Bose-Einstein Condensate Research Articles

Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross-Pitaevskii equation in Bose-Einstein condensations with attractive interaction.

This paper investigates dynamical behaviors and controllability of some nonautonomous localized waves based on the Gross-Pitaevskii equation with attractive interatomic interactions. Our approach is a relation constructed between the Gross-Pitaevskii equation and the standard nonlinear Schrödinger equation through a new self-similarity transformation which is to convert the exact solutions of the latter to the former's. Subsequently, one can obtain the nonautonomous breather solutions and higher-order rogue wave solutions of the Gross-Pitaevskii equation. It has been shown that the nonautonomous localized waves can be controlled by the parameters within the self-similarity transformation, rather than relying solely on the nonlinear intensity, spectral parameters, and external potential. The control mechanism can induce an unusual number of loosely bound higher-order rogue waves. The asymptotic analysis of unusual loosely bound rogue waves shows that their essence is energy transfer among rogue waves. Numerical simulations test the dynamical stability of obtained localized wave solutions, which indicate that modifying the parameters in the self-similarity transformation can improve the stability of unstable localized waves and prolong their lifespan. We numerically confirm that the rogue wave controlled by the self-similarity transformation can be reproduced from a chaotic initial background field, hence anticipating the feasibility of its experimental observation, and propose an experimental method for observing these phenomena in Bose-Einstein condensates. The method presented in this paper can help to induce and observe new stable localized waves in some physical systems.

Quantum control of classical motion: piston dynamics in a Rabi-coupled Bose–Einstein condensate

We develop a model and explore the dynamics of a hybrid classical-quantum system consisting of a classical piston and a self-interacting pseudospin 1/2 Bose–Einstein condensate with a time-dependent Rabi coupling. We investigate the mechanical work produced by the piston moving as a result of the quantum pressure of the condensate. The time-dependent Rabi field redistributes the condensate density between the spin components and, as a result, causes a time-dependent pressure acting on the piston. Correspondingly, the motion of the piston produces quantum evolution of the condensate mass- and spin density profiles. We show how by optimised design of the time-dependent direction of the Rabi field based on a quasi-stationary quantum pressure approximation, one can control both the position and velocity of the piston.

Spin Faraday waves in periodically modulated spin-orbit-coupled Bose gases

This paper investigates the formation of Spin Faraday waves in spin-orbit-coupled Bose-Einstein condensate under the stripe phase and explores the dispersion relation under three different phases. We discover that the SFW exhibit temporal and spatial patterns, and appear with resonant waves and higher order harmonics when the interaction is modulated periodically. SFW can be excited even when the modulation frequency resonates with the trap frequency. Furthermore, we study the dispersion relation of these Faraday modes through periodic modulation, which agrees well with our theoretical results under three quantum phases. Our work indicates novel physical phenomena originating from the introduction of spin-orbit coupling and provides a possible method for studying the dispersion of Bose gases.

Two-dimensional quantum droplets in binary quadrupolar condensates

We study the stability and characteristics of two-dimensional (2D) quasi-isotropic quantum droplets (QDs) of fundamental and vortex types, formed by binary Bose–Einstein condensate with magnetic quadrupole–quadrupole interactions (MQQIs). The magnetic quadrupoles are built as pairs of dipoles and antidipoles polarized along the x-axis. The MQQIs are induced by applying an external magnetic field that varies along the x-axis. The system is modeled by the Gross–Pitaevskii equations including the MQQIs and Lee-Huang-Yang correction to the mean-field approximation. Stable 2D fundamental QDs and quasi-isotropic vortex QDs with topological charges S⩽4 are produced by means of the imaginary-time-integration method for configurations with the quadrupoles polarized parallel to the system’s two-dimensional plane. Effects of the norm and MQQI strength on the QDs are studied in detail. Some results, including an accurate prediction of the effective area, chemical potential, and peak density of QDs, are obtained in an analytical form by means of the Thomas-Fermi approximation. Collisions between moving QDs are studied by means of systematic simulations.

Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

A delicate balance between dissipative and nonlinear forces allows traveling waves termed solitons to preserve their shape and energy for long distances without steepening and flattening out. Solitons are so widespread that they can generate both destructive waves on oceans’ surfaces and noise-free message propagation in silica optic fibers. They are naturally observed or artificially produced in countless physical systems at very different coarse-grained scales, from solar winds to Bose–Einstein condensates. We hypothesize that some of the electric oscillations detectable by scalp electroencephalography (EEG) could be assessed in terms of solitons. A nervous spike must fulfill strict mathematical and physical requirements to be termed a soliton. They include the proper physical parameters like wave height, horizontal distance and unchanging shape; the appropriate nonlinear wave equations’ solutions and the correct superposition between sinusoidal and non-sinusoidal waves. After a thorough analytical comparison with the EEG traces available in the literature, we argue that solitons bear striking similarities with the electric activity recorded from medical conditions like epilepsies and encephalopathies. Emerging from the noisy background of the normal electric activity, high-amplitude, low-frequency EEG soliton-like pathological waves with relatively uniform morphology and duration can be observed, characterized by repeated, stereotyped patterns propagating on the hemispheric surface of the brain over relatively large distances. Apart from the implications for the study of cognitive activities in the healthy brain, the theoretical possibility to treat pathological brain oscillations in terms of solitons has powerful operational implications, suggesting new therapeutical options to counteract their detrimental effects.

Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics.

Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue wave-like dynamics in a reaction-diffusion system that arise as a result of a subcritical Turing instability. This state is present in a regime where all time-independent states are unstable and consists of intermittent excitation of spatially localized spikes, followed by collapse to an unstable state and subsequent regrowth. We characterize the spatiotemporal organization of spikes and show that in sufficiently large domains the dynamics are consistent with a memoryless process.

Vortex Formation in Spin-Orbit Coupled Spin-1 Bose Condensates with Magnetic Field

Vortex Formation in Spin-Orbit Coupled Spin-1 Bose Condensates with Magnetic Field

Dissipation-Driven Superradiant Phase Transition of a Two-Dimensional Bose–Einstein Condensate in a Double Cavity

Abstract We study superradiant phase transitions in a hybrid system of a two-dimensional Bose-Einstein condensate of atoms and two cavities arranged with a tilt angle. By adjusting the loss rate of cavities, we map out the phase diagram of steady states within a mean field framework. We find that when the loss rates of the two cavities are different, superradiant transitions may not occur at the same time in the two cavities. A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance. In the case of both cavities are superradiant, a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate. The photon current shows a non-monotonic dependence on the loss rate difference, owing to the competition of photon number difference and cavity field phase difference. Our findings can be realized and detected in experiments.

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement.

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose-Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit.

High-order rogue wave and mixed interaction patterns for the three-component Gross-Pitaevskii equationsin F=1 spinor Bose-Einstein condensates.

Under investigation are the three-component Gross-Pitaevskii equationsin F=1 spinor Bose-Einstein condensates. Various localized waves' generation mechanisms have been derived from plane wave solutions using modulation instability. The perturbed continuous waves produce a large number of rogue wave structures through the split-step Fourier numerical method. Based on the known Lax pair, we construct the generalized iterative (n,N-n)-fold Darboux transformation to generate various high-order solutions, including the bright-dark-bright structure of rogue waves, periodic waves, and their mixed interaction structures. Numerical simulations show that rogue waves with a two-peaked structure have robust noise resistance and stable dynamical behavior. The asymptotic states of high-order rogue waves as the parameter approaches infinity are also predicted using the large parameter asymptotic technique. In addition, the position of these localized wave patterns can be controlled by some special parameters. These results may help us understand the dynamic behavior of spinor condensates for the mean-field approximation.

Optical spin hall effect in exciton-polariton condensates in lead halide perovskite microcavities.

An exciton-polariton condensate is a hybrid light-matter state in the quantum fluid phase. The photonic component endows it with characters of spin, as represented by circular polarization. Spin-polarization can form stochastically for quasi-equilibrium exciton-polariton condensates at parallel momentum vector k|| ∼ 0 from bifurcation or deterministically for propagating condensates at k|| > 0 from the optical spin-Hall effect (OSHE). Here, we report deterministic spin-polarization in exciton-polariton condensates at k|| ∼ 0 in microcavities containing methylammonium lead bromide perovskite (CH3NH3PbBr3) single crystals under non-resonant and linearly polarized excitation. We observe two energetically split condensates with opposite circular polarizations and attribute this observation to the presence of strong birefringence, which introduces a large OSHE at k|| ∼ 0 and pins the condensates in a particular spin state. Such spin-polarized exciton-polariton condensates may serve not only as circularly polarized laser sources but also as effective alternatives to ultracold atom Bose-Einstein condensates in quantum simulators of many-body spin-orbit coupling processes.

