Dimensional Bose-Einstein Condensate Research Articles

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose–Einstein condensate (BEC) described by the deformed one-dimensional Gross–Pitaevskii equation (GPE). Analytical solutions were derived for null potential while we used variational and numerical methods for a harmonic oscillator potential. The effects of EUP on stability, probability density, position, and momentum uncertainties of BEC are analyzed. The EUP is found to be applicable for the free dark soliton solution and in the presence of a harmonic potential within specific ranges of the deformation parameter α, while it is not valid for the free bright soliton solution.

A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities

We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and in a parabolic trap, for the ideal non-interacting case. Secondly, the method allows one to obtain algebraic equations for the trajectories of the position of phase singularities present in the initial condensate along with time (the vortex lines). With these equations, one can predict quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. For the homogeneous case, this method was introduced in the context of photonics. Here, we adapt it to the context of Bose-Einstein condensates, and we extend it to the trapped case for the first time. Also, we offer numerical simulations in the non-linear case, for repulsive and attractive interactions. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the interactions. We illustrate the method with several simple cases of interest, both in the homogeneous and parabolically trapped systems.

Information theoretic approach to effects of spin–orbit coupling in quasi-one-dimensional Bose–Einstein condensates

We consider a spin-orbit coupled (SOC) one dimensional Bose–Einstein condensate (BEC) with attractive atom-atom interaction and make use of Shannon entropy (S), and Fisher information (I) to study the response of atomic density profiles to changes in κ L , the strength of the spin–orbit coupling for fixed values of Rabi frequency (Ω). Density profiles of our interest are characterized by (i) (region 1) and (ii) (region 2). We also pay attention to a spatially modulated density profile representing stripe phase of the condensate. Our numbers for S and I show that in region 1 the profile becomes localized as κ L increases while in region 2 we observe delocalization. Values of I in the stripe phase provide an evidence for the supersolid properties of the SOC BEC and indicate that supersolidity is a purely quantum phenomenon.

Departing from Thermality of Analogue Hawking Radiation in a Bose-Einstein Condensate.

We study the quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

Rogue waves for a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential in the Bose–Einstein condensate

The Bose–Einstein condensates (BECs) are seen during the studies in atomic optics, cavity opto-mechanics, cavity quantum electrodynamics, black-hole astrophysics, laser optics and atomtronics. Under investigation in this paper is a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential which describes the dynamics of a (2+1)-dimensional BEC. Based on the Kadomtsev–Petviashvili hierarchy reduction, we construct the bilinear forms and the Nth order rogue-wave solutions in terms of the Gramian. With the help of the analytic and graphic analysis, we exhibit the first- and second-order rogue waves under the influence of the strength of the interatomic interaction, α(t), and of Ω(t)=ωR̃∕ωZ, where t is the scaled time, ωR̃ and ωZ are the confinement frequencies in the radial and axial directions: When Ω(t)=0, the first-order rogue wave exhibits as an eye-shaped distribution; When Ω(t) is a periodic function, the rogue wave periodically raises; When Ω(t) is an exponential function, the rogue wave appears on the exponentially increasing background; When α(t) decreases, background and amplitude of the rogue wave both increase. The second-order rogue waves reach the maxima only once or three times when Ω(t) is a constant. With Ω(t) being the exponential function, the backgrounds of the second-order rogue waves exponentially increase with t increasing.

Evanescent modes and step-like acoustic black holes

We consider a model of an acoustic black hole formed by a quasi-one dimensional Bose–Einstein condensate with a step-like horizon. This system is analyzed by solving the corresponding Bogoliubov–de Gennes equation with an appropriate matching condition at the jump. When the step is between a subsonic and supersonic flow, a sonic horizon develops and in addition to the scattering coefficients we compute the distribution of the accompanying analogue Hawking radiation. Additionally, in response to the abrupt variation in flow and non-linear Bogoliubov dispersion relation, evanescent solutions of the Bogoliubov–de Gennes equation also appear and decay out from the horizon. We bound this decay length and show that these modes produce a modulation of observables outside the event horizon by their interference with outgoing Hawking flux. We go further and find specific superpositions of ingoing eigenmodes which exhibit coherent cancellation of the Hawking flux outside the horizon but nevertheless have evanescent support outside the black hole. We conclude by speculating that when quasiparticle interactions are included, evanescent modes may yield a leakage of information across the event horizon via interactions between the real outgoing Hawking flux and the virtual evanescent modes, and that we may expect this as a generic feature of models which break Lorentz invariance at the UV (Planck) scale.

Entanglement sudden death and revival in quantum dark-soliton qubits

We study the finite time entanglement dynamics between two dark soliton qubits due to quantum fluctuations in a quasi one dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long life time. We explore the entanglement decay for an entangled state of two phonon coherences and the qubits to be in the diagonal basis of so called Dicke states. We observe the collapse and revival of the entanglement, depending critically on the collective damping term but independent of the qubit-qubit interaction for both the initial states. The collective behavior of the dark soliton qubits demonstrate the dependence of entanglement evolution on the interatomic distance.

Effective Equations for Repulsive Quasi‐One Dimensional Bose–Einstein Condensates Trapped with Anharmonic Transverse Potentials

AbstractOne‐dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar‐shaped atomic repulsive Bose‐Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas‐Fermi, and crossover regimes were verified numerically by comparing the ground‐state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three‐dimensional Gross‐Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement even in the presence of an axial vorticity.

Entanglement of two hybrid optomechanical cavities composed of BEC atoms under Bell detection

In this paper, firstly, we consider bipartite entanglement between each part of an optomechanical cavity composed of one dimensional Bose-Einstein condensate (BEC). we investigate atomic collision on the behavior of the BEC in the week photon-atom coupling constant, and use Bogoliubov approximation for the BEC. Secondly under above condition, we propose a scheme for entanglement swapping protocol wich involves tripartite systems. In our investigation, we consider a scenario where BECs, moving mirrors, and optical cavity modes are given in a Gaussian state with a covariance matrix (CM). By applying the Bell measurment to the output optical field modes, we show how the remote entanglement between two BECs, two moving mirrors, and BEC-mirror modes in different optomechanical cavity can be generated.

Bouncing dynamics of Bose–Einstein condensates under the effects of gravity

Bouncing dynamics of quasi-one dimensional Bose–Einstein condensates (BECs) falling under gravity on delta-function potentials is investigated. First, we consider a single component BEC in the presence of cubic-quintic nonlinearity and study dynamical behavior of different parameters of the system using variational and numerical approaches. We see that the quintic nonlinearity plays a dominant role over cubic nonlinear interaction to extend the bouncing dynamics in the non-linear regime. We find that a matter-wave performs bouncing motion only for certain discrete values of initial position above the reflecting potential. We then consider bouncing dynamics of binary BECs. It is shown that the pair of matter-waves bounces together if inter-species interaction is attractive. However, their pairing breaks down if the inter-species interaction is made repulsive.

Dark solitons and rouge waves for a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential in the Bose–Einstein condensate

Under investigation in this paper is a (2+1)-dimensional Gross–Pitaevskii equation with time-varying trapping potential, which describes the dynamics of the (2+1)-dimensional Bose–Einstein condensate. Employing the Hirota method and symbolic computation, we obtain the dark one-soliton, two-soliton, three-soliton, breather-wave and rouge-wave solutions, respectively. We graphically study the dark solitons with the time-varying harmonic potential and scaled scattering length. Parallel and period solitons are observed. We obtain that when the external trapping potential increases with time, amplitudes of the dark solitons increase and widths of those solitons become narrower; when the external trapping potential is a periodic function, amplitudes and widths of the dark solitons periodically change. Decrease in the scaled scattering length leads to the narrower solitons’ widths, but does not affect the solitons’ amplitudes. Breather waves and rouge waves are also displayed: Rouge waves emerge when the period of the breather waves go to the infinity.

