Cloaking a qubit in a cavity

Abstract

Cavity quantum electrodynamics (QED) uses a cavity to engineer the mode structure of the vacuum electromagnetic field such as to enhance the interaction between light and matter. Exploiting these ideas in solid-state systems has lead to circuit QED which has emerged as a valuable tool to explore the rich physics of quantum optics and as a platform for quantum computation. Here we introduce a simple approach to further engineer the light-matter interaction in a driven cavity by controllably decoupling a qubit from the cavity's photon population, effectively cloaking the qubit from the cavity. This is realized by driving the qubit with an external tone tailored to destructively interfere with the cavity field, leaving the qubit to interact with a cavity which appears to be in the vacuum state. Our experiment demonstrates how qubit cloaking can be exploited to cancel the ac-Stark shift and measurement-induced dephasing, and to accelerate qubit readout. In addition to qubit readout, applications of this method include qubit logical operations and the preparation of non-classical cavity states in circuit QED and other cavity-based setups.

Fig. 1. Concept and device.

a Schematic illustration of a qubit (green) coupled to a driven cavity represented by two mirrors (blue). A drive ${\mathcal{E}}_1$ on the cavity displaces the cavity field, which effectively acts as a classical drive on the qubit. This results in qubit ac-Stark shift and measurement-induced dephasing (i.e. level broadening), see the full white lines. b A second drive ${\mathcal{E}}_2$ of appropriate time-dependent amplitude, frequency, and phase cloaks the qubit from the effective classical field resulting from ${\mathcal{E}}_1$ interferometrically canceling the ac-Stark shift and broadening. c Optical image of the device which includes a transmon qubit (green), a readout cavity (dark blue), and a Purcell filter (gray).

Fig. 2. Vacuum Rabi oscillations in a filled cavity.

a Red and black solid lines correspond to damped vacuum Rabi oscillations of the resonant cavity and qubit, respectively, in the absence of any drive. The qubit–cavity Jaynes–Cummings coupling rate $g^{\prime }$ is set to 100/7 of the cavity decay rate κ. With a cavity drive ϵ₁ = 46κ/7 and the cancellation turned on, the cavity field (dashed orange) oscillates on top of ∣α_t∣² (dashed-dotted gray), swapping a single quantum of excitation back and forth with the qubit (dashed light blue). b Computed Wigner distributions of the cavity field at 3/2 and 1 Rabi periods with the drives on, as indicated by the symbols in (a). At 1 Rabi period, the cavity is in a coherent state, while it is in a displaced Fock state at 3/2 Rabi periods.

Fig. 3. Cancellation of the ac-Stark shift and measurement-induced dephasing.

a Numerical simulation of a two-level qubit spectral density without cancellation (top) and with cancellation (bottom) for various drive amplitudes ε₁/2π from 10 to 60 MHz. The simulation parameters are ω_q/2π = 5.7 GHz, ω_r,1/2π = 7.6 GHz, $g^{\prime }/2\pi =200$ MHz, and κ/2π = 50 MHz. b Dots: Experimentally measured increased dephasing rate δΓ (top) and qubit frequency shift δω (bottom) as a function of drive power extracted from Ramsey interferometry without cancellation (blue) and with cancellation (red). Error bars are statistical. Solid lines: Numerical simulations of the measurement-induced dephasing and ac-Stark shift. The simulation which accounts exactly for the $\cos {\widehat{\phi }}_{\mathrm{tr}}$ potential of the Josephson junction is performed using the bare parameters ω_r/2π = 7.66 GHz, E_J/h = 16.83 GHz, E_C/h = 199.7 MHz, g/2π = 140.6 MHz, and κ/2π = 10.1 MHz resulting in dressed parameters that match the experimentally measured ones. The cavity drive frequency is ω₁/2π = 7.6648 GHz.

Fig. 4. Arm and release qubit readout.

a Full-cosine numerical simulation of the phase-space trajectories of the cavity field in standard dispersive readout, i.e., square pulse, (dashed line) and the arm and release readout approach (full lines) with an arm-step coherent state α = 2.8i. The path of the arming step is here chosen to reproduce the experiment of panel b, but it can be tailored at will. The colored dots indicate different times in the evolution. In both readout approaches, the qubit is prepared in the ground state and a π pulse is applied (red lines) or not (blue lines) before the readout step. Simulation parameters are the same as in Fig. 3b. b Experimental qubit measurement error obtained from the overlap between the distributions of the accumulated heterodyne signal over 10⁶ repetitions of the experiment. Full line: arm-and-release approach. Dashed line: standard dispersive measurement. c Arm-and-release pulse sequence used to obtain panels a and b. The arm phase (t < 0) is absent in the case of dispersive readout.

Fig. 5. Gate error.

Measured error (dots) on qubit X gate (randomized benchmarking) as a function of the steady-state cavity photon number ${\overline{n}}_{\mathrm{s}}$ when the qubit is cloaked (red) or not (blue). The control drive on the qubit is optimized in the absence of cavity drive and cancellation tone to maximize the gate fidelity and kept identical for all further measurements. The corresponding measured average X gate error and its error bar at zero cavity drive amplitude are represented as a horizontal gray line and gray area. The dashed red line is the average gate error under cloaking obtained from numerical simulations including the Purcell filter (see Supplementary Note 1). Error bars account for statistical uncertainty.