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arXiv:1907.03945 · Physical Review A

Faraday patterns generated by Rabi oscillation in a binary Bose-Einstein condensate

Terun Chen, Kosuke Shibata, Yujiro Eto, Takuya Hirano, Hiroki Saito

Published Dec 5, 2019• 23 citations
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Abstract

The interaction between atoms in a two-component Bose-Einstein condensate (BEC) is effectively modulated by the Rabi oscillation. This periodic modulation of the effective interaction is shown to generate Faraday patterns through parametric resonance. We show that there are multiple resonances arising from the density and spin waves in a two-component BEC and investigate the interplay between the Faraday-pattern formation and the phase separation.

DOI
10.1103/physreva.100.063610

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The interaction between atoms in a two-component Bose-Einstein condensate (BEC) is effectively modulated by the Rabi oscillation. This periodic modulation of the effective interaction is shown to generate Faraday patterns through parametric resonance. We show that there are multiple resonances arising from the density and spin waves in a two-component BEC and investigate the interplay between the Faraday-pattern formation and the phase separation.
We investigate parametric excitation and pattern formation in a harmonically trapped two-component Bose-Einstein condensate. We assume the condensate to be in the miscible phase, but near the miscible-immiscible phase transition, where total-density and spin-density excitations are decoupled. By periodically modulating the atomic scattering lengths, Faraday patterns can be generated in both density and spin channels. In an elongated condensate, the pattern in the spin channel corresponds to a one-dimensional standing wave with the two components exhibiting an out-of-phase density oscillation, where the modulation frequency and the oscillation period are related to the velocity of the spin sound. After the spin pattern is fully developed, the system quickly enters a nonlinear destabilization regime. For a pancake-shaped condensate, a two-dimensional Faraday pattern is generated with an interesting lll-fold rotational symmetry. The number of nodes along the radial and angular directions increases with larger modulation frequencies. We also compare the growth rates of spin Faraday patterns generated with different modulation protocols, which are accessible to current experiments.
We study the Faraday patterns generated by spin-orbit-coupling induced parametric resonance in a spinor Bose-Einstein condensate with repulsive interaction. The collective elementary excitations of the Bose-Einstein condensate, including density waves and spin waves, are coupled as the result of the Raman-induced spin-orbit coupling and a quench of the relative phase of two Raman lasers without the modulation of any of the system's parameters. We observed several higher parametric resonance tongues at integer multiples of the driving frequency and investigated the interplay between Faraday instabilities and modulation instabilities when we quench the spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to plane-wave phase. If the detuning is equal to zero, the wave number of combination resonance barely changes as the strength of spin-orbit coupling increases. If the detuning is not equal to zero after a quench, a single combination resonance tongue will split into two parts.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.