Abstract
Quantum polyspectra of up to fourth order are introduced for modeling and evaluating quantum transport measurements offering a powerful alternative to methods of the traditional full counting statistics. Experimental time traces of the occupation dynamics of a single quantum dot are evaluated via simultaneously fitting their second-, third-, and fourth-order spectra. The scheme recovers the same electron tunneling and spin relaxation rates as previously obtained from an analysis of the same data in terms of factorial cumulants of the full counting statistics and waiting-time distributions. Moreover, the evaluation of time traces via quantum polyspectra is demonstrated to be feasible also in the weak measurement regime even when quantum jumps can no longer be identified from time traces and methods related to the full counting statistics cease to be applicable. A numerical study of a double dot system shows strongly changing features in the quantum polyspectra for the transition from the weak measurement regime to the Zeno regime where coherent tunneling dynamics is suppressed. Quantum polyspectra thus constitute a general unifying approach to the strong and weak regime of quantum measurements with possible applications in diverse fields as nanoelectronics, circuit quantum electrodynamics, spin noise spectroscopy, or quantum optics.
Highlights
The evaluation of time traces via quantum polyspectra is demonstrated to be feasible in the weak measurement regime even when quantum jumps can no longer be identified from time traces and methods related to the full counting statistics cease to be applicable
Quantum measurements are at the heart of many fields in physics like quantum electronics, quantum optics, circuit quantum electrodynamics [1], or the quickly developing field of quantum sensing [2]
We presented quantum polyspectra within a stochastic master equation approach as a viable alternative to full counting statistics approaches for evaluating time traces of transport measurements
Summary
Quantum measurements are at the heart of many fields in physics like quantum electronics, quantum optics, circuit quantum electrodynamics [1], or the quickly developing field of quantum sensing [2]. Classical rate equations or the so-called n-resolved master equation have been used to calculate cumulants of the counting statistics [10,11], factorial cumulants [12,13], or secondand third-order spectra of the frequency-resolved counting statistics [14] All these approaches to characterizing quantum transport dynamics assume and require a strong continuous quantum measurement where the quantum system is immediately forced to reveal its state of occupation. [22,31] and discussion after Eq (6)], a direct derivation of multitime moments from the very general SME had been found by three different groups independently only in 2018 [25,32,33] This paved the way for finding compact expressions for second-, third-, and fourth-order cumulants as well as their corresponding quantum polyspectra and developing recipes for an efficient numerical evaluation [25,26].
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