Matter-wave collimation to picokelvin energies with scattering length and potential shape control

The sensitivity of atom interferometers depends on their ability to realize long pulse separation times and prevent loss of contrast by limiting the expansion of the atomic ensemble within the interferometer beam through matter-wave collimation. Here we investigate the impact of atomic interactions on collimation by applying a lensing protocol to a 39K Bose-Einstein condensate at different scattering lengths. Tailoring interactions, we measure energies corresponding to (340 ± 12) pK in one direction. Our results are supported by an accurate simulation, which allows us to extrapolate a 2D ballistic expansion energy of (438 ± 77) pK. Based on our findings we propose an advanced scenario, which enables 3D expansion energies below 16 pK by implementing an additional pulsed delta-kick. Our results pave the way to realize ensembles with more than 1 × 105 atoms and 3D energies in the two-digit pK range in typical dipole trap setups without the need for micro-gravity or long baseline environments.

Spin Rotations in a Bose-Einstein Condensate Driven by Counterflow and Spin-Independent Interactions.

We observe spin rotations caused by atomic collisions in a nonequilibrium Bose-condensed gas of ^{87}Rb. Reflection from a pseudomagnetic barrier creates counterflow in which forward- and backward-propagating matter waves have partly transverse spin directions. Even though inter-atomic interaction strengths are state independent, the indistinguishability of parallel spins leads to spin dynamics. A local magnetodynamic model, which captures the salient features of the observed spin textures, highlights an essential connection between four-wave mixing and collisional spin rotation. The observed phenomenon is commonly thought not to occur in Bose condensates; our observations and model clarify the nature of these effective-magnetic spin rotations.

Breakdown of Temporal Coherence in Photon Condensates.

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.

Multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate in a cavity

Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.

Perturbation theory for the Gross–Pitaevskii equation modeling stationary Bose–Einstein condensates

In this article a perturbative solution of the Gross–Pitaevskii(GP) equation in the D-dimensional space RD with a general continuous non-negative external potential is studied. The solution describes the condensate wave-function of a gas containing N Bose particles. A criteria for the validity of the perturbative solution is developed. Furthermore expressions for the particle density, the chemical potential, the internal energy and the mean-square radius of the condensate are derived corrected to first order in the coupling constant. The scheme is then applied to obtain the solution of the GP equation in D=1,2,3 for external harmonic potentials, and the results are compared with the numerical solutions. It is shown, in each case, that if N exceeds a certain value the perturbative solution breaks down.

Exciton polariton condensation from bound states in the continuum at room temperature

Exciton–polaritons (polaritons) resulting from the strong exciton–photon interaction stimulates the development of novel low-threshold coherent light sources to circumvent the ever-increasing energy demands of optical communications1–3. Polaritons from bound states in the continuum (BICs) are promising for Bose–Einstein condensation owing to their theoretically infinite quality factors, which provide prolonged lifetimes and benefit the polariton accumulations4–7. However, BIC polariton condensation remains limited to cryogenic temperatures ascribed to the small exciton binding energies of conventional material platforms. Herein, we demonstrated room-temperature BIC polariton condensation in perovskite photonic crystal lattices. BIC polariton condensation was demonstrated at the vicinity of the saddle point of polariton dispersion that generates directional vortex beam emission with long-range coherence. We also explore the peculiar switching effect among the miniaturized BIC polariton modes through effective polariton−polariton scattering. Our work paves the way for the practical implementation of BIC polariton condensates for integrated photonic and topological circuits.

Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase

Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.

Selective Excitation of Exciton-Polariton Condensate Modes in an Annular Perovskite Microcavity.

Exciton-polariton systems composed of a light-matter quasi-particle with a light effective mass easily realize Bose-Einstein condensation. In this work, we constructed an annular trap in a halide perovskite semiconductor microcavity and observed the spontaneous formation of symmetrical petal-shaped exciton-polariton condensation in the annular trap at room temperature. In our study, we found that the number of petals of the petal-shaped exciton-polariton condensates, which is decided by the orbital angular momentum, is dependent on the light intensity distribution. Therefore, the selective excitation of perovskite microcavity exciton-polariton condensates under all-optical control can be realized by adjusting the light intensity distribution. This could pave the way to room-temperature topological devices, optical cryptographical devices, and new quantum gyroscopes in the exciton-polariton system.

Dynamical Tunneling in More than Two Degrees of Freedom.

Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.