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arXiv:1506.00795 · Laser Physics

Controlled generation of nonlinear resonances through sinusoidal lattice modes in Bose–Einstein condensate

Priyam Das, Prasanta K Panigrahi

Published Oct 29, 2015• 9 citations
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Abstract

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.

DOI
10.1088/1054-660x/25/12/125501

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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.
In this work, we realize the soliton's negative mass regime, when a Bose-Einstein condensate is subjected to a harmonic confinement. We also discuss that this system is favorable for the formation of a bound state when an additional species is considered. When a time modulated optical lattice potential is introduced, the sinusoidal lattice modes lead to the generation of nonlinear resonances. A classical dynamical phase transition is also identified in this case through a superfluid to the insulating phase transition.
The nonlinear coupled Gross-Pitaevskii equation governing the dynamics of the two-component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating-wave solutions in quasi-one-dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates a procedure for coherent control of these modes through temporal modulation of the parameters, like scattering length and oscillator frequency. The effects of time-dependent coupling and the trap variation on the condensate profile are explained. The TBEC has also been investigated in the presence of an optical lattice potential, where the superfluid phase is found to exist under general conditions.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
We predict a dynamical classical superfluid–insulator transition in a Bose–Einstein condensate (BEC) trapped in combined optical and axially symmetrical harmonic potentials initiated by the periodic modulation of the radial trapping potential. The transition is marked by a loss of phase coherence in the BEC and a subsequent destruction of the interference pattern upon free expansion. For a weak modulation of the radial potential the phase coherence is maintained. For a stronger modulation and a longer holding time in the modulated trap, the phase coherence is destroyed thus signalling a classical superfluid–insulator transition. The results are illustrated by a complete numerical solution of the axially symmetrical mean-field Gross–Pitaevskii equation for a repulsive BEC. Suggestions for future experimentation are made.
We investigate the response of a Bose-Einstein condensate of trapped, neutral atoms to weak and strong sinusoidal perturbation of the trapping potential both by solving the Bogoliubov equations and by direct integration of the time-dependent, driven Ginzburg-Pitaevskii-Gross equation. We find that the distortion of the condensate is maximal when the frequency of the perturbation equals one of the mode positions of the condensate's excitation spectrum. On resonance, the condensate exhibits a strong nonlinear response that can be used as a clear signature of the mode frequency in an experiment where the trap potential is weakly perturbed. For strong driving, we find evidence for an array of nonlinear effects such as harmonic generation and frequency mixing. These phenomena are the matter-wave analogs of conventional nonlinear optics and should be straightforward to study in evaporatively cooled samples of alkali-metal atoms. \textcopyright{} 1996 The American Physical Society.