Adiabatic radio-frequency potentials for the coherent manipulation of matter waves

Adiabatic dressed state potentials are created when magnetic substates of trapped atoms are coupled by a radio-frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one to implement numerous configurations, including double wells, Mach-Zehnder, and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips.

Figure 1

(Color online) (a) Experimental realization of the double-well configuration. The quadrupole field is created by a surface-mounted dc four-wire structure. The rf field is generated by a central broad ac wire. Sufficiently close to the surface its rf field can considered to be homogeneous. (b) Depending on the actual rf field strength either a single- or a double-well is established. The potential bottom of the individual curves has been subtracted. (c),(d) Longitudinally modulating the shape of the rf wire results in a $z$-dependent variation of the rf amplitude. This can either be used to achieve a confinement along the longitudinal $\left(z\right)$ axis (c) or a spatially dependent splitting which would result in an interferometer (d). Undesirable variations of the potential bottom can be, for example, compensated by placing a charged wire underneath the chip (red structure).

Figure 2

(Color online) (a) Experimental setup for realizing a ring-shaped potential. The static quadrupole field is generated by a three wire configuration. The two outer wires also carry rf currents which generate two phase shifted and orthogonally polarized oscillating homogeneous fields in the vicinity of the quadrupole center. (b) Depending on the phase shift $\delta$ either a single well, a double-well, or a ring-shaped potential emerge. (c) A 3D confinement is achieved by introducing a spatially dependent rf amplitude of the form $B_{\mathrm{rf}}\left(z\right)=1.3\mathrm{G}+0.05(\mathrm{G}∕{\mathrm{m}}^2)z^2$. Visualization of the $m_F{g}_{F}E=k_B\times 1.1\mathrm{\mu }\mathrm{K}$ isosurface for this case.