Reversible state transfer between superconducting qubits and atomic ensembles

We examine the possibility of coherent reversible information transfer between solid-state superconducting qubits and ensembles of ultracold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near resonantly with the atoms via their optically excited Rydberg states. The solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical readout of quantum information.

Figure 1

(Color online) (a) CPW cavity with strip-line length $L$ and electrode distance $w$. SC qubits are placed at the antinodes of the standing-wave field and ensembles of UC atoms are trapped near the CPW surface. (b) SC qubit (left) and ensemble qubit (right) can couple to a common mode of the CPW cavity.

Figure 2

(Color online) (a) Atomic Rydberg states $|i⟩$ and $|r⟩$ and relevant couplings for the excitation transfer from the CPW cavity to the atomic storage state $|s⟩$. (b) Propagation geometry of the corresponding optical fields and the beam stop and metallic mirrors on top of the SC electrodes of the CPW cavity.

Figure 3

(Color online) Numerical simulations of the three-step excitation transfer from the SC qubit to the UC atomic ensemble. Top panel illustrates the sequence of $\left(\pi -\right)$ pulses: first the SQ qubit is brought to resonance with the CPW cavity, by pulsing ${\Delta }_{qc}\left(t\right)=0$ for time ${\tau }_{qc}$; next, the ${\Omega }_{gi}\left(t\right)$ field is pulsed for time ${\tau }_{gr}$; and finally, the ${\Omega }_{rs}\left(t\right)$ field is pulsed for time ${\tau }_{rs}$. Central and lower panels show the dynamics of occupation numbers for the qubit exited state $⟨{\widehat{\sigma }}^{+}{\widehat{\sigma }}^{-}⟩$, the cavity field $⟨{\widehat{n}}_c⟩\equiv ⟨{\widehat{c}}^{†}\widehat{c}⟩$ and the collective atomic states $⟨{\widehat{n}}_r⟩\equiv ⟨{\widehat{r}}^{†}\widehat{r}⟩$, and $⟨{\widehat{n}}_s⟩\equiv ⟨{\widehat{s}}^{†}\widehat{s}⟩$. Initially, the mean thermal photon number is $⟨{\widehat{n}}_c\left(0\right)⟩=0$ in the central panel and $⟨{\widehat{n}}_c\left(0\right)⟩=0.5$ in the lower panel.

Figure 4

(Color online) Conditional $F_{\psi }$ and mean $\overline{F}$ transfer fidelities vs temperature $k_{\text{B}}T$ (lower horizontal axis) or mean thermal photon number $⟨{\widehat{n}}_c⟩$ (upper horizontal axis). In $F_{\psi }$, $\psi =0,1,\pm$ correspond to states $|0⟩$, $|1⟩$, and $\frac{1}{\sqrt{2}}\left[|0⟩\pm \left(i\right)|1⟩\right]$.