Creating versatile atom traps by applying near-resonant laser light in magnetic traps

We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over conventional trapping potentials. One can easily convert the type of the trap, for example, from a single-well to a double-well trap. Atoms in different internal states can be trapped in different trap types, thereby enabling the realization of experiments with multicomponent Bose-Einstein condensates. Moreover, one can achieve variations of the trapping potential on small length scales without the need of microstructures. We present the potential surfaces for different setups, demonstrate their tunability, give a semianalytical expression for the potential, and propose experiments which can be realized within such a trap.

Figure 1

State linkage diagram of the unperturbed atom. The solid arrows denote the transitions allowed for ${\sigma }^{+}$ and ${\sigma }^{-}$ light, whereas the dashed arrows indicate allowed transitions with $\pi$-polarized light. The energy gap between the $5P_{1/2}$, $F=1$ and the $5P_{1/2}$, $F=2$ manifold is ${\Delta }_{\mathrm{hfs}}=2\pi \hslash \times 0.8$ GHz [21].

Figure 2

(a) Setup showing the propagation direction of the laser beams (large arrows) and the configuration of the magnetic trap. The Helmholtz coils generate the homogeneous Ioffe field oriented along the $Z$ direction and the Ioffe bars the quadrupole field in the $X$-$Y$ plane, shown in panel (b).

Figure 3

Potential curves for $Y=0$ (solid line) and for $X=0$ (dashed line). Two components show an attractive potential in two dimensions, whereas one component is exposed to a repulsive potential. The individual potential surfaces are well separated.

Figure 4

Difference of the potential differences for adjacent components for $X=0$ (solid line) and $Y=0$ (dashed line). The deviation between the transition frequencies of adjacent potential surfaces is nonzero and depends on the center-of-mass position of the atom.

Figure 5

Contour plot of the potential surface for the $m_F=0$ component for $\Delta \Phi =0$, $\sigma =10$ $\mu$m, $G=0.1$ G/$\mu$m, and (a) $B_I=10$ G, (b) $B_I=1$ G, (c) $B_I=0.5$ G, and (d) $B_I=0.1$ G. The gray coded values of the potential are given in nK. By modulating the magnitude of the Ioffe field, one can transform the potential smoothly from a single-well to a double-well potential.

Figure 6

Contour plot of the potential surface for the $m_F=0$ component for $G=0.1$ G/$\mu$m, $\sigma =10$ $\mu$m, $B_I=0.1$ G, and for (a) $\Delta \Phi =0$, (b) $\Delta \Phi =\pi /2$, (c) $\Delta \Phi =\pi$, and (d) $\Delta \Phi =3\pi /2$. A phase difference of $\Delta \Phi$ between the Raman lasers leads to rotation of $\Delta \Phi /2$ of the potential surface around the $Z$ axis.

Figure 7

Potential surface for the case of a single ${\sigma }^{-}$-polarized laser for $\sigma =10$ $\mu$m, $G=0.1$ G/$\mu$m, and $B_I=0.1$ G. The potential is ring shaped.

Figure 8

(a) Contour plot of the effective potential for $Y=0$ for fixed $\sigma =10$ $\mu$m as a function of $\xi$. With increasing $\xi$ the barrier gets lower and broader. (b) Same potential for fixed $\xi =1\hspace{0.5em}\mu$m and as a function of $\sigma$. For $\sigma >\xi$, the shape of the barrier close to the origin is almost conserved. However, the position of the minima increases with increasing $\sigma$. In both panels, the dashed line indicates the positions of the minima.

Figure 9

Dependence of the height of the barrier $\Delta V$ on $\xi$ for different $\sigma$. With increasing $\xi$ the height of the barrier decreases monotonically.