Manipulation of ultracold atoms in dressed adiabatic radio-frequency potentials

We explore properties of atoms whose magnetic hyperfine sublevels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this class of potentials and demonstrate their potential use to build atom optical elements such as double wells, interferometers, and ringtraps. Moreover, we perform simulations of interference experiments carried out in rf induced double-well potentials. We discuss how the nature of the atom-field coupling mechanism gives rise to a decrease of the interference contrast.

Figure 1

(Color online) Propagation of a wave packet from a single well into a double well for $G=20\mathrm{T}∕\mathrm{m}$, $B_I=0.75\mathrm{G}$, $g_F=-\frac{1}{2}$, $m_F=-1$, and $\delta =\pi$. $B_{\mathrm{RF}}$ is linearly ramped from zero to $0.515\mathrm{G}$ within $7.6\mathrm{ms}$. The radio frequency is $\omega =2\pi \times 500\mathrm{kHz}$. Shown is the probability density ${\mid \Psi (x,y)\mid }^2$.

Figure 2

(Color online) Propagation of a wave packet from a single well into a ring potential for $G=20\mathrm{T}∕\mathrm{m}$, $B_I=0.75\mathrm{G}$, $g_F=-\frac{1}{2}$, and $m_F=-1$. $B_{\mathrm{RF}}$ is linearly ramped from zero to $0.446\mathrm{G}$ within $7.6\mathrm{ms}$. The radio frequency is $\omega =2\pi \times 500\mathrm{kHz}$. Shown is the probability density ${\mid \Psi (x,y)\mid }^2$.

Figure 3

(Color online) (a) Real and imaginary parts of the wave function components which occupy the spinor orbitals $\mid m_s⟩$. The state shown is the final state of the propagation presented in Fig. 1. For each plot the same color map was used. (b) Cut along $x=y$ through the interference pattern after a time-of-flight experiment. The interference contrast is significantly smaller than 100%. This is essentially a consequence of the different spin states of the two interfering clouds.

Figure 4

(Color online) (a) 2D plot of the double well potential (31) for $\delta =0$. In order to study the dependence of the interference contrast on the splitting distance $2x_0$ we consider only the 1D motion along the indicated axis. (b) Sketch of the spin orientation in an rf double-well potential along the axis being shown in part (a). The spin orientation is assumed to follow adiabatically the local direction of the effective magnetic field. Hence the interference contrast of two interfering clouds depends in general on the relative orientation of the two spin vectors.

Figure 5

(Color online) (a) Contrast pattern along the axis connecting the two potential minima of the double well (see Fig. 4). The same parameters as in Fig. 1 have been used. The snapshot is taken at $\omega t=0$. The position of the potential minimum is indicated by the vertical line. The interference contrast decreases as ${\rho }_0$ increases. For $\rho \to \infty$ the contrast goes to zero as both wave packets occupy orthogonal spin states. (b) Time dependence of the interference if both wave packets are released from the double-well minima. One can clearly recognize the dependence of the interference pattern on the rf phase.