Diverging current fluctuations in critical Kerr resonators

Abstract

The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behaviour which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient-which characterises the long-time current fluctuations-directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

“…Indeed, under standard assumptions, critical protocols can achieve the Heisenberg scaling—a quadratic growth of parameter-estimation precision—both with respect to the number of probes and with respect to the measurement time. Furthermore, a recent theoretical work [ 15 ] demonstrated that the optimal limits of precision can be achieved using finite-component phase transitions [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ], which are criticalities that take place in quantum optical systems where the thermodynamic limit is replaced by a scaling of the system parameters [ 20 , 29 , 30 , 31 , 32 , 33 , 34 ]. Critical quantum sensors can then also be implemented with controllable small-scale quantum devices, without requiring the control of complex many-body systems.…”