Control of spin current in a Bose gas by periodic application of $\pi$ pulses

We generate spin currents in an ${}^{87}\mathrm{Rb}$ spin-2 Bose-Einstein condensate by application of a magnetic field gradient. The spin current destroys the spin polarization, leading to a sudden onset of two-body collisions. In addition, the spin coherence, as measured by the fringe contrast using Ramsey interferometry, is reduced drastically but experiences a weak revival due to in-trap oscillations. The spin current can be controlled using periodic $\pi$ pulses (bang-bang control), producing longer spin-coherence times. Our results show that spin coherence can be maintained even in the presence of spin currents, with applications to quantum sensing in noisy environments.

Figure 1

(a) Typical absorption images of condensates obtained using sequences 1 and 2. (b) $T_{\mathrm{hold}}$ dependence of the relative c.m. position of $m_F=\pm 2$ and $\pm 1$ (top) and $m_F$ populations (bottom). The c.m. position of $m_F=0$ at each $T_{\mathrm{hold}}$ is assumed to be $z=0$ and the distance traveled by each component during the measurement is corrected using data at $T_{\mathrm{hold}}\sim 0$. The inset of the top panel shows the applied rf pulse sequence (sequence1). (c) The experimental results obtained using sequence 2. $\tau$ is fixed to 10 ms. The inset above the top panel shows the applied rf pulse sequence (sequence 2). The solid curves in (b) and (c) indicate numerical simulation results from coupled GP equations including MDDI. The dashed curves in the bottom panel of (b) indicate numerical simulations without MDDI. See Ref. [20].

Figure 2

Total atom number vs $T_{\mathrm{hold}}$.

Figure 3

Dynamics of the $m_F$ sublevel populations after application of a single $\pi$ pulse. The inset shows the sequence used for these measurements. The $\pi$ pulse is applied at $t=T_{\mathrm{hold}}/2$. The solid curves indicate numerical simulation results from coupled GP equations.

Figure 4

Larmor precession signal obtained using the Ramsey interferometer. (a) Sequences used to realize the Ramsey interferometer, where $\tau =10$ ms. (b) $S_z$ vs $\varphi$ at $T_{\mathrm{hold}}=0.1$ ms. (c) $S_z$ vs $T_{\mathrm{hold}}$. The solid curves indicate envelopes of numerical simulation results from coupled GP equations.