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arXiv:1304.5919 · Physical Review A

Feedback control of Rabi oscillations in circuit QED

Wei Cui, Franco Nori

Published Dec 10, 2013• 43 citations
arXivHTMLPDF

Abstract

We consider the feedback stabilization of Rabi oscillations in a superconducting qubit which is coupled to a microwave readout cavity. The signal is readout by homodyne detection of the in-phase quadrature amplitude of the weak-measurement output. By multiplying the time-delayed Rabi reference, one can extract the signal, with maximum signal-to-noise ratio, from the noise current. We further track and stabilize the Rabi oscillations by using Lyapunov feedback control to properly adjust the input Rabi drives. Theoretical and simulation results illustrate the effectiveness of the proposed control law.

DOI
10.1103/physreva.88.063823

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We investigate the stabilization of the dynamical state of a superconducting qubit. In a series of papers, A. Korotkov and his co-workers suggested that continuous weak measurement of the state of a qubit and applying an appropriate feedback on the amplitude of a Rabi drive, should maintain the coherence of the Rabi oscillations for arbitrary time. Here, in the aim of addressing a metrological application of these persistent Rabi oscillations, we explore a new variant of such strategies. This variant is based on performing strong measurements in a discrete manner and using the measurement record to correct the phase of the Rabi oscillations. Noting that such persistent Rabi oscillations can be viewed as an amplitude-to-frequency convertor (converting the amplitude of the Rabi microwave drive to a precise frequency), we propose another feedback layer consisting of a simple analog phase locked loop to compensate the low frequency deviations in the amplitude of the Rabi drive.
We propose a scheme of stabilizing the persistent-current Rabi oscillation based on the flux qubit-resonator-atom hybrid structure. The low-QQQ LCLCLC resonator weakly interacts with the flux qubit and maps the persistent-current Rabi oscillation of the flux qubit onto the intraresonator electric field. This oscillating electric field is further coupled to a Rydberg-Rydberg transition of the 87Rb^{87}\mathrm{Rb}87Rb atoms. The Rabi-frequency fluctuation of the flux qubit is deduced from measuring the atomic population via the fluorescence detection and stabilized by feedback controlling the external flux bias. Our numerical simulation indicates that the feedback-control method can efficiently suppress the background fluctuations in the flux qubit, especially in the low-frequency limit. This technique may be extensively applicable to different types of superconducting circuits, paving a way to long-term-coherence superconducting quantum information processing.
Quantum feedback in strongly coupled systems can probe a regime where one quantum of excitation is a large fluctuation. We present theoretical and experimental studies of quantum feedback in an optical cavity QED system. The time evolution of the conditional state, following a photodetection, can be modified by changing the drive of the cavity. For the appropriate feedback, the conditional state can be captured in a new steady state and then released. The feedback protocol requires resonance operation, and proper amplitude and delay for the change in the drive. We demonstrate the successful use of feedback in the suppression of the vacuum Rabi oscillations for the length of the feedback pulse and their subsequent return to steady state. The feedback works only because we have an entangled quantum system, rather than an analogous correlated classical system.
We propose a superconducting circuit-atom hybrid, where the Rabi oscillation of single excess Cooper pair in the island is stabilized via the common atomic clock technique. The noise in the superconducting circuit is mapped onto the voltage source which biases the Cooper-pair box via an inductor and a gate capacitor. The fast fluctuations of the gate charge are significantly suppressed by an inductor–capacitor resonator, leading to a long-relaxation-time Rabi oscillation. More importantly, the residual low-frequency fluctuations are further reduced by using the general feedback-control method, in which the voltage bias is stabilized via continuously measuring the dc-Stark-shift-induced atomic Ramsey signal. The stability and coherence time of the resulting charge-qubit Rabi oscillation are both enhanced. The principal structure of this Cooper-pair-box oscillator is studied in detail.
Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit.