# Theoretical Physics

**11 May 2016**

**Time:**15:00 to 16:00

**Location:**EC Stoner 7.83

Theoretical Physics Seminar: Katarzyna Macieszczak (Nottingham)

EC Stoner 7.83, 15:00

Dynamical phase transitions as a resource for enhanced quantum metrology

Abstract: We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. “Heisenberg scaling”). In fact, the QFI is identical to the variance of the dynamical observable that characterises the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. For the systems near a transition, i.e., those displaying metastability, the QFI is quadratic in time for times shorter than the correlation time of the dynamics. A proper definition of metastable phases and their coexistence can be constructed mathematically from the eigenvectors of the master operator governing the system dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both the system and the output. As a particular realisation of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase-shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

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