Optical control of the internal and external angular momentum of a Bose-Einstein condensate

We present experimental results on the coherent transfer of orbital angular momentum (OAM) from optical fields to the center-of-mass motion of a Bose-Einstein condensate (BEC), using an approach which results in negligible linear momentum change. Two collinear optical beams of differing OAM are used to couple discrete sublevels of the atomic ground state via a stimulated Raman process. We demonstrate several of the possible optical field configurations which place the BEC into various spinor and vortex states. We also show how this approach can be used to create coherent superpositions of these states and use the interference patterns of such superpositions to confirm the presence of quantized vortices.

Figure 1

Energy and momentum representation of the two-photon interaction used in the experiment. The atomic states shown are part of the ${}^{87}\mathrm{Rb}$ $D1$ hyperfine structure. Atoms in the BEC, initially in the $\mid F=2,m_F=2⟩$ state, are coupled into the $\mid F=2,m_F=0⟩$ state by the application of the indicated laser fields ${\Omega }_1$, ${\Omega }_2$.

Figure 2

Schematic of the experiment geometry showing the orientation of the optical pulses with respect to the BEC, magnetic field, and gravity. The boxed insets show axial views of one possible choice of optical beam modes and the resulting coreless vortex state of the BEC [e.g., Fig. 3d].

Figure 3

Axial images of the BEC after spin-state separation. (a) No optical fields applied. (b) Coherent transfer ∣2⟩ → ∣0⟩ with Gaussian (G) beam modes. (c) ∣2⟩ → ∣0⟩ with Stokes (pump) beams in ${\mathrm{LG}}_0^{-1}$ $\left({\mathrm{LG}}_0^{-1}\right)$ modes, respectively. For (d) and (e) the beams are detuned $-500\mathrm{MHz}$ from $\mid 1^{\prime }⟩$. (d) ∣2⟩ → ∣0⟩ using Stokes (pump) modes G $\left({\mathrm{LG}}_0^{-1}\right)$. (e) Sequential coupling: ∣2⟩ → ∣0⟩ using G $\left({\mathrm{LG}}_0^{-1}\right)$ modes, then $\mid 0⟩\to \mid -2⟩$ using G $\left({\mathrm{LG}}_0^1\right)$. The direction of gravity and the B-field gradient is indicated. In the absence of the field gradient, the spin components physically overlap. The field of view of each image is $0.5\times 2\mathrm{mm}$.

Figure 4

Coherent superposition of $l=1$ and $l=-1$ vortex states with resulting interference pattern. (a) and (b) Two successive transfers of part of the BEC to the ∣0⟩, $l=1$ vortex state [using G $\left({\mathrm{LG}}_0^{-1}\right)$ Stokes (pump) beam modes]. (c) and (d) Transfer to the ∣0⟩, $l=1$ vortex state, followed by transfer to the ∣0⟩, $l=-1$ state [G $\left({\mathrm{LG}}_0^{-1}\right)$ modes, then G $\left({\mathrm{LG}}_0^1\right)$]. The graph is a circular lineout from (d), with a ${\sin }^2(\varphi -{\varphi }_0)$ fit to the data. The field of view in (b) and (d) is $280\times 280\mu \mathrm{m}$.