Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

Abstract

We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage in the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, despite existing works suggesting a requirement of N -body coupling terms.

Exponential precision by reaching a quantum critical point

“…Our results, together with those reported recently by Gietka et al [25], highlight that systems featuring a quantum phase transition are a valuable resource in quantum metrology as they can yield an exponential advantage for parameter estimation.…”

“…[1], showing that it is made possible by the exponential growth of the number of excitations generated by the control strategy. This general understanding also covers the results of a recent work where exponential scaling of the QFI is achieved [25]. Furthermore, in order to characterize the performances of the proposed protocols for practical applications, we analyze the effect of dissipative processes and of finite-size corrections.…”

“…Current solid-state and atomic technology allow for the implementation of these models in a controllable way, where their parameters can be tuned in real time. Intense research efforts [1,[25][26][27][28][29][30] are now dedicated to identifying the optimal control strategies that maximize the estimation precision.…”

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

“…The presented idea may be used as a new tool to study quantum phase transitions [1,44], the quantum Kibble-Zurek mechanism [45][46][47][48][49] both theoretically and experimentally, and the quantum Lieb-Robinson bound for how fast correlations can spread in a quantum system [11]. The results of this work can be also applied in quantum metrology for precise measurements of ω and Ω [50][51][52] as well as for the preparation of squeezed states, simulations of the inflation of the early Universe [53][54][55][56], the Unruh effect [57,58], Hawking radiation [59], quantum chaos [60,61], and potentially to study many other aspects of physics in which the inverted harmonic oscillator has been harnessed as an underlying mechanism (see Ref. [20] for the recent review).…”

Squeezing by Critical Speeding-up: Applications in Quantum Metrology

“…In particular, we have shown that although critical quantum metrology with the Lipkin-Meshkov-Glick model can reach the super-Heisenberg scaling with T (or greater than linear scaling with N ), the absolute sensitivity is lower than the standard quantum limit. The optimal metrological strategies should create the quantum resources quickly, for example, by exploiting quenches into the critical phase to first prepare a suitable initial state and then to imprint the information about the unknown parameter or do it at the same time [31]. As a matter of fact, quenches in the Lipkin-Meshkov-Glick model are a common way of preparing spin-squeezing [32,33] which can be later used in a metrological task [34].…”