Description
Ramsey spectroscopy is a cornerstone technique for precision frequency estimation, but its standard analysis assumes a classical noise environment that can be reset before each measurement. We investigate the impact of genuinely quantum noise on sequential Ramsey spectroscopy of a single probe qubit coupled to a bosonic bath through a purely dephasing interaction. Unlike a classical source, a quantum bath cannot be fully reset between measurements: its state retains a nontrivial imprint of the entire measurement history, so the outcomes are no longer independent and identically distributed. Using a cumulant expansion, exact for the zero-mean, Gaussian, stationary noise of the spin–boson model, we derive closed-form expressions for the probability of an arbitrary measurement record over $M$ projective measurements and for the unconditional expectation value of $\sigma_x$ at the $M$-th shot. The latter factorizes into a classical decoherence factor, the standard Ramsey oscillation, and a cumulative product of cosines that encodes the quantum-noise contribution. Governed by the antisymmetric spectrum $S^-(\omega)$, this factor vanishes identically for classical noise and produces a systematic, $M$-dependent suppression of the Ramsey signal that biases standard frequency estimators. A ratio estimator combining complementary $\sigma_x$ and $\sigma_y$ measurements cancels this bias exactly, at the cost of a reduced signal-to-noise ratio, whereas inserting an idle “pillow time” between cycles suppresses only the $M$-dependent inter-cycle memory, leaving a residual single-cycle phase that prevents full recovery of the classical fringe. Our analysis provides an analytical framework for understanding and controlling nonclassical noise in sequential quantum measurements, with implications for quantum sensing, quantum computing, and noise characterisation.
| I am the presenting author | Yes |
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