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

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

doi:10.1103/physreva.100.063610

Cited by 19 publications

(23 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(33) by following the method used in Ref. [26]: For a fixed wavenumber, we numerically solve Eq. (33) from t = 0 to T with the initial conditions (S A , S B ) T = (1, 0) T and (0, 1) T , obtaining S 1 (T ) and is the numerically obtained one shown in Fig.…”

Section: Resonant Conditionsmentioning

confidence: 99%

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

Imaeda¹,

Fujimoto²,

Kawaguchi³

2021

Preprint

View full text Add to dashboard Cite

We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein condensate periodically driven by a quadratic Zeeman coupling. This phenomenon is closely related to the Shapiro steps in superconducting Josephson junctions, and the previous experimental work [Evrard et al., Phys. Rev. A 100, 023604 (2019)] for a spin-1 bosonic system observed the resonant dynamics and then called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii equation, we study the Shapiro resonance beyond the single-mode approximation used in the previous work, which assumes that all components of the spinor wavefunction have the same spatial configuration. Considering resonant dynamics starting from a polar state, we analytically calculate the Floquet-Lyapunov exponents featuring an onset of the resonance under a linear analysis and find that spin waves with finite wavenumbers can be excited. This kind of non-uniform excitation cannot be described by the single-mode approximation. Furthermore, to study the long-time resonant dynamics beyond the linear analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii equation, finding that the nonresonant hydrodynamic variables also grow at wavelengths of even multiples of the resonant one due to the nonlinear effect.

show abstract

Section: Resonant Conditionsmentioning

confidence: 99%

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

Imaeda¹,

Fujimoto²,

Kawaguchi³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In a recent paper [28], the authors found that the Faraday patterns can also be excited from a quench of the phase of the Rabi coupling without any modulation of the system's parameters. The effective modulation of interaction can be realized when the interaction coefficients satisfy g 2 12 = g 11 g 22 and the average populations of two hyperfine states of the spinor BEC experience Rabi oscillation.…”

Section: Introductionmentioning

confidence: 99%

“…However, according to the simulation in Ref. [28], it takes a long time for the Faraday patterns to emerge and in a practical experiment, the tuning range of |g 2 12 − g 11 g 22 | is limited. Motivated by Ref.…”

Section: Introductionmentioning

confidence: 99%

Faraday patterns in spin-orbit coupled Bose-Einstein condensates

Zhang,

Liu,

Zhang

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…The phenomenon of parametric resonances (PRs) is ubiquitious in nature and is a widely examined fundamental physical property. Today, PRs are one of the outstanding features observed in Bose-Einstein condensates (BECs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] where resonances are usually the result of modulating one of the system parameters such as the scattering length [11,[19][20][21][22]. They are also generated by external means such as a time-dependent trapping geometry [11], laser stirring [2], and laser-intensity modulation [1].…”

Section: Introductionmentioning

confidence: 99%

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Sakhel,

Sakhel

2021

Preprint

View full text Add to dashboard Cite

We report parametric resonances (PRs) in the mean-field dynamics of a one-dimensional dipolar Bose-Einstein condensate (DBEC) in widely varying trapping geometries. The chief goal is to characterize the energy levels of this system by analytical methods and the significance of this study arises from the commonly known fact that in the presence of interactions the energy levels of a trapped BEC are hard to calculate analytically. The latter characterization is achieved by a matching of the PR energies to energy levels of the confining trap using perturbative methods. Further, this work reveals the role of the interplay between dipole-dipole interactions (DDI) and trapping geometry in defining the energies and amplitudes of the PRs. The PRs are induced by a negative Gaussian potential whose depth oscillates with time. Moreover, the DDI play a role in this induction. The dynamics of this system is modeled by the time-dependent Gross-Pitaevskii equation (TDGPE) that is numerically solved by the Crank-Nicolson method. The PRs are discussed basing on analytical methods: first, it is shown that it is possible to reproduce PRs by the Lagrangian variational method that are similar to the ones obtained from TDGPE. Second, the energies at which the PRs arise are closely matched with the energy levels of the corresponding trap calculated by time-independent perturbation theory. Third, the most probable transitions between the trap energy levels yielding PRs are determined by time-dependent perturbation theory. The most significant result of this work is that we have been able to characterize the above mentioned energy levels of a DBEC in a complex trapping potential.

show abstract

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

Cited by 19 publications

References 28 publications

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

Faraday patterns in spin-orbit coupled Bose-Einstein condensates

Characterization of the energy level-structure of a trapped dipolar Bose gas via mean-field parametric resonances

Contact Info

Product

Resources

About