity for an arbitrary optical system) in present BEC-cavity coupling system which pumped by a strong light and probed by a weak light. Theoretical results show that the transmission of the probe can be suppressed or promoted greatly by the pump due to optical nonlinearity and the Stokes/anti-Stokes scattering. To our most interest, two kinds of ONDT respectively induced by the nonlinear incoherent light-controlling and the nonlinear coherent interference have been uncovered, which have promising prospect in producing hyper-stable light source since it provides an unusual negative feedback.

Breathing modes of repulsive polarons in Bose-Bose mixtures

We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.

Observation of quantum depletion in a non-equilibrium exciton-polariton condensate

Superfluidity, first discovered in liquid ⁴He, is closely related to Bose–Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations—the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton–polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton–polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton–polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton–polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.

Many aspects of polariton condensate behaviour can be captured by mean-field theories but interactions introduce additional quantum effects. Here the authors observe quantum depletion in a driven-dissipative condensate and find that deviations from equilibrium predictions depend on the excitonic fraction.

Magnetic Phase Transition in a Mixture of Two Interacting Superfluid Bose Gases at Finite Temperature

The miscibility condition for a binary mixture of two interacting Bose-Einstein condensates is shown to be deeply affected by interaction driven thermal fluctuations. These give rise to a first order phase transition to a demixed phase with full spatial separation of the two condensates, even if the mixture is miscible at zero temperature. Explicit predictions for the isothermal compressibility, the spin susceptibility, and the phase transition temperature T_{M} are obtained in the framework of Popov theory, which properly includes beyond mean-field quantum and thermal fluctuations in both the spin and density channels. For a mixture of two sodium condensates occupying the hyperfine states |F=1⟩,|m_{F}=1⟩ and |F=1,m_{F}=-1⟩, respectively, T_{M} is predicted to occur at about 0.7 times the usual BEC critical temperature.

Particle Fluctuations in Mesoscopic Bose Systems

Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d > 2 above T c and in a box of d > 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D > 2 above T c and of a confining dimension D > 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d > 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.

Purely Kerr nonlinear model admitting flat-top solitons

We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of the linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with k=1 and 2 nodes, as well as vortices with winding number m=1, are completely stable. For multipoles with k≥3 and vortices with m≥2, alternating stripes of stability and instability are identified in their parameter spaces.

Polaritonic Cross Feshbach Resonance

We demonstrate the existence of a cross Feshbach resonance by strongly driving a lower polariton mode and by monitoring in time the transmission of a short optical pulse at the energy of the upper polariton mode in a semiconductor microcavity. From the signatures of the optical resonance, strength, and sign of the energy shift, we attribute the origin of the scattering process between polariton modes with opposite circular polarization to a biexciton bound state. From this study, we infer the conditions required for a strong enhancement of the generation of entangled photon pairs.

30 W, sub-kHz frequency-locked laser at 532 nm

We report on the realization of a high-power, ultranarrow-linewidth, and frequency-locked 532 nm laser system. The laser system consists of single-pass and intra-cavity second harmonic generation of a continuous-wave Ytterbium doped fiber laser at 1064 nm in the nonlinear crystal of periodically poled lithium niobate and lithium triborate, respectively. With 47 W infrared input, 30 W green laser is generated through the type I critical phase matching in the intracavity lithium triborate crystal. The laser linewidth is measured to be on the order of sub-kHz, which is achieved by simultaneously locking the single-pass frequency doubling output onto the iodine absorption line R69 (36-1) at 532 nm. Furthermore, the phase locking between the laser system and another slave 1064 nm laser is demonstrated with relative frequency tunability being up to 10 GHz. Our results completely satisfy the requirements of 532 nm laser for quantum simulation with ultracold atoms.

Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap's Form and Boundary Conditions in the Thermodynamic Limit

We analytically calculate the statistics of Bose-Einstein condensate (BEC) fluctuations in an interacting gas trapped in a three-dimensional cubic or rectangular box with the Dirichlet, fused or periodic boundary conditions within the mean-field Bogoliubov and Thomas-Fermi approximations. We study a mesoscopic system of a finite number of trapped particles and its thermodynamic limit. We find that the BEC fluctuations, first, are anomalously large and non-Gaussian and, second, depend on the trap's form and boundary conditions. Remarkably, these effects persist with increasing interparticle interaction and even in the thermodynamic limit-only the mean BEC occupation, not BEC fluctuations, becomes independent on the trap's form and boundary conditions.