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arXiv:2408.12243 · Physical Review Letters

Critical Quantum Metrology beyond Adiabaticity in Collectively Pumped Superradiance

Anonymous, Ephraim Shahmoon

Published Jul 14, 2026• 0 citations
arXivHTMLPDF

Abstract

Critical metrology relies on the high sensitivity of systems to parameter changes near a phase transition to extract information with high precision. Such methods usually require working under adiabatic conditions, which implies long preparation times due to critical slowing down. Here instead we demonstrate how favorable sensitivity can be maintained for preparation rates exceeding the adiabatic limit by exploiting knowledge of the nonequilibrium dynamics of the system. Our work focuses on a model of collective dissipation (superradiance) balanced by collective pumping, analyzing the sensitivity around a first order dissipative phase transition. We devise a sensing protocol based on characterizing the hysteresis formed beyond adiabatic conditions, finding the sensing uncertainty r^{α}/N, exhibiting a favorable Heisenberg-like scaling with the particle number N and only a weak power-law dependence α≈0.17 on the preparation rate r. We discuss the implementation of the model and potential applications to metrology within cavity QED setups.

DOI
10.1103/rp9s-tgp7

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Critical metrology relies on the high sensitivity of systems to parameter changes near a phase transition to extract information with high precision. Such methods usually require working under adiabatic conditions, which implies long preparation times due to critical slowing down. Here instead we demonstrate how favorable sensitivity can be maintained for preparation rates exceeding the adiabatic limit by exploiting knowledge of the nonequilibrium dynamics of the system. Our work focuses on a model of collective dissipation (superradiance) balanced by collective pumping, analyzing the sensitivity around a first order dissipative phase transition. We devise a sensing protocol based on characterizing the hysteresis formed beyond adiabatic conditions, finding the sensing uncertainty r^{α}/N, exhibiting a favorable Heisenberg-like scaling with the particle number N and only a weak power-law dependence α≈0.17 on the preparation rate r. We discuss the implementation of the model and potential applications to metrology within cavity QED setups.
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.
Abstract We investigate the non-equilibrium dynamics and quantum metrological potential of an ensemble of four-level atoms interacting with a dissipative optical cavity. By deriving an effective master equation for the atomic degrees of freedom, we identify first-order dissipative phase transitions driven by the competition between coherent driving and collective decay. Focusing on a specific parametric trajectory, we employ Liouvillian spectral projections in the thermodynamic limit to rigorously delineate the basins of attraction corresponding to the multistable phases. Furthermore, the mean-field superradiance potential reveals that the dissipative phase transition manifests as a saddle-node bifurcation where a metastable trapping potential vanishes. In the vicinity of the critical point, the system exhibits critical slowing down, leading to a vanishing Liouvillian spectral gap. Utilizing the matrix product state formalism, we demonstrate that due to this dissipative phase transition, the system possesses the potential to achieve Heisenberg-limited precision in continuous sensing. Our results confirm that the driven four-level superradiant model serves as a robust platform for exploiting critical dynamics to enhance metrological performance.
Physical systems close to a quantum phase transition exhibit a divergent susceptibility, suggesting that an arbitrarily high precision may be achieved by exploiting quantum critical systems as probes to estimate a physical parameter. However, such an improvement in sensitivity is counterbalanced by the closing of the energy gap, which implies a critical slowing down and an inevitable growth of the protocol duration. Here, we design different metrological protocols that exploit the superradiant phase transition of the quantum Rabi model, a finite-component system composed of a single two-level atom interacting with a single bosonic mode. We show that, in spite of the critical slowing down, critical quantum optical probes can achieve a quantum-enhanced time scaling of the sensitivity in frequency-estimation protocols.
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 relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cram\'er-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 NNN in the cavity, even in the absence of NNN-body coupling terms.
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 Cramer-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 NNN in the cavity, despite existing works suggesting a requirement of NNN-body coupling terms.
The critical quantum metrology, which exploits the quantum phase transition for high precision measurement, has gained increasing attention recently. The critical quantum metrology with the continuous quantum phase transition, however, is experimentally very challenging since the continuous quantum phase transition only exists at the thermal dynamical limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with the first order quantum phase transition. By employing the Landau-Zener anticrossing, we can not only encode the unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. We experimentally implement the adiabatic scheme on the nuclear magnetic resonance and show that the achieved precision attains the Heisenberg scaling. The advantages of the scheme-easy implementation, robust against the decay, tunable energy gap-are critical for practical applications of quantum metrology.