Hybrid atom-photon quantum gate in a superconducting microwave resonator

We propose a hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $>0.99$ are possible on submicrosecond time scales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.

Figure 1

Hybrid quantum gate scheme. (a) An atom trapped above the electric field antinode of a superconducting microwave coplanar waveguide resonator. (b) Level scheme for an atom-photon conditional phase gate. The atom is prepared using hyperfine ground states as the qubit basis. A $\pi$-pulse excitation maps $|1\rangle \to |r\rangle$, which is resonantly coupled to close-lying state $|r^{\prime }\rangle$ via the microwave cavity and undergoes a $2\pi$ rotation conditional upon the presence of a cavity photon. A second $\pi$ pulse from $|r\rangle \to |1\rangle$ with the resulting phase controlled by the microwave photon.

Figure 2

Contour plot of the $|{\Psi }^{+}\rangle$ Bell state preparation fidelity $F$ using the hybrid quantum gate. At high $Q$ the fidelity is limited by spontaneous decay of the Rydberg levels during the conditional rotation time $\tau =\pi /g$. Dashed lines show analytic fidelity estimate.

Figure 3

(a) Zero-point electric field distribution around superconducting CPW cavity with a center trace of 20 $\mu$m and a 10 $\mu$m gap. (b) Field distribution and vacuum coupling strength to the 90$s_{1/2}\to 90p_{3/2}$ transition as a function of height above the surface for both the resonator midpoint and gap center, which falls off rapidly on a length scale comparable to the slot width $w$.

Figure 4

Finite temperature effects due to thermal occupation of the cavity mode. $F_{\gamma }$ represents the fidelity of preparing the cavity in state $(|0\rangle +|1\rangle )/\sqrt{2}$ via resonant interaction with a superconducting qubit which drops rapidly above 40 mK due to the thermal occupation of the cavity. $F_{{\Psi }^{+}}$ is the resulting Bell-state preparation fidelity which follows approximately linearly with $F_{\gamma }$. Inset: zoom in around zero temperature.