Suppression of relative flow by multiple domains in two-component Bose-Einstein condensates

We investigate flow properties of immiscible Bose-Einstein condensates composed of two different Zeeman spin states of ${}^{87}\mathrm{Rb}$. Two spatially overlapping condensates in the optical trap are prepared by application of a resonant radio-frequency pulse, and then the magnetic field gradient is applied in order to produce the atomic flow. We find that the spontaneous multiple-domain formation arising from the immiscible nature drastically changes the fluidity. The homogeneously overlapping condensates readily separate under the magnetic field gradient, and they form a stable configuration composed of the two layers. In contrast, the relative flow between two condensates is largely suppressed in the case where the magnetic field gradient is applied after spontaneous domain formation.

Figure 1

Radio-frequency spectroscopy. The initial state $|2\rangle$ is irradiated by an rf pulse. The rf pulse shape is a Gaussian function with a standard deviation of $9.5\mu \mathrm{s}$. (a) Frequency and (b) intensity dependence of population of each $m_F$ component. In (b), the frequency of the rf pulse is set to be 8.145 MHz. Each point represents the average over three measurements with the error bars giving the standard deviation over those measurements.

Figure 2

(a) Experimentally observed and (b) numerically simulated phase-separation dynamics. Absorption images are obtained at $T_{\mathrm{hold}}=0$, 20, 40, 60, and 80 ms from left to right. The two-component BECs of $|1\rangle$ and $|2\rangle$ states are initially prepared in the ratio of 2:1. The magnetic field gradient to create the state-dependent potential is not applied in this experiment and numerical simulation.

Figure 3

Relative c.m. motion between the two-component BECs, $z_2-z_1$, as a function of time after the preparation of two-component BECs. The open circles represent the data calculated from results of Fig. 2; namely, they correspond to the free evolution without magnetic field gradient. The solid circles (cross marks) are measured by changing $T_{\mathrm{grad}}$ with the fixed value of $T_{\mathrm{hold}}=0$ ms ($T_{\mathrm{hold}}=40$ ms), where the magnetic field gradient of 15 mG/cm is applied during $T_{\mathrm{grad}}$. The c.m. positions after TOF differ from those in the trap, and their values might be affected by the in-trap velocity. However, the red points in (b) seem to scale with those of the in-trap positions [inset in (b)] thanks to the short TOF of 15 ms and small magnetic field gradient of 15 mG/cm.

Figure 4

Structural change and c.m. motion induced by the application of a magnetic field gradient, where the distance traveled by SG measurement is compensated. (a) Typical absorption images obtained at $T_{\mathrm{hold}}=0$ ms and $T_{\mathrm{grad}}=10$ ms. (b) Typical absorption images obtained at $T_{\mathrm{hold}}=40$ ms and $T_{\mathrm{grad}}=10$ ms. (c) Center-of-mass positions ($z_1$ and $z_2$) calculated from data of (a) and (b) versus the applied magnetic field gradient. Top and bottom panels represent the experimental and numerical results, respectively. In the experimental data, the magnitude of the effective magnetic field gradient is larger than the horizontal axis in (c) due to the overshoot of the applied magnetic field gradient. See Ref. [27].