Trapped Bose-Einstein Condensate Research Articles

Impact of Density Inhomogeneity on the Critical Velocity for Vortex Shedding in a Harmonically Trapped Bose–Einstein Condensate

Impact of Density Inhomogeneity on the Critical Velocity for Vortex Shedding in a Harmonically Trapped Bose–Einstein Condensate

Monte Carlo Simulation for the Frequency Comb Spectrum of an Atom Laser

A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model describes the analytical derivation of the frequency comb spectrum for an atomic laser realized from modeling a coherent atomic beam of condensate and non-condensate quantum field components released from a trapped Bose–Einstein condensate at a given repetition phase and frequency. The condensate part of the atomic vapor is assumed to be subjected to thermal noise induced by the temperature of the surrounding thermal atomic cloud. This new quantum approach uses time periodicity and an orthogonal decomposition of the quantum field in a complex-valued quantum field representation to derive and model the quantum field's forward- and backward-propagating components as a standing wave field in the same unique time and temperature domain without quantitative singularities at finite temperatures. The complex-valued atom laser field, the resulting frequency comb, and the repetition frequency distribution with the varying shape of envelopes are numerically monitored within a Monte Carlo sampling method, as a function of temperature and trap frequency of the external confinement.Quanta 2023; 12: 171–179.

Fragmentation and correlations in a rotating Bose–Einstein condensate undergoing breakup

The theoretical investigation of rotating Bose–Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons. We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose–Einstein condensate breaks up under rotation.

Quantum frequency interferometry: With applications ranging from gravitational wave detection to dark matter searches

We introduce a quantum interferometric scheme that uses states that are sharp in frequency and delocalized in position. The states are frequency modes of a quantum field that is trapped at all times in a finite volume potential, such as a small box potential. This allows for significant miniaturization of interferometric devices. Since the modes are in contact at all times, it is possible to estimate physical parameters of global multimode channels. As an example, we introduce a three-mode scheme and calculate precision bounds in the estimation of parameters of two-mode Gaussian channels. This scheme can be implemented in several systems, including superconducting circuits, cavity-QED, and cold atoms. We consider a concrete implementation using the ground state and two phononic modes of a trapped Bose–Einstein condensate. We apply this to show that frequency interferometry can improve the sensitivity of phononic gravitational waves detectors by several orders of magnitude, even in the case that squeezing is much smaller than assumed previously, and that the system suffers from short phononic lifetimes. Other applications range from magnetometry, gravimetry, and gradiometry to dark matter/energy searches.

Simulating the Dicke lattice model and quantum phase transitions using an array of coupled resonators

A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. An array of coupled mechanical resonators (MRs) can homogeneously interact with a group of trapped Bose–Einstein condensates (BECs) via the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave fields, each subsystem with the BEC-MR interaction can mimic the Dicke type spin-phonon interaction, and the whole system is therefore extended to a lattice of Dicke models with the additional adjacent phonon-phonon hopping couplings. In view of this lattice model with the Z 2 symmetry, its quantum phase transitions behavior can be controlled by this periodic phonon-phonon interactions in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behaviors of the collective spins through the external mechanical method.

Chaotic dynamics of Bose–Einstein condensate induced by density-dependent gauge field

In this work we study the effect of density-dependent gauge field on the collective dynamics of a harmonically trapped Bose–Einstein condensate (BEC), beyond the linear response regime. The density-dependent gauge field, as a backaction of the condensate, can in turn affect the condensate dynamics, resulting in highly nonlinear equations of motion. The dipole and breathing oscillations of the condensate along the direction of gauge field are coupled by this field. We find that, in the presence of this coupling, the collective motion of a quasi-one-dimensional condensate is still regular, i.e., periodic or quasiperiodic. In contrast, for a quasi-two-dimensional condensate, the collective dynamics of the condensate can become chaotic, when the density-dependent gauge field is strong. The mechanism is that the gauge field can also induce a Hall effect, manifested as an additional coupling between dipole and breathing oscillations in perpendicular direction, and chaotic motion is resulted from the interplay between these oscillations. Our findings reveal an important effect of dynamical gauge field on the nonlinear dynamics of a BEC.

Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

Hyperspherical approach to dipolar droplets beyond the mean-field limit

We apply a hyperspherical formulation to a trapped Bose-Einstein condensate with dipolar and contact interactions. Central to this approach is a general correspondence between K-harmonic hyperspherical methods and a suitable Gaussian ansatz to the Gross-Pitaevskii equation, regardless of the form of the interparticle potential. This correspondence allows one to obtain hyperspherical potential energies for a wide variety of physical problems. In the case of the dipolar Bose-Einstein condensate, this motivates the inclusion of a beyond-mean field term within the hyperspherical picture, which allows us to describe the energies and wavefunctions of excitations of self-bound dipolar droplets outside of the mean-field limit.

Arnold web and dynamical tunneling in a four-site Bose–Hubbard model

We present the quantum and classical study of a four-well trapped Bose–Einstein condensate (BEC) modeled by the Bose–Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Analyzing the energy levels of a trapped Bose–Einstein condensate (BEC) can be difficult when dipole-dipole interactions (DDIs) are present. To address this issue, this study focuses on the parametric resonances (PRs) in the mean-field dynamics of a one-dimensional dipolar BEC (DBEC) over widely varying trapping geometries, with the primary objective of characterizing the energy levels of this system via analytical methods. This is achieved by matching the PR energies to the energy levels of the confining trap using perturbative methods. Further, this research reveals the role of the interplay between DDIs and the trapping geometry in defining the energies and amplitudes of the PRs. The PRs are induced by a negative Gaussian potential with a depth that oscillates with respect to time; DDIs also play a role in this induction. The dynamics of this system are modeled using the time-dependent Gross–Pitaevskii equation (TDGPE), which is numerically solved via the Crank–Nicolson method. The PRs are discussed based on analytical methods. First, we show that PRs similar to the ones obtained from the TDGPE can be reproduced via the Lagrangian variational method. Second, the energies at which the PRs occur are closely matched with the energy levels of the corresponding trap, calculated using the time-independent perturbation theory. Third, the most probable transitions between the trap energy levels yielding PRs are determined based on the time-dependent perturbation theory. The primary contribution of this research is that the energy levels of a DBEC within a complex trapping potential could be characterized.

Morphology of an Interacting Three-Dimensional Trapped Bose–Einstein Condensate from Many-Particle Variance Anisotropy

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

Multiparticle entanglement dynamics of quantum chaos in a Bose-Einstein condensate

We study the particle-entanglement dynamics witnessed by the quantum Fisher information (QFI) of a trapped Bose-Einstein condensate governed by the kicked rotor Hamiltonian. The dynamics is investigated with a beyond mean-field approach. We link the time scales of the validity of this approximation in, both, classical regular and chaotic regions, with the maximum Lyapunov exponents of the classical system. This establishes an effective connection between the classical chaos and the QFI. We finally study the critical point of a quantum phase transition using the beyond mean-field approximation by considering a two-mode bosonic Josephson junction with attractive interparticle interaction.

Many-body collisional dynamics of impurities injected into a double-well trapped Bose-Einstein condensate

We unravel the many-body dynamics of a harmonically trapped impurity colliding with a bosonic medium confined in a double-well upon quenching the initially displaced harmonic trap to the center of the double-well. We reveal that the emerging correlation dynamics crucially depends on the impurity-medium interaction strength allowing for a classification into different dynamical response regimes. For strong attractive impurity-medium couplings the impurity is bound to the bosonic bath, while for intermediate attractions it undergoes an effective tunneling. In the case of weak attractive or repulsive couplings the impurity penetrates the bosonic bath and performs a dissipative oscillatory motion. Further increasing the impurity-bath repulsion results in the pinning of the impurity between the density peaks of the bosonic medium, a phenomenon that is associated with a strong impurity-medium entanglement. For strong repulsions the impurity is totally reflected by the bosonic medium. To unravel the underlying microscopic excitation processes accompanying the dynamics we employ an effective potential picture. We extend our results to the case of two bosonic impurities and demonstrate the existence of a qualitatively similar impurity dynamics.

Formation of vortex rings and hopfions in trapped Bose–Einstein condensates

The topological transition of vortex lines to vortex rings and hopfions is numerically investigated by the Gross–Pitaevskii equation in three-dimensional trapped Bose–Einstein condensates. The shape of the vortex rings formed by the two vortex lines of the vortex dipole depends strongly on the initial separation of the lines. An approximately perfect vortex ring can be obtained by choosing some suitable values of the separation. The deformation of the formed rings depends on the shape of the rings in turn. Furthermore, we show a feasible approach to generate vortex hopfions by imprinting a vortex line in the center of the generated vortex rings. Specifically, the movement of the vortex rings can excite helical waves along the central vortex line of the hopfion structure if the vortex ring is not perfect.

