Protocol for high-fidelity readout in the photon-blockade regime of circuit QED

E. Ginossar, Lev S. Bishop, D. I. Schuster, and S. M. Girvin

Phys. Rev. A 82, 022335 – Published 31 August 2010

Abstract

The driven-damped Jaynes-Cummings model in the regime of strong coupling is found to exhibit a coexistence between the quantum photon blockaded state and a quasicoherent bright state. We characterize the slow time scales and the basin of attraction of these metastable states using full quantum simulations. This form of bistability can be useful for implementing a qubit readout scheme that does not require additional circuit elements. We propose a coherent control sequence that makes use of a simple linear chirp of drive amplitude and frequency as well as qubit frequency. By optimizing the parameters of the system and the control pulse, we demonstrate theoretically very high readout fidelities ( $>$ $98 %$ ) and high contrast with experimentally realistic parameters for qubits implemented in the circuit QED architecture.

Received 28 April 2010

DOI:https://doi.org/10.1103/PhysRevA.82.022335

Authors & Affiliations

E. Ginossar, Lev S. Bishop, D. I. Schuster, and S. M. Girvin

Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA

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Vol. 82, Iss. 2 — August 2010

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Images

Figure 1
A schematic of the dim state (left histogram) in the quantum part of the JC ( $+$ ) manifold and the QCS in the semiclassical part (right histogram). Application of a readout pulse sequence dynamically maps the initial qubit state into one of the states with high fidelity. The inset shows the lifetimes of several QCSs with increasing drive strength and mean photon number, while for these parameters the dim state is photon blockaded (the coexistence regime), and the qubit decay ( $T_{1}$ ) has a distinct influence on the lifetime ( $τ_{b}$ ) of the QCS.Reuse & Permissions
Figure 2
Readout control pulse. (a) Time trace of the drive amplitude. A fast and selective initial chirp (10 ns) can selectively steer the initial state, while the qubit is detuned from the cavity [ $(ω_{q} - ω_{c}) / 2 π \approx 2 g$ ]. It is followed by a slow displacement to increase contrast and lifetime of the latching state, while the qubit is resonant with the cavity ( $κ / 2 π = 2.5 MHz$ ). The drive amplitude ramp is limited so that the photon blockade is not broken, but the contrast is enhanced by additional driving at the highest drive amplitude. (b) A diagram of transition frequencies shows how the drive frequency chirps through the JC ladder frequencies of the ( $+$ ) manifold and how the manifold changes due to the time-dependent qubit frequency. (c) Wave-packet snapshots at selected times [indicated by bullet points on panel (b)] of the chirping drive frequency of panel (b) conditioned on the initial state of the qubit.Reuse & Permissions
Figure 3
Cumulative probability distributions for the number of photons ( $N$ ) emitted from the cavity during the driving time $t_{f}$ for different qubit decay times ( $T_{1}$ ), including a very long $T_{1} = 15$ $μ$ s, indicating that $T_{1}$ is not limiting the readout fidelity. For low detection thresholds ( $N_{th} \approx 20$ ) for distinguishing $| ↑ 〉 (N > N_{th})$ from $| ↓ 〉 (N < N_{th})$ , the fidelity can be very high ( $>$ $98 %$ ) for realistic values of qubit decay in cQED (a few microseconds) and of high contrast for more moderate fidelities ( $>$ $90 %$ ). The distributions also show almost no false positives for higher thresholds $N_{th} > 20$ (here $t_{h} = 194$ ns and other parameters as for Fig. 2).Reuse & Permissions
Figure 4
Probability for the QCS to decay after being initialized as a coherent-state wave packet $| α e^{i θ} 〉$ and driven for a time $κ^{- 1}$ . The equal probability contours trace out two basins of attraction: States initialized inside the low-decay probability contour ( $P_{d} < 1 %$ ) end up long lived ( $τ_{b} ≫ κ^{- 1}$ ), whereas states initialized left of $P_{d} = 90 %$ quickly decay to the ground state and remain photon blockaded. The parameters are $g / 2 π = 100 MHz$ , $κ / 2 π = 4.05 MHz$ , $ξ / 2 π = 9.9 MHz$ , $(ω_{d} - ω_{c}) / 2 π = 12.3 MHz$ , $(ω_{c} - ω_{q}) / 2 π = 9.7 MHz$ , $T_{1} = 1591$ ns ( $ω_{d}$ is the drive frequency).Reuse & Permissions

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