This work provides a universal characterization of nonclassical, non-Gaussian environmental fluctuations in the frequency domain, based on the Keldysh approach to quantum noise characterization. The authors also present a calculation of frequency-resolved third cumulant, i.e., quantum bispectrum, of a nontrivial quantum bath. They show that the quantum bispectrum reveals that quantum fluctuations can break detailed balance.
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.
The existence of the third cumulant
S3 of voltage fluctuations has demonstrated the non-Gaussian aspect of shot noise in electronic transport. Until now, measurements have been performed at low frequency, \textit{i.e.} in the classical regime
ℏω<eV,kBT where voltage fluctuations arise from charge transfer process. We report here the first measurement of
S3 at high frequency, in the quantum regime
ℏω>eV,kBT. In this regime, experiment cannot be seen as a charge counting statistics problem anymore. It raises central questions of the statistics of quantum noise: 1) the electromagnetic environment of the sample has been proven to strongly influence the measurement, through the possible modulation of the noise of the sample. What happens to this mechanism in the quantum regime? 2) For
ℏω>eV, the noise is due to zero point fluctuations and keeps its equilibrium value:
S2=Gℏω with
G the conductance of the sample. Therefore,
S2 is independent of the bias voltage and no photon is emitted by the conductor. Is it possible, as suggested by some theories, that
S3=0 in this regime? With regard to these questions, we give theoretical and experimental answers to the environmental effects showing that they involve dynamics of the quantum noise. Using these results, we investigate the question of the third cumulant of quantum noise in the a tunnel junction.
We investigate the transitions induced by non-Gaussian external fluctuations on a small quantum system. The rates for the transitions between the energy states are calculated using the real-time Keldysh formalism for the density matrix evolution. We detail the effects of the third cumulant of current fluctuations coupled to a quantum system with a discrete level spectrum and propose a setup for detecting the frequency-dependent third cumulant through the transitions it induces. We especially discuss a scheme where the fluctuations are coupled to a Josephson flux qubit.
Efficient control of quantum devices requires the knowledge of their environmental noise, yet the commonly measured power spectrum does not fully characterize non-Gaussian fluctuations of realistic environments. Here we show that exceptional points (EPs) in the noise-averaged dephasing response can expose observable signatures of non-Gaussian statistics, distinguishing environments with identical lower-order statistics. We also introduce a theoretical model that describes dephasing environments in terms of identical independent noise sources while preserving the power spectrum. Given a calibrated single-source model, the largest EP order extracted from the measured dephasing response determines the number of sources and predicts the higher-order statistics of the combined noise. We illustrate an atomtronic readout that maps distinct EP signatures onto an evolving ensemble-averaged atomic interference pattern. Our results connect non-Hermitian dynamics to environmental noise statistics, providing a route to characterize noise in quantum devices used in computing, metrology, and precision measurement.
We present general quantum mechanical expressions for higher-order moments, cumulants, and spectra of continuously measured quantum systems with applications in spin noise spectroscopy, quantum transport, and measurement theory in general. Starting from the so-called stochastic master equation of continuous measurement theory, we find that the leading orders of the fluctuating detector output
z(t) with respect to the measurement strength $\ensuremath{\beta}$ are a white shot noise background, a constant measurement offset, and the leading order quantum noise of the measured operator
A. Starting from quantum expressions for the multitime moments $\ensuremath{\langle}z({t}_{n})\ensuremath{\cdots}z({t}_{1})\ensuremath{\rangle}$ we derive three- and four-time cumulants that are valid in all orders of $\ensuremath{\beta}$ covering the full regime between the weak- and strong-measurement limit (Zeno limit). Intriguingly, quantum expressions for the cumulants were found that exhibit the same simple structure as those for the moments after introduction of only a slightly modified system propagator. Very compact expressions for the cumulant-based third- and fourth-order spectra (bispectrum and trispectrum) follow naturally. We illustrate the usefulness of higher-order spectra by treating a real-world two-spin system with strong hyperfine interaction. Moreover, spin noise spectroscopy is shown to have the potential for investigating the transition from weak measurements to the famous quantum Zeno regime for realistic probe laser intensities.