Cavity Quantum Electrodynamics with Separate Photon Storage and Qubit Readout Modes

We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband-based measurement of photon coherence, generation of $n$ photon Fock states and the scaling of the sideband Rabi frequency with $\sqrt{n}$ using a scheme that may be extended to realize sideband-based two-qubit logic gates.

Figure 1

(a) Crossed optical Fabry-Perot cavities with two atoms for experiments with two different photon lifetimes. (b) Circuit diagram of center coupled transmission line resonator with qubits ($A$, $B$) at each end. The resonator is driven through port 1, transmission is measured at port 2. Qubits can be directly driven through ports 3 and 4. Resonator end ports 5 and 6 were included only in a test device without qubits. Also depicted are the field amplitude of the first three resonator modes at frequencies $f_{0,1,2}$. (c) Optical image (colorized) of the device, with two transmon qubits. Grounding bond wires are shown schematically at position $X$.

Figure 2

Normalized transmission spectrum for a four-port center and end-coupled resonator (device I). Transmission between the end ports $S_{65}$ (blue, closed circles) and the center ports $S_{21}$ (green, open circles) at the fundamental (a), 1st (b) and 2nd harmonic (c) are shown.

Figure 3

Rabi oscillations on the blue sideband with the low $Q$ 1st harmonic (green, open circles), and with the high $Q$ 2nd harmonic (blue, closed circles). Master equation simulations with the photon lifetime and sideband drive rate as fit parameters are shown as solid lines.

Figure 4

(a) Measurement of the lifetime of a single photon in the high $Q$ mode, $T_1^{\kappa 2}=1.45\mu \mathrm{s}$. Inset: Pulse scheme for the experiment with sideband pulses shaded in blue. (b) Results of a Ramsey experiment to measure the photon dephasing time $T_2^{*\kappa 2}=1.9\mu \mathrm{s}$. The pulse sequence is shown in the inset of (a) and described further in the text. Master equation simulations are shown as solid lines.

Figure 5

(a) Pulse sequence for generation of Fock states in the high $Q$ mode, and driving of sideband Rabi oscillations $|g,n-1⟩⟷|e,n⟩$. (b) Measurements for the sequence depicted in (a), for $n=1$, 2, 3, 4, 5 (blue points). Fits to a cosine with an exponential decay envelope are shown as solid lines, while master equation simulations are shown as dashed lines. (c) Plot of ${\Omega }_n^2/{\Omega }_1^2$ vs $n$ (blue points), where ${\Omega }_n$ is the Rabi frequency extracted from the fits shown in (b). Expected dependence ${\Omega }_n^2/{\Omega }_1^2=n$ is shown as a black line.