One-dimensional Bose-Einstein Condensate Research Articles

Weakly nonlocal matter-wave droplets and soliton trains engineering in a Bose-Einstein condensate

We propose a comprehensive analysis of the modulational instability (MI) phenomenon in one-dimensional Bose-Einstein condensate (BEC) in the context of mutually symmetric components in the binary mixture. The proposed model considers weak nonlocal cubic mean-field and quadratic beyond mean-field interactions arising from quantum fluctuations. The instability regions are analyzed using linear stability analysis of a continuous wave, considering maximum perturbation wavenumber and growth rate. The regions for quantum droplets (QDs) and solitons are identified by varying the nonlocality parameter. Numerical simulations confirm analytical predictions, revealing that nonlocality influences the formation of various QD profiles and instability time. Furthermore, solitonic patterns exhibit nonlocality-dependent behavior. Our study opens new doors to a better characterization of QDs in binary mixtures in the presence of higher-order beyond mean-field effects.

Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates

In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. This study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or sech-like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of captivating behaviors in the matter-wave smooth positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate density profile of matter-wave smooth positons in BECs, providing valuable insights into their controllable behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects.

Dynamics of vector bright solitons in one-dimensional Bose–Einstein condensate with time-dependent Raman coupling

We consider the dynamic stabilities of two solitons in one-dimensional trapless Bose–Einstein condensate with periodical tunable Raman coupling via numerical simulating and variational approximating the time-dependent Gross–Pitaevskii equations. It is found that dynamically stabilized vector bright solitons can be formed by modulating Raman coupling for cases of ɛsin(ωt) and ɛcos(ωt), and its evolution and movement show consistence with theoretical results. In addition, we found that the strength of spin–orbit coupling exerted a main effect on the moving distance of condensate, and different modulation frequency of Raman coupling exhibited different evolution of peak density for solitons.

Kink soliton dynamics in one-dimensional Bose–Einstein condensate with higher-order nonlinear interactions

We investigated the soliton behavior in one-dimensional Bose–Einstein condensates. Based on the modified Gross–Pitaevskii equation (GPE) model with higher-order nonlinear interaction and through the F-expansion method, we derived the analytical kink soliton solution of the one-dimensional GPE. The typical kink soliton features under the specific experimental setting are identified, and the physical implication of the analytical results is also demonstrated. The derived theoretical results can be used to guide the experimental study of kink soliton in ultracold atomic systems with higher-order nonlinearity.

Stability of trapped Bose-Einstein condensate under a density-dependent gauge field.

We study the ground-state stability of the trapped one-dimensional Bose-Einstein condensate under a density-dependent gauge field by variational and numerical methods. The competition of density-dependent gauge field and mean-field atomic interaction induces the instability of the ground state, which results in irregular dynamics. The threshold of the gauge field for exciting the instability is obtained analytically and confirmed numerically. When the gauge field is less than the threshold, the system is stable, and the gauge field induces chiral dynamics of the wave packet. When the gauge field is greater than the threshold, the system is unstable, and the ground-state wave packet will be deformed and fragmented. Interestingly, we find that as the gauge field approaches the threshold, strong dipolar and breathing dynamics take place, and strong modes mixing occurs, the instability of the system sets in. In addition, we show that the stability of the system can be well controlled by periodical modulation of the trapping potential. We provide theoretical evidence to understand and control the irregular dynamics associated with chiral superfluid induced by density-dependent gauge field.

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 (Alon et al 2008 Phys. Rev. A 77 033613) 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 Bruce et al (2011 Phys. Rev. A 84 053410). 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.

Search for rogue waves in Bose-Einstein condensates via a theory-guided neural network

An important and incompletely answered question is whether machine learning methods can be used to discover the excitation of rogue waves (RWs) in nonlinear systems, especially their dynamic properties and phase transitions. In this work, a theory-guided neural network (TgNN) is constructed to explore the RWs of one-dimensional Bose-Einstein condensates. We find that such method is superior to the ordinary deep neural network due to theory guidance of underlying problems. The former can directly give any excited location, timing, and structure of RWs using only a small amount of dynamic evolution data as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the first-order RW phase from the non-RW phase. The results not only greatly reduce computational time for exploring RWs, but also provide a promising technique for discovering phase transitions in parameterized nonlinear systems.

Control of matter-wave solitons using an accelerating atomic mirror

We present a possible way to control matter-wave solitons, which is through the collision between solitons and an accelerating atomic mirror. The acceleration of the mirror has a nontrivial effect on the dynamical characters of the reflected solitons. In the one-dimensional Bose–Einstein condensates, when the acceleration of the mirror has the identical direction with the initial soliton’s velocity, the soliton will diffuse after collision; in the contrasting case, the soliton will shrink and then diffuse. We quantitatively explain the above dynamical phenomena by analyzing the atoms’ movement in the soliton, and demonstrate that the method can generate a similar effect to the phase imprinting technology. Moreover, considering the dipolar effect between atoms, this approach can be used for the generation and control of breathing solitons.

Dynamics of optomechanical droplets in a Bose-Einstein condensate

We investigate numerically a one-dimensional Bose-Einstein condensate illuminated by off-resonant laser light which is retroreflected by a single feedback mirror. Studying the ground states of the system, we find density structures which are self-trapped via the optomechanical action of the diffracted light. We show that these structures are stable and exhibit Newtonian dynamics. We propose that these results allow continuous, nondestructive monitoring of condensate dynamics via the optical intensity and may offer opportunities for optical control and transport of coherent matter via gradients in optical phase alone.

Disorder in order: Localization without randomness in a cold-atom system

We present a mapping between the Edwards model of disorder describing the motion of a single particle subject to randomly positioned static scatterers and the Bose polaron problem of a light quantum impurity interacting with a Bose-Einstein condensate (BEC) of heavy atoms. The mapping offers an experimental setting to investigate the physics of Anderson localization where, by exploiting the quantum nature of the BEC, the time evolution of the quantum impurity emulates the disorder-averaged dynamics of the Edwards model. Valid in any space dimension, the mapping can be extended to include interacting particles, arbitrary disorder, or confinement and can be generalized to study many-body localization. Moreover, the corresponding exactly solvable disorder model offers means to benchmark variational approaches used to study polaron physics. Here we illustrate the mapping by focusing on the case of an impurity interacting with a one-dimensional BEC through a contact interaction. While a simple wave function based on the expansion in the number of bath excitations misses the localization physics entirely, a coherent state Ansatz combined with a canonical transformation captures the physics of disorder and Anderson localization.

Dynamics of a hybrid optomechanical system in the framework of the generalized linear response theory

In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose–Einstein condensate to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atom–atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy.

Emission of Solitons From an Obstacle Moving in the Bose-Einstein Condensate

Dark solitons dynamically generated from a potential moving in a one-dimensional Bose-Einstein condensate are displayed. Based on numerical simulations of the Gross-Pitaevskii equation, we find that the moving obstacle successively emits a series of solitons which propagate at constant speeds. The dependence of soliton emission on the system parameters is examined. The formation mechanism of solitons is interpreted as interference between a diffusing wavepacket and the condensate background, enhanced by the nonlinear interactions.PACS numbers: 03.75.Mn, 03.75.Lm, 05.30.Jp

Breathing solitons induced by collision in dipolar Bose–Einstein condensates

We numerically study the breathing dynamics induced by collision between bright solitons in one-dimensional Bose–Einstein condensates with strong dipole–dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested in their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom number, rather than initial phase difference. Moreover, a collision between breathing solitons can produce new after-two-collision breathing solitons, whose breathing amplitude can be adjusted and reaches the maximum (or minimum) when the peak–peak (or dip–dip) collision happens.

Quantum Monte Carlo simulation of BEC-impurity tunneling

Polaron tunneling is a prominent example of a problem characterized by different energy scales, for which the standard quantum Monte Carlo methods face a slowdown problem. We propose a new quantum-tunneling Monte Carlo (QTMC) method which is free from this issue and can be used for a wide range of tunneling phenomena. We apply it to study an impurity interacting with a one-dimensional Bose-Einstein condensate and simultaneously trapped in an external double-well potential. Our scheme works for an arbitrary coupling between the particle and condensate and, at the same time, allows for an account of tunneling effects. We discover two distinct quasi-particle peaks associated, respectively, with the phonon-assisted tunneling and the self-trapping of the impurity, which are in a crossover regime for the system modeled. We observe and analyze changes in the weights and spectral positions of the peaks (or, equally, effective masses of the quasi-particles) when the coupling strength is increased. Possible experimental realizations using cold atoms are discussed.

On-demand generation of dark soliton trains in Bose-Einstein condensates

Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schr\"odinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

Supersolidity of cnoidal waves in an ultracold Bose gas

A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as "cnoidal waves". We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a non-equilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of two Goldstone (gapless) modes -- associated with the spontaneous breaking of $\mathrm{U}(1)$ symmetry and of continuous translational invariance -- at large wavelength is verified. We also calculate the static structure factor and the compressibility of cnoidal waves, which show a divergent behavior at the edges of each Brillouin zone.

Characterising arbitrary dark solitons in trapped one-dimensional Bose-Einstein condensates (a) (a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we provide numerical evidence that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we discuss implications for vortex detection in three-dimensional Bose-Einstein condensates.

Coupled dynamics of polaron and Bose–Einstein condensate in a parabolic potential

We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.

Exact N -point-function mapping between pairs of experiments with Markovian open quantum systems

We formulate an exact spacetime mapping between the $\mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A \textbf{94}, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $\mathcal{N}$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schr\"odinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $\mathcal{N}$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation.

Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap are investigated by combining techniques of variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Control schemes considered in the paper include imaginary trap frequencies at short time scales, i.e., the HO potential replaced by the quadratic repulsive one. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help us to address fundamental problems of the quantum speed limit and thermodynamics.