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

Karol Gietka, Lewis Ruks, and Thomas Busch

Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan

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We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and 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 using 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, even in the absence of $N$-body coupling terms.

Quantum metrology makes use of non-classical correlations in order to make ultra precise measurements beyond the standard quantum limit. For example, operating state-of-the-art optical lattices at the ultimate Heisenberg limit of precision, one could keep time with an error of hundreds of milliseconds over the entire age of the universe.

Systems exhibiting quantum phase transitions have been the recent subject of intense focus due to their extreme sensitivity in the vicinity of the critical point. However, preparation of the critical ground state must be performed over long time scales in order to avoid excitations, which has so far resulted in sub-optimal scaling of sensitivity with time accounted for as a resource.

In our work, we depart from the traditional notion of metrology near a critical point, instead showing that sensitivity can be enhanced exponentially in a dynamical protocol by quenching past the critical point. We mathematically prove in the paradigmatic setting of cavity QED that a sensitivity exponentially growing in time can be obtained by quenching through a superradiant phase transition. We show that this is associated with a macroscopic occupation of the photonic mode, and that a basic homodyne detection scheme then yields the optimal measurement. Our result offers an exponential speed-up in time over existing protocols acting near the critical point in a general class of superradiant systems, and opens a new avenue for dynamical quantum metrology in critical systems.

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