Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage

We propose a single-site addressing implementation based on the subwavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level $\Lambda$ system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the initial ground state. This technique allows for the preparation, manipulation, and detection of atoms with a spatial resolution better than the diffraction limit, which either relaxes the requirements on the optical setup used or extends the achievable spatial resolution to lattice spacings smaller than accessible to date. In comparison to techniques based on coherent population trapping, SLAP gives a higher addressing resolution and has additional advantages such as robustness against parameter variations, coherence of the transfer process, and the absence of photon induced recoil. Additionally, the advantages of our proposal with respect to adiabatic spin-flip techniques are highlighted. Analytic expressions for the achievable addressing resolution and efficiency are derived and compared to numerical simulations for ${}^{87}$Rb atoms in state-of-the-art optical lattices.

Figure 1

(a) Physical system under investigation: the pump and Stokes light pulses, with Rabi frequencies ${\Omega }_P$ and ${\Omega }_S$, propagate in the $-z$ direction and interact with the atoms of a single-occupancy optical lattice located in the ($x,y$) plane. (b) Scheme of the $\Lambda$-type three-level atoms, initially in state $|1\rangle$, that interact with pump and Stokes pulses. Excited level $|2\rangle$ has spontaneous transition rate ${\gamma }_{21}$ (${\gamma }_{23}$) to level $|1\rangle$ ($|3\rangle$) and ${\Delta }_P$ (${\Delta }_S$) is the detuning of the pump (Stokes) field.

Figure 2

(a) Parameter values of $R$ needed to perform SSA as a function of $w_P$, using SLAP (solid line) and CPT (dashed line) techniques. The addressing probability distribution widths are taken as $\Delta x=\lambda /4$ in both cases. (b) ${\left(\Delta x\right)}_{\mathrm{SLAP}}$ (solid line) and ${\left(\Delta x\right)}_{\mathrm{CPT}}$ (dashed line) as a function of $R$. The FWHM of the atomic distribution, ${\left(\Delta x\right)}_{\mathrm{at}}=\lambda /10$ corresponds to the horizontal dotted line and we have taken $w_P={\lambda }_L$. The parameters used in both (a) and (b) are $w_S=32{\lambda }_L=24\lambda$, ${\Omega }_{S0}T=19$, and $A=20$.

Figure 3

Numerical results for the probability of finding the atom located at $x_0$ in state $|1\rangle$ (a), the probability to transfer it from $|1\rangle$ to another state (b), and the efficiency $\eta$ as a function of $R$ (c), for the SSA with SLAP (circles) and CPT (crosses) techniques. Analytical curves for SLAP (solid line) and CPT (dashed lines), computed from Eqs. (12) and (13), are added in (c) for comparison (see text for the rest of the parameters).

Figure 4

(a) Spatial profile of the pump pulse with its node focused at $x=0$. (b) Final population distribution remaining in $|1\rangle$ using SLAP (circles) and CPT (crosses) single-site addressing techniques for $R=10$. The initial atomic distribution in $|1\rangle$, ${\rho }_{\mathrm{lat}}\left(x\right)$, is shown as a solid line (see text for the parameters values).