Coherence and Raman Sideband Cooling of a Single Atom in an Optical Tweezer

We investigate quantum control of a single atom in a tightly focused optical tweezer trap. We show that inevitable spatially varying polarization gives rise to significant internal-state decoherence but that this effect can be mitigated by an appropriately chosen magnetic bias field. This enables Raman sideband cooling of a single atom close to its three-dimensional ground state (vibrational quantum numbers ${\overline{n}}_x={\overline{n}}_y=0.01$, ${\overline{n}}_z=8$) even for a trap beam waist as small as $w=900\mathrm{nm}$. The small atomic wave packet with $\delta x=\delta y=24\mathrm{nm}$ and $\delta z=270\mathrm{nm}$ represents a promising starting point for future hybrid quantum systems where atoms are placed in close proximity to surfaces.

Figure 1

(a) Relevant levels and transitions in ${}^{87}\mathrm{Rb}$. The eigenstates of the harmonic potential for the ground state are indicated with dashed lines. Atomic levels are defined in the $|F,m_F⟩$ basis. See the text for beam orientations and polarizations. (b) The origin of the elliptical polarization near the focus (see the text). In the figure, (C)CW refers to (counter-)clockwise rotation of the polarization vector. (c) A cut through the focal plane for $\alpha =0.43$. The contour lines show ${\tilde{C}}_x$, which is $C_x$ scaled to the local intensity $|E(\overrightarrow{r}){|}^2/|E({\overrightarrow{r}}_{\max }){|}^2$. The background shading shows the Gaussian intensity profile for comparison. (d) Dephasing rate between the states $|1⟩$ and $|2⟩$ as a function of bias field, with ${\lambda }_T=815\mathrm{nm}$. The improvement at large bias fields is due to suppression of the polarization gradient. The fit is to the model described in the text: ${\eta }_0+{\eta }_{\mathrm{circ}}$ are background dephasing rates from the finite detuning and slight elliptical polarization of the incident dipole trap beam; ${\eta }_{\mathrm{pg}}$ arises from the longitudinal polarization near the focus. Inset: Ramsey measurement of the dephasing rate between $|1⟩$ and $|2⟩$ at $B_z=10.5\mathrm{G}$.

Figure 2

(a) Release-and-recapture temperature measurement. The closed and open circles show measurements before and after radial cooling, respectively. A Monte Carlo model yields kinetic energies $K$ such that $2K/k_B=52(4)\mu \mathrm{K}$ before cooling, and $(2K_r/k_B,2K_a/k_B)=[2.4(1),158(14)]\mu \mathrm{K}$ after cooling. (b), (c) Doppler measurement of the axial kinetic energy before and after cooling the axial mode. (b) After radial cooling only, $2K_a/k_B=129(19)\mu \mathrm{K}$. (c) After radial and axial cooling, $2K_a/k_B=8.1(1)\mu \mathrm{K}$.

Figure 3

Sidebands showing final occupations in the (a) radial and (b) axial directions. In (a), the red- and blue-detuned sidebands are fit to independent Lorentzians; their ratio yields a radial temperature ${\overline{n}}_r={0.01}_{-0.01}^{+0.06}$. Inset: Same measurement with a shorter pulse length, so the carrier is also resolved. In (b), nine peaks are fit with independent heights but equal spacings and widths. The heights are well described by a thermal distribution with ${\overline{n}}_a=8.1(1)$.