Quantum Sensing near Critical Points of Dissipative Phase Transition

Recently, there is a growing interest in studying quantum sensing near the critical points of phase transitions in unitarily evolving systems. However, in many practical systems, dissipation plays important role and hence it is of great importance to study quantum sensing capabilities near the critical points of dissipative phase transitions. In optical systems Kerr nonlinearities are ubiquitous. The leakage from the cavity serves as the dissipation parameter and is treated via Lindblad master equation. The sensing capabilities of such systems treated in mean field approximation are well known and root down to its bistable behavior. However, such a system in quantum framework has a unique steady state while the bistable states are manifested as metastable states, and the question arises about the sensing capability of the quantum counter part of such systems. The system is described by the Hamiltonian H/hbar = ∆a^†a +Ua^†aa^†a + Ω(a^† + a), a is the annihilation operator of the oscillator mode, ∆ is the detuning between the oscillator frequency and the drive, U is the nonlinearity, Ω is the Rabi frequency. The dissipative phase transition can be strictly defined in the thermodynamic limit, where Ω√U is fixed and U = U₀ε, ε → 0. On the timescale of metastable states, despite the fact that the classical hysteresis loop is smoothened out by quantum fluctuations, the max quantum Fisher information (QFI) for ∆ is around the classical hysteresis boundary and scales as 1/ε whereas the max QFI for U scales as 1/ε³.