Effects of quantum corrections on the modulational instability of Bose–Einstein condensates trapped in a periodic optical lattice

Through a semiquantal procedure, we study the perturbed modulation of amplitude and phase of Gross-Piteavskii equation describing trapped Bose–Einstein condensates in an optical lattice potential. By introducing quantum correctional parameters, the problem is quantized and leads to the derivation of a novel dynamical instability criterion. Additional degrees of freedom carrying quantum properties play a central role on the refine of the instability bandwidth, and, combined to the strength of optical lattice potential, entail unstable modes into full stability. A set of computational tools exhibited various features that bear instability characteristics, to confirm analytically predicted results. The quantum fluctuations thus have a stabilizing effect on the dynamics of harmonically trapped Bose–Einstein condensates in an optical lattice potential.

Interplay of three-body and higher-order interactions on the modulational instability of Bose–Einstein condensate

We investigate the modulational instability (MI) of trapped Bose–Einstein condensates with three-body and higher-order interactions employing both semi-analytical and numerical methods. Using the time-dependent variational approach, we derive variational equations for the time evolution of the amplitude, phase of modulational perturbation, and effective potential of the system. By means of an effective potential, we retrieve the corresponding MI condition of the dynamical system under consideration. The interplay between three-body interaction and higher-order interaction is discussed in detail. The semi-analytical predictions are confirmed through numerical simulations.

Intra-scales energy transfer during the evolution of turbulence in a trapped Bose-Einstein condensate(a)(a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

In turbulence phenomena, including the quantum turbulence in superfluids, an energy flux flows from large to small length scales, composing a cascade of energy. A universal characteristic of turbulent flows is the existence of a range of scales where the energy flux is scale-invariant: this interval of scales is often referred to as inertial region. This property is fundamental as, for instance, in turbulence of classical fluids it characterizes the behavior of statistical features such as spectra and structure functions. Here we show that also in decaying quantum turbulence generated in trapped Bose-Einstein condensates (BECs), intervals of momentum space where the energy flux is constant can be identified. Indeed, we present a procedure to measure the energy flux using both the energy spectrum and the continuity equation. A range of scales where the flux is constant is then determined employing two distinct protocols and in the same range, the momentum distribution measured is consistent with previous work. The successful identification of a region with constant flux in turbulent BECs is a manifestation of the universal character of turbulence in these quantum systems. These measurements pave the way for studies of energy conservation and dissipation in trapped atomic superfluids, and also analogies with the related processes that take place in ordinary fluids.

Localized nonlinear dissipative matter waves controlled by quantum fluctuations

The dynamics of matter waves in a trapped Bose–Einstein condensate including three-body losses, atomic feeding and quantum fluctuations is investigated theoretically and numerically. We use a generalized variational approach which allows us to express the influence of the condensate parameters on the time evolution of the amplitude, width and chirp, through a set of differential equations. Emphasis is placed on the strength of quantum fluctuations which deeply modifies the wave dynamics. Direct numerical simulations confirm the analytical results. Importantly, we extend numerical experiments and show that the localized modes split into two or three trains of solitary waves which can be controlled by the quantum fluctuations.

Cloud shape of a molecular Bose–Einstein condensate in a disordered trap: a case study of the dirty boson problem

We investigate, both experimentally and theoretically, the static geometric properties of a harmonically trapped Bose–Einstein condensate of 6Li2 molecules in laser speckle potentials. Experimentally, we measure the in situ column density profiles and the corresponding transverse cloud widths over many laser speckle realizations. We compare the measured widths with a theory that is non-perturbative with respect to the disorder and includes quantum fluctuations. Importantly, for small disorder strengths we find quantitative agreement with the perturbative approach of Huang and Meng, which is based on Bogoliubov theory. For strong disorder our theory perfectly reproduces the geometric mean of the measured transverse widths. However, we also observe a systematic deviation of the individual measured widths from the theoretically predicted ones. In fact, the measured cloud aspect ratio monotonously decreases with increasing disorder strength, while the theory yields a constant ratio. We attribute this discrepancy to the utilized local density approximation, whose possible failure for strong disorder suggests a potential future improvement.

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.