ABSTRACT Precision measurement has been a driving force in physics, from the uncertainty principle to modern quantum sensing, enabling the exploration of phenomena across microscopic and cosmic scales. We demonstrate significant sensitivity enhancement in a two‐mode continuous‐variable bosonic system by leveraging a first‐order superradiant phase transition (SPT) induced by parametric nonlinearity. The SPT causes the divergence of quantum fluctuations, enhancing the sensitivity. We characterize the sensitivity through a dimensionless quantum Fisher information. Compared to a continuous‐variable system without SPT, the sensitivity near the critical point exhibits an enhancement of three orders of magnitude. The universal theory represents a truly macroscopic quantum detection approach that can be demonstrated in general quantum systems and applied to a variety of nonlinear models.
ABSTRACT Precision measurement has been a driving force in physics, from the uncertainty principle to modern quantum sensing, enabling the exploration of phenomena across microscopic and cosmic scales. We demonstrate significant sensitivity enhancement in a two‐mode continuous‐variable bosonic system by leveraging a first‐order superradiant phase transition (SPT) induced by parametric nonlinearity. The SPT causes the divergence of quantum fluctuations, enhancing the sensitivity. We characterize the sensitivity through a dimensionless quantum Fisher information. Compared to a continuous‐variable system without SPT, the sensitivity near the critical point exhibits an enhancement of three orders of magnitude. The universal theory represents a truly macroscopic quantum detection approach that can be demonstrated in general quantum systems and applied to a variety of nonlinear models.
Abstract Critical phenomena of quantum systems are useful for enhancement of quantum sensing. However, experimental realizations of criticality enhancement are confined to very few systems, owing to the stringent requirements, including the thermodynamical or scaling limit, and fine control of interacting quantum subsystems or particles. Here, a simple critical quantum sensing scheme is proposed that requires neither of these conditions. The critical system is realized with a single parametrically‐driven bosonic mode involving many non‐interacting bosons. The quantum Fisher information is calculated, which confirms the criticality‐enabled enhancement. The response of one of the quadratures to the variation of the control parameter is further detailed. The numerical results reveal that its inverted variance exhibits a diverging behavior at the critical point. Based on the presently available control techniques of parametric driving, it is expected that scheme can be realized in different systems, e.g., ion traps and superconducting circuits.
Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter-estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a superconducting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens up perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a phase transition.
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\ensuremath{\Delta}x\ensuremath{\Delta}p$ diverges at the quantum critical point as N1/6. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two-level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamics.
We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.
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.
Interacting many-body systems display enhanced sensitivity close to critical transition points due to diverging quantum fluctuations. This criticality-based enhancement has been suggested as a potential resource for applications in precision metrology. Here we demonstrate many-body critical enhanced metrology for the sensing of external microwave electric fields in a non-equilibrium Rydberg atomic gas. We show that small variations in external driving lead to a large variation in the population of Rydberg states around criticality and to a notable change in the optical transmission signal. For continuous optical transmission at the critical point, we quantify the enhanced sensitivity extracting the Fisher information, which shows a three orders of magnitude increase due to many-body effects compared with single-particle systems. These results demonstrate that critical properties of many-body systems are promising resources for sensing and metrology applications. Interacting quantum systems near criticality have been proposed as potential probes for quantum metrology. An experiment with Rydberg atoms now proves the enhanced sensitivity of critical many-body systems to small variations in external parameters.