Creation and transfer of nonclassical states of motion using Rydberg dressing of atoms in a lattice

We theoretically investigate the manipulation of the motional states of trapped ground-state atoms using Rydberg dressing via nonresonant laser fields. The forces resulting from Rydberg state interaction between dressed neighboring atoms in an array of microtraps or an optical lattice can strongly couple their motion. We show that intensity modulation of the dressing field allows us to squeeze the relative motion of a pair of atoms and generate nonclassical mechanical states. Extending this pairwise scheme to one-dimensional chains provides flexible control over the mechanical degrees of freedom of the whole system. We illustrate our findings with protocols to manipulate all motional degrees of freedom of a pair of atoms and create entangled states. We also present a method to transfer nonclassical correlations along an atomic chain of nontrivial length. The long-lived nature of motional states, together with the high tunability of Rydberg dressing, makes our proposal feasible for current experimental setups.

Figure 1

Sketch of the considered setup. Two atoms are confined in individual, approximately harmonic, traps whose minima are separated by distance $R_0$.

Figure 2

(a) The effective interaction potential and (b) coupling strengths for a pair of dressed atoms (in units of kHz). We assume ${}^{87}\mathrm{Rb}$ atoms in a trap with oscillation frequency ${\omega }_m/2\pi =2\mathrm{kHz}$ and the $n=53$ Rydberg state [25] dressed with a laser of Rabi frequency $\mathrm{\Omega }/2\pi =10\mathrm{MHz}$ and detuning $\mathrm{\Delta }=10\mathrm{\Omega }$.

Figure 3

Variance of the two collective modes of motion of two atoms 1 and 2 after squeezing their relative motion with a pulse of area ${\xi }_P{t}_1$ and coupling one of them to an auxiliary atom with a beam-splitter-like pulse of area ${\xi }_T{t}_2$. The top and lower surfaces give the variance of the center of mass and relative mode, respectively. The variance is normalized to its value in the ground state of the noninteracting system.

Figure 4

Variances of the most squeezed quadratures of the individual atoms, 1 (solid black line) and 2 (dashed light blue line), the relative motion (dotted blue line) and the center-of-mass motion (dot-dashed red line) of atoms 1 and 2 for a two-pulse sequence optimized to squeeze the variance of the center-of-mass motion. Both pulses have equal strength ${\xi }_P$. The initial pulse squeezing the relative motion lasts until the dotted line, ${\xi }_{P}t=0.5$. The second pulse parametrically amplifies the relative motion of atom 2 and the auxiliary. All variances are normalized to their values in the ground state of the unperturbed system.

Figure 5

Violation of the SPH criterion of the motional state of two atoms after applying a tailored sequence of pulses involving a single (solid black line), two (dashed red line), and three (dotted blue line) parametric amplifications in the pulse sequence. The units of $S$ are dimensionless, as defined in Eq. (27).

Figure 6

Violation of the Cauchy-Schwarz inequality during the transfer sequence. The value of $C_{ij}$ (a) after the modulated squeezing pulse, (b) half way during the transfer, and (c) after the completion of the protocol. The quantity $C_{ij}$ is dimensionless, as given in Eq. (24). (d) The excitation number $\langle {\widehat{a}}_j^{†}{\widehat{a}}_j\rangle$ in oscillator $j$ during the transfer. The dashed vertical lines give the times for (a) and (b).