Having accurate tools to describe nonclassical, non-Gaussian environmental fluctuations is crucial for designing effective quantum control protocols and understanding the physics of underlying quantum dissipative environments. We show how the Keldysh approach to quantum noise characterization can be usefully employed to characterize frequency-dependent noise, focusing on the quantum bispectrum (i.e., frequency-resolved third cumulant). Using the paradigmatic example of photon shot noise fluctuations in a driven bosonic mode, we show that the quantum bispectrum can be a powerful tool for revealing distinctive nonclassical noise properties, including an effective breaking of detailed balance by quantum fluctuations. The Keldysh-ordered quantum bispectrum can be directly accessed using existing noise spectroscopy protocols.
Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).
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