Seminar by Filippo Troiani

In the last years, it has become possible to measure single electron spins, both in molecular and solid-state systems.
Electron spins can thus be used as sensitive quantum probes, which enable the read out of nearly isolated quantum systems (e.g., nuclear spins) and the estimate of classical fields with quantum-enhanced precision. Here, we discuss two representative examples of quantum measurements of the spin.

In the first case, we consider the continuous measurement of a single-ion magnet, undergoing a Landau-Zener transition in a spin transistor geometry. In our joint experimental and theoretical investigation [1], we focus on the deviations from a coherent (Landau-Zener) spin dynamics, which, rather counterintuitively, are more pronounced for fast than for slow spin manipulation. Such behavior is successfully simulated by means of an adiabatic master equation, with time averaged dephasing operators. The spin decoherence is tentatively interpreted in terms of the back-action of the continuous measurement, where the time average accounts for the finite time resolution of the measurement.

In the second case, we theoretically investigate metrological protocols for the estimation of a magnetic field [2]. We show that quantum-enhanced precision may be achieved by probing the field with an arbitrary spin at thermal equilibrium. We derive a general expression for the ultimate achievable precision, as given by the quantum Fisher information, and express this quantity in terms of common thermodynamic quantities. We show that the optimal observable simply corresponds to the spin projection along a suitable direction, defined by a universal function of the spin temperature. Finally, we prove the robustness of our scheme against deviations of the measured spin projection from optimality.

References:

[1] Landau-Zener transition in a continuously measured single-molecule
spin transistor, F. Troiani, C. Godfrin, S. Thiele, F. Balestro,
W. Wernsdorfer, S. Klyatskaya, M. Ruben, and M. Affronte,
Phys. Rev. Lett. 118, 257701 (2017).

[2] Universal quantum magnetometry with spin states at equilibrium,
F. Troiani and M. G. A. Paris, Phys. Rev. Lett. (in press).