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arXiv:1711.05020 · Physical review. E

Autoresonant excitation of Bose-Einstein condensates

Serge Vasil'evich Batalov, A. G. Shagalov, L. Frièdland

Published Mar 21, 2018• 14 citations
arXivHTMLPDF

Abstract

Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters P_{1,2,3} are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the P_{1,2,3} parameter space, the system may exhibit two very different evolutions, i.e., the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analyzed both in theory and simulations with the emphasis on the effect of the interaction parameter P_{3}. In particular, the transition thresholds on the driving parameter P_{1} and their width in P_{1} in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and deexcitation of the condensate.

DOI
10.1103/physreve.97.032210

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Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters P_{1,2,3} are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the P_{1,2,3} parameter space, the system may exhibit two very different evolutions, i.e., the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analyzed both in theory and simulations with the emphasis on the effect of the interaction parameter P_{3}. In particular, the transition thresholds on the driving parameter P_{1} and their width in P_{1} in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and deexcitation of the condensate.
The interplay between quantum-mechanical and classical evolutions in a chirped-driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms, i.e., a successive two-level transitions (ladder climbing) and a continuing classicallike nonlinear phase locking (autoresonance). The persistent 1:1 and 2:1 resonances between the driving and the Keplerian frequencies are studied in detail and characterized in terms of two dimensionless parameters P1,2{P}_{1,2}P1,2​ representing the driving strength and the nonlinearity in the problem, respectively. The quantum-mechanical rotating wave and the classical single-resonance approximations are used to describe the regimes of efficient classical or quantum-mechanical excitation in this two-parameter space.
The autoresonant approach to generation of solitary structures in Bose-Einstein condensates by chirped frequency space-time modulation of the interaction strength is proposed. Both a spatially periodic case and a finite-size trap are studied numerically within a Gross-Pitaevskii equation. Weakly nonlinear theory of the process is developed in the spatially periodic case using Whitham's averaged variational principle. The theory also describes the threshold phenomenon setting the lowest bound on the amplitude of modulations of the interaction strength for autoresonant excitation.
We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state.
A parametrically forced Bose-Einstein condensate (BEC) is studied in the mean field approach for the case of a general moving optical lattice. The interaction between the atoms in the condensate and the time dependent lattice potential leads to a novel propagating superfluid matter wave, which can be controlled through chirp management. This system, when placed in a trap, accelerates and undergoes rapid nonlinear compression, controlled by the chirp. The density achieves its maximum, precisely when the matter wave changes direction. A dynamical phase transition is identified, which takes the superfluid phase to an insulating state. The exact expression for energy is obtained and analyzed in detail to gain physical understanding of the chirp management of the sinusoidal excitations and also the dynamical phase transition.
The dynamics of a Bose?Einstein condensate under the influence of a confining double-well potential and a periodic potential (optical lattice) is studied by the well-known variational method. The variational principle leads to coupled nonlinear differential equations for the amplitude (width), chirp, center position and the center frequency of the condensate. The interplay between the condensate parameters leads to various regimes of its time evolution which depend on the relative strengths of the double-well and the periodic potentials. In particular, we show that by adjusting the strengths of the applied potentials appropriately, one can control and manipulate the condensate in several ways including tunneling from one well to the other and the to-and-fro motion between the two wells.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.