Quantum Thermometry with a Dissipative Quantum Rabi System

Abstract

Dissipative quantum Rabi System, a finite-component system composed of a single two-level atom interacting with an optical cavity field mode, exhibits a quantum phase transition, which can be exploited to greatly enhance the estimation precision of unitary parameters (frequency and coupling strength). Here, using the quantum Langevin equation, standard mean field theory and adiabatic elimination, we investigate the quantum thermometry of a thermal bath surrounding the atom with quantum optical probes. With the increase of coupling strength between the atom and the cavity field, two kinds of singularities can be observed. One type of singularity is the exceptional point (EP) in the anti-parity-time (anti-PT ) symmetrical cavity field. The other type of singularity is the critical point (CP) of phase transition from the normal to superradiant phase. We show that the optimal measurement precision occurs at the CP, instead of the EP. And the direct photon detection represents an excellent proxy for the optimal measurement near the CP. In the case where the thermal bath to be tested is independent of the extra thermal bath interacting with the cavity field, the estimation precision of the temperature always increases with the coupling strength. Oppositely, if the thermal bath to be tested is in equilibrium with the extra bath interacting with the cavity field, noises that suppress the information of the temperature will be introduced when increasing the coupling strength unless it is close to the CP.

The Jaynes-Cummings model and its descendants

“…Such a term does not break the Z 2 parity symmetry of the Dicke model and the criticality survives this modification [829], but the critical coupling is now shifted. At the mean-field level, including photon losses with a rate κ and spontaneous emission of the atoms with a rate Γ, the new critical coupling becomes [895]…”

Critical parametric quantum sensing

“…Furthermore, it has been shown [18] that finitecomponent phase transitions [19][20][21][22][23]-where the thermodynamic limit is replaced by a scaling of the system parameters [24][25][26][27][28]-can also be applied in sensing protocols. Surprisingly, quantum criticalities are versatile sensing resources that do not require the complexity of many-body system, as demonstrated by efficient dynamical protocols [29], the inclusion of quantum-control methods [30] or ancillary probes [31], the design of multiparameter estimation protocols [32] and of a critical quantum-thermometer [33], and by first experimental implementations [34].…”

Exponential precision by reaching a quantum critical point

“…It has also been shown [15,16] that, in spite of the critical slowing down, the framework of critical quantum metrology makes it possible to achieve the Heisenberg scaling, where the QFI grows quadratically in time and number of probes. Recent works [16][17][18][19][20][21][22][23][24] have shown that the framework of critical quantum metrology can be applied to a broad class of quantum optical models. 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.…”