Higher order spin noise spectroscopy of coherently interacting quan- tum systems
Theoretical Condensed Matter Physics
Final Report Abstract
The results of the project contribute to the theory of quantum measurements. We introduced socalled quantum polyspectra as new very general approach for characterizing and evaluating a broad class of measurements on a quantum level. The discovery of quantum mechanics almost 100 years brought us the insight that the outcome of a quantum measurement can generally not be predicted with certainty. Nature does in principle only allow for calculating the probabilities of certain measurement outcomes. For example, the arrival of photons (particles of light) in a detector leads to peaks in the measurement record at unpredictable times. The intensity of a laser (which is the most stable source of light) is never measurable with certainty. Similarly, a single photon can either be reflected on a semi-transparent mirror or can travers the mirror with a 50% probability each – while classical physics would have predicted an even split of the corresponding lightwave. The theory of quantum measurements deals therefore with the question of what can be learned from noisy measurement records. The description of spin noise spectroscopy poses a challenge for quantum theories of measurement and was therefore the main goal of our project. A small quantum system in a semiconductor is probed via polarization fluctuations of a laser beam that traverses the system. The behavior of the quantum system is thus indirectly probed via its effect on the laser beam. The laser beam itself is also quantum exhibiting so-called shot noise in the time-dependent measurement record z(t) of the randomly detected photons. The key idea of our project was to work with equations that allow for a simulation of the highly stochastic z(t), a quantity that is directly accessible in the experiment. Unlike in other approaches like the full counting statistics, a postprocessing of data (denoising, threshold, etc.) is not necessary. As z(t) is highly random, it is not possible to directly compare experimental and simulated records. The typical behavior of z(t), however, is captured in its multi-time correlations, usual power spectra, or so-called polyspectra. We became the first to provide very general quantum formulas that allow for the theoretical calculations of “quantum polyspectra” from a standard description of quantum systems (the Liouvillian). The estimation of parameters of the measured quantum system is then possible by fitting quantum polyspectra to the polyspectra obtained from experiment. We were able to also describe electron transport experiments from nano-electronics despite the fact that typical measurement records look very different (telegraph noise) from that of spin noise experiments (mostly white noise). The new theory covers also all experiments that can be tuned between those regimes surpassing earlier theories. Many experiments can now be evaluated, e.g., in quantum optics, single photon spectroscopy, or circuit quantum electrodynamics.
Publications
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Higher-order moments, cumulants, and spectra of continuous quantum noise measurements. Physical Review B, 98(20).
Hägele Daniel & Schefczik Fabian
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Ready-to-Use Unbiased Estimators for Multivariate Cumulants Including One That Outperforms x3
Fabian Schefczik & Daniel Hagele
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Erratum: Higher-order moments, cumulants, and spectra of continuous quantum noise measurements [Phys. Rev. B 98, 205143 (2018)]. Physical Review B, 102(11).
Hägele, Daniel; Sifft, Markus & Schefczik, Fabian
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Quantum polyspectra for modeling and evaluating quantum transport measurements: A unifying approach to the strong and weak measurement regime. Physical Review Research, 3(3).
Sifft, M.; Kurzmann, A.; Kerski, J.; Schott, R.; Ludwig, A.; Wieck, A. D.; Lorke, A.; Geller, M. & Hägele, D.
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Random-time quantum measurements. Physical Review A, 107(5).
Sifft, Markus & Hägele, Daniel
