Observing Quantum State Diffusion by Heterodyne Detection of Fluorescence

Abstract

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 perform 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 verification 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 field quadratures, 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.

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Plain Language Summary

Light emitted via fluorescence is associated with matter decaying in energy, and this light can be viewed as a probe that carries information about the state of its emitter. When this information is lost, the fragile quantum properties of the emitter are destroyed, a process known as decoherence. Using a superconducting qubit, we demonstrate how the sole measurement of fluorescence makes it possible to accurately track the quantum state in time. The observed evolution is erratic, which is expected based on the random backaction of measurements in quantum mechanics.

We continuously measure the amplitude of the fluorescence field emitted by a superconducting qubit using an amplifier close to the quantum limit; our measurements are obtained at cryogenic temperatures. From each fluorescence record, we can reconstruct a quantum trajectory, which is the succession of states the qubit occupies on a single relaxation event. We collect independent measurements of the qubit state at an arbitrary time during relaxation. These measurements follow the statistics that are expected from the quantum trajectories, thereby verifying the reconstructed quantum states. By repeating the experiment millions of times, we are able to determine the distribution of quantum trajectories. Strikingly, monitoring fluorescence can generate a superposition of states and counterintuitively lead to a temporary increase in the qubit excitation probability.

Our work provides an experimental demonstration of the quantum-state diffusion associated with spontaneous emission that triggered the field of quantum trajectories in the 1990s. We expect that our findings, which enlighten the correspondence between decoherence and measurement by the environment, will contribute to the progress of quantum error correction.