Spin Faraday Waves in Periodically Modulated Spin-Orbit-Coupled Bose Gases

Abstract

This paper investigates the formation of Spin Faraday waves in spin-orbit-coupled Bose-Einstein condensate under the stripe phase and explores the dispersion relation under three different phases. We discover that the SFW exhibit temporal and spatial patterns when the interaction is modulated periodically, and appear with resonant waves and higher order harmonics. SFW can be excited even when the modulation frequency resonates with the trap frequency. Furthermore, we study the dispersion relation of these Faraday modes through periodic modulation, which agrees well with our theoretical results under three quantum phases. Our work indicates novel physical phenomena originating from the introduction of spin-orbit coupling and provides a possible method for studying the dispersion of Bose gases.

Figures (7)

• Figure 1: A schematic of atomic cloud localized in a 2D harmonic trap, where $a_{11}$ and $a_{22}$ are time-dependent, and $a_{12}$ is constant. Different colors represent atoms occupying different finestates.
• Figure 2: Spin Faraday patterns excited by in-phase modulation $\omega_i=200$ Hz and $\Delta a=6a_0$ in the stripe phase $\Omega=0.1E_r$. (a) Density distribution of two components in x-y direction. (b) Total density oscillation (black dash) and spin density oscillation (red line) that stands for the formation of SFW. (c) 1D Fourier transform of panel (b). The peaks pointed by the blue and red arrows represent density and spin Faraday waves, respectively.
• Figure 3: Comparison of in-phase (a-c) and out-of-phase (d-f) modulation results when driving frequency $\omega_i=100$ Hz in the stripe phase. Panel (a) and Panel (d) show 2D density of spin up component. Other parameters are the same as Fig. \ref{['200']}.
• Figure 4: The temporal evolution of the system from 0 to 300 ms, resulted from in-phase modulation under the stripe phase. (a) The evolution of spin density $n_s$. (b) The evolution of total energy before and after the formation of SFW. Red dotted line indicates 235 ms and the green one is 250 ms. (c) The Fourier transform of $n_1$. Parameters are $\Omega=0.1E_r$, $\omega_i=220$ Hz, $\Delta a=8a_0$.
• Figure 5: Comparation of the dispersion relation between SOC and two-component BEC. The blue line and red line correspond to density and spin mode of binary BEC. The red points resulte from in-phase modulation, while blue triangles result from out-of-phase modulation. The frequency of the red square and star are $\omega_i=200$ Hz and $\omega_i=100$ Hz. The down triange is $\omega_i=100$ Hz.