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arXiv:1602.05479 · Physical Review Letters

Using Spontaneous Emission of a Qubit as a Resource for Feedback Control

Philippe Campagne-Ibarcq, S. Jézouin, Nathanaël Cottet, Pierre Six, Landry Bretheau, F. Mallet, Alain Sarlette, Pierre Rouchon, Benjamin Huard

Published Aug 1, 2016• 40 citations
arXivHTMLPDF

Abstract

Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.

DOI
10.1103/physrevlett.117.060502

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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.
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.
We implement a permanent quantum feedback procedure. It prepares on-demand and stabilizes photon-number states in a high-quality superconducting microwave cavity. The feedback uses sensitive circular atoms to probe the cavity field in a Quantum Non Demolition way. This information is used by a controller and an actuator to feed small coherent amplitudes into the cavity, leading it deterministically towards the target state with a high fidelity. Quantum jumps of the photon number are detected and their effect is then actively compensated, protecting this fragile quantum resource against decoherence.
Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit WWW state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processing but also to create and stabilize the target WWW state through adaptive quantum feedback control. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than 0.90.90.9 can be achieved and maintained for a considerably long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented.