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arXiv:1311.5605 · Physical Review Letters

Observing Interferences between Past and Future Quantum States in Resonance Fluorescence

Philippe Campagne-Ibarcq, Landry Bretheau, Emmanuel Flurin, Alexia Auffèves, F. Mallet, Benjamin Huard

Published May 5, 2014• 92 citations
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Abstract

The fluorescence of a resonantly driven superconducting qubit is measured in the time domain, providing a weak probe of the qubit dynamics. Prior preparation and final, single-shot measurement of the qubit allows us to average fluorescence records conditionally on past and future knowledge. The resulting interferences reveal purely quantum features characteristic of weak values. We demonstrate conditional averages that go beyond classical boundaries and probe directly the jump operator associated with relaxation. The experimental results are remarkably captured by a recent theory, which generalizes quantum mechanics to open quantum systems whose past and future are known.

DOI
10.1103/physrevlett.112.180402

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The fluorescence of a resonantly driven superconducting qubit is measured in the time domain, providing a weak probe of the qubit dynamics. Prior preparation and final, single-shot measurement of the qubit allows us to average fluorescence records conditionally on past and future knowledge. The resulting interferences reveal purely quantum features characteristic of weak values. We demonstrate conditional averages that go beyond classical boundaries and probe directly the jump operator associated with relaxation. The experimental results are remarkably captured by a recent theory, which generalizes quantum mechanics to open quantum systems whose past and future are known.
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In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix (t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix (t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix (t) with only diagonal elements in a given basis |n> may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal (t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.
When the main source of qubit relaxation comes from its coupling to a photonic channel, each relaxation event is associated with the release of a photon. The corresponding discrete quantum jumps of the qubit state can be observed by counting the number of photons emitted by fluorescence. This discreteness of the quantum jumps is in fact related to the nature of the light detector. What does the evolution of the qubit state become if fluorescence is measured using a heterodyne detector instead? In this talk, an experiment will be discussed, in which the records of heterodyne measurements of fluorescence is used to reconstruct the quantum trajectories of a qubit during relaxation. Using a large number of experiments, it is shown that these trajectories can be used to better predict the probability to find given measurement outcomes during the evolution. This heterodyne measurement of the fluorescence is a quantum demolition continuous measurement, which is very different from the more common dispersive measurement sensitive to qubit occupation. These trajectories are thus expected to exhibit some exotic properties, particularly when using past and future knowledge. Besides, using measurement based feedback based on the fluorescence signal alone, it is possible to stabilize any chosen qubit state. This work thus demonstrates that relaxation into an efficiently monitored channel is not a limit for quantum information protocols but can instead be a resource.
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.
A qubit can relax by fluorescence, which prompts the release of a photon into its electromagnetic environment.By counting the emitted photons, discrete quantum jumps of the qubit state can be observed.The succession of states occupied by the qubit in a single experiment, its quantum trajectory, depends in fact on the kind of detector.How are the quantum trajectories modified if one measures continuously the amplitude of the fluorescence field instead?Using a superconducting parametric amplifier, we have performed heterodyne detection of the fluorescence of a superconducting qubit.For each realization of the measurement record, we can reconstruct a different quantum trajectory for the qubit.The observed evolution obeys quantum state diffusion, which is characteristic of quantum measurements subject to zero point fluctuations.Independent projective measurements of the qubit at various times provide a quantitative validation of the reconstructed trajectories.By exploring the statistics of quantum trajectories, we demonstrate that the qubit states span a deterministic surface in the Bloch sphere at each time in the evolution.Additionally, we show that when monitoring fluorescence, coherent superpositions are generated during the decay from excited to ground state.Counterintuitively, measuring light emitted during relaxation can give rise to trajectories with increased excitation probability.