Initial Boundary Value Problem for Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity

In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for quasi-two dimensional Bose-Einstein condensates with spatially modulated nonlinearity. Suppose initial data sufficiently small, one has the existence and uniqueness of the generalized solution to the problem by a priori integral estimates and Galerkin method.

Collective excitations of a quasi two-dimensional BEC: beyond mean field theory

Collective excitations of a quasi two dimensional Bose-Einstein Condensate, which is subjected to an effective potential including beyond mean field effects, are studied. In the mean field regime, the sudden increase of the collective excitation frequency to infinity, indicating a collapse of the condensate is followed by its reappearance. It is found that the beyond mean field modifications prevent the reappearance of the excitation frequencies. Modifications in the potential are also found to prevent both attractively and repulsively interacting condensates from supporting the constant frequency breathing mode.

Spontaneous crystallization and filamentation of solitons in dipolar condensates

Inter-site interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one dimensional Bose-Einstein condensates develops a correlated modulational instability in the non-overlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or a crystal of solitons that can be so created for the first time in ultra-cold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.

Quantum fluctuations around black hole horizons in Bose-Einstein condensates

We study several realistic configurations allowing to realize an acoustic horizon in the flow of a one dimensional Bose-Einstein condensate. In each case we give an analytical description of the flow pattern, of the spectrum of Hawking radiation and of the associated quantum fluctuations. Our calculations confirm that the non local correlations of the density fluctuations previously studied in a simplified model provide a clear signature of Hawking radiation also in realistic configurations. In addition we explain by direct computation how this non local signal relates to short range modifications of the density correlations.

Quantum Fluctuations of Low Dimensional Bose-Einstein Condensates in Optical Systems

A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.

Exact density oscillations in the Tonks-Girardeau gas and their optical detection

We construct the exact time dependent density profile for a superposition of the ground and singly excited states of a harmonically trapped one dimensional Bose gas in the limit of strongly interacting particles, the Tonks-Girardeau gas. We obtain analytic results that allows one to determine the number of particles in the gas, as well as the quantum amplitudes in the superposition, from measurement results in an off-resonant light scattering experiment.

Construction of localized atomic wave packets

It is shown that highly localized solitons can be created in lower dimensional Bose–Einstein condensates (BECs), trapped in a regular harmonic trap, by temporally varying the trap frequency. A BEC confined in such a trap can be effectively used to construct a pulsed atomic laser emitting coherent atomic wave packets. In addition to having a complete control over the spatio-temporal dynamics of the solitons, we can separate the equation governing the Kohn mode (centre of mass motion). We investigate the effect of the temporal modulation of the trap frequency on the spatio-temporal dynamics of the bright solitons and also on the Kohn mode. The dynamics of the solitons and the variations in the Kohn mode with time are compared with those in a BEC confined in a trap with unmodulated trap frequency.

Quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity

We investigate the localized nonlinear matter waves of the quasi-two dimensional Bose-Einstein condensates with spatially modulated nonlinearity in harmonic potential. It is shown that the whole Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their novel properties are determined by the principle quantum number n and secondary quantum number l: the parity of the matter wave functions and the corresponding energy levels depend only on n, and the numbers of density packets for each quantum state depend on both n and l which describe the topological properties of the atom packets. We also give an experimental protocol to observe these novel phenomena in future experiments.

Phase separation of two-component Bose–Einstein condensates

Recently, coupled systems of nonlinear Schrödinger equations have been used extensively to describe mixtures Bose–Einstein condensates. In this paper, we study the distribution of two different hyperfine spin states of a binary mixture of three dimensional Bose–Einstein condensates. In a double condensate, an interface may occur due to large intraspecies and interspecies scattering lengths. We prove that there is an asymptotic separation of different phases in the strong coupling (Thomas–Fermi) limit.