Dynamics of a Bose-Einstein condensate in optical trap (original) (raw)
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Physica D: Nonlinear Phenomena, 2003
In this work we consider the oscillations and associated resonance of a 2D Bose-Einstein condensate under periodic and random modulations of the atomic scattering length. For random oscillations of the trap potential and of the atomic scattering length we are able to calculate the mean growth rate for the width of the condensate. The results obtained from the reduced ODE's for oscillations of the width of condensate are compared with the numerical simulations of the full 2D Gross-Pitaevskii equation with modulated in time coefficients.
The Dynamic of Trapped Bose-Einstein Condensate Under Noise
Journal of Physics: Conference Series, 2018
It is known that Bose-Einstein Condansate is well described by the non-linear Schrodinger equation known as the Gross Pitaevskii Equation (GPE) with the macroscopic wave function which evaluates with time and space. Many studies have been performed on nonlinear properties in Bose-Einstein Condansate. In this study, we present some numerical results of the Gross-Pitaevskii Equation with the external potential under noise. The phase portraits and Poincaré sections of the system are simulated numerically both with and without noise.
Dynamical quantum noise in trapped Bose-Einstein condensates
Physical Review A, 1998
We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations, and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate, and compare results to those for single-mode models.
Chaotic dynamics of a Bose-Einstein condensate in a double-well trap
Journal of Physics B: Atomic, Molecular and Optical Physics, 2002
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.
The Bose-stimulated self-organization of a quasi-two-dimensional nonequilibrium Bose-Einstein condensate in an in-plane potential is proposed.We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a solitonlike shape for spatially homogeneous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, can spontaneously rotate. Stability of the condensate soliton in the spatially asymmetric trap is analyzed. In addition to the nonlinear dynamics of nonequilibrium Bose-Einstein condensates of ultracold atoms, our findings can be applied to the condensates of quantum well excitons and cavity polaritons in semiconductor heterostructure, and to the condensates of photons.
Statics and dynamics of quasi one-dimensional Bose–Einstein condensate in harmonic and dimple trap
Laser Physics, 2016
We investigate a quasi one-dimensional 87 Rb Bose-Einstein condensate in a harmonic trap with an additional dimple trap (dT) in the center. Within a zero-temperature Gross-Pitaevskii mean-field description we provide a one-dimensional physical intuitive model, which we solve by both a time-independent variational approach and numerical calculations. With this we obtain at first equilibrium results for the emerging condensate wave function which reveal that a dimple trap potential induces a bump or a dip in case of a red-or a blue-detuned Gaussian laser beam, respectively. Afterwards, we investigate how this dT induced bump/dip-imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the generic case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the dT induced bump in the condensate wave function remains present, whereas the dip starts decaying after a characteristic time scale which decreases with increasing blue-detuned dT depth. Secondly, once the red-or blue-detuned dT is switched off, we find that bright shock-waves or gray/dark bi-soliton trains emerge which oscillate within the harmonic confinement with a characteristic frequency.
Continuous quantum measurement of a Bose-Einstein condensate: A stochastic Gross-Pitaevskii equation
Physical Review A, 2002
We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed within the Gross-Pitaevskii mean-field approach. Continuous weak measurements allow instead to replace, for timescales short enough, the exact problem with its mean-field approximation through a stochastic analogue of the Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark soliton undergoing a continuous imaging. 03.75.Fi,05.30.Jp, The interplay between quantum and classical descriptions of the physical world and the role of the measurement process are still at the heart of the understanding of quantum mechanics [1]. The related theoretical debate has been greatly enriched in the last decades by the realization of new experimental techniques aimed at producing quantum states without classical analogue, such as entangled or squeezed states, or to explore phenomena which are intrinsically quantum mechanical, like quantum jumps. All this occurred also having in mind practical implications, such as the improvement of sensitivity of various devices operating at or near the quantum limit .
Instability of a Bose-Einstein condensate with an attractive interaction
Physical Review A, 2000
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically 7 Li. Our method is to solve the time-dependent nonlinear Schrödinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number N c. For N > N c , the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of 1 trap period. Within numerical uncertainty, the results are consistent with the formation of a "black hole" of infinite density fluctuations, as predicted by Ueda and Huang [16]. We obtain numerically N c ≈ 1251. We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding "thermal cloud", and the loss due to two-and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain N c ≈ 1260 as the maximum value in the oscillations.
The European Physical Journal D, 2016
We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.
Frictionless dynamics of Bose–Einstein condensates under fast trap variations
Journal of Physics B: Atomic, Molecular and Optical Physics, 2009
A method is proposed to design the time dependence of the trap frequency and achieve in a short time an adiabatic-like (frictionless) evolution of Bose-Einstein condensates governed by the Gross-Pitaevskii equation. Different cases depending on the effective dimension of the trap and the interaction regimes are considered. 2D traps are particularly suitable as the method can be applied without the need to impose any additional time-dependent change in the strength of the interatomic interaction or a Thomas-Fermi regime as it occurs for 1D and 3D traps.