Strong Magnetic Coupling of an Ultracold Gas to a Superconducting Waveguide Cavity

Placing an ensemble of ${10}^6$ ultracold atoms in the near field of a superconducting coplanar waveguide resonator with a quality factor $Q\sim {10}^6$, one can achieve strong coupling between a single microwave photon in the coplanar waveguide resonator and a collective hyperfine qubit state in the ensemble with $g_{\mathrm{eff}}/2\pi \sim 40\mathrm{kHz}$ larger than the cavity linewidth of $\kappa /2\pi \sim 7\mathrm{kHz}$. Integrated on an atomchip, such a system constitutes a hybrid quantum device, which also can be used to interconnect solid-state and atomic qubits, study and control atomic motion via the microwave field, observe microwave superradiance, build an integrated micromaser, or even cool the resonator field via the atoms.

Figure 1

(a) Schematic of the CPWR including a solid-state qubit and a cloud of ultracold atoms trapped above one of the gaps. (b) The magnetic field strength of a single photon as a function of lateral distance $1\mu \mathrm{m}$ from the chip surface and (c) as a function of distance to the chip surface at the gap (full line) and at the central conductor (dashed line). (d) Vector plot of the magnetic field in the resonator.

Figure 2

Response of the atom-cavity system as illustrated by its complex impedance $Z$: (a) The real part of $Z$ is related to the spectrum, and (b) the phase of $Z$ directly illustrates the phase shift of the transmitted microwave radiation. The calculations are for $Q={10}^6$, $N={10}^6$, and $N={10}^5$ and plotted vs incident field detuning from the resonance frequency.