We investigate quantum-enhanced metrology in a triple point criticality and discover that quantum criticality does not always enhance measurement precision. We have developed suitable adiabatic evolution protocols to effectively restrain excitations, which could accelerate the adiabatic evolutions and lead to an exponential super-Heisenberg scaling. This scaling behavior is quite valuable in practical parameter estimating experiments with limited coherence time. Dissipation can strengthen the super-Heisenberg scaling until decoherence increases to dominate in the dissipative dynamics. Additionally, measurement precisions beyond Heisenberg scaling can be experimentally achieved in the trapped ion system. Our findings strongly indicate that criticality-enhanced metrology can indeed significantly enhance measurement precisions to a super-Heisenberg scaling when combining a triple point and beneficial parameter modulations, which will be conducive to the exploration of other super-Heisenberg scaling and their applications.
We investigate quantum-enhanced metrology in a triple point criticality and discover that quantum criticality does not always enhance measurement precision. We have developed suitable adiabatic evolution protocols to effectively restrain excitations, which could accelerate the adiabatic evolutions and lead to an exponential super-Heisenberg scaling. This scaling behavior is quite valuable in practical parameter estimating experiments with limited coherence time. Dissipation can strengthen the super-Heisenberg scaling until decoherence increases to dominate in the dissipative dynamics. Additionally, measurement precisions beyond Heisenberg scaling can be experimentally achieved in the trapped ion system. Our findings strongly indicate that criticality-enhanced metrology can indeed significantly enhance measurement precisions to a super-Heisenberg scaling when combining a triple point and beneficial parameter modulations, which will be conducive to the exploration of other super-Heisenberg scaling and their applications.
Super-Heisenberg scaling, which scales as N − β with β > 1 in terms of the number of particles N or T − β in terms of the evolution time T , is better than Heisenberg scaling in quantum metrology. It has been proven that super-Heisenberg scaling can be achieved when the Hamiltonian of the system involves many-body interactions or time-dependent terms. We demonstrate that nonlinear quantum scrambling facilitates the achievement of super-Heisenberg scaling T − β when the generator of the parameter is time-independent. More importantly, in dissipative systems, we can still obtain super-Heisenberg scaling. In the optical cavity system, an exponential improvement in measurement precision over time can be achieved by combining injected external squeezing and intracavity squeezing. Our work provides an optimal method for leveraging nonlinear resources to enhance the measurement precision of the driving field.
Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.
Quantum metrology refers to the use of quantum resources in parameter-estimation protocols, aiming at enhancing its precision. The quantum Fisher information is a key quantity in this context, setting the ultimate achievable precision with respect to available resources, such as the total time of the protocol. In this work, we report a scheme where the quantum Fisher information features an exponential scaling with the protocol duration. This is achieved by performing a periodic modulation of the coupling of a quantum critical system close to the its critical value. This modulation leads to an exponential growth of the excitation number in time. Relying on the precision bound derived by Garbe et al. [L. Garbe et al., Quantum Sci. Technol. 7, 035010 (2022)], we show that the quantum Fisher information inherits this exponential time scaling, which is corroborated by numerical simulations. Finally, the impact of dissipation and finite-size effects are analyzed, showing that the exponential time scaling is robust to dissipation, although its exponent decreases for larger values of the dissipation rate. Therefore, our work illustrates the novel metrological opportunities that quantum critical systems can offer.
Abstract The Heisenberg limit is acknowledged as the ultimate precision limit for parameter estimation in quantum metrology. Recent studies have demonstrated super-Heisenberg-scaling limits, where the root mean square errors of estimation decrease faster-than-linearly with the number of probes or evolution processes. This casts doubt on what the ultimate precision limit of quantum metrology really is and, in particular, whether there is a deeper connection with Heisenberg's uncertainty principle. By linking the dynamics of the metrological process with properties in parameter space, we construct a Heisenberg's uncertainty relation between the unknown parameter and its canonical momentum. We propose a novel quantum metrological scheme that utilizes a generating process with indefinite time direction to increase the canonical momentum nonlinearly. This approach achieves a nonlinear-scaling precision limit that improves quadratically with the increase in evolution time length or the number of processes, in accordance with Heisenberg's uncertainty relation. Then we experimentally demonstrate in quantum optical systems that this nonlinear-scaling enhancement can be achieved with a fixed amount of energy in the probes. Consequently, our results provide a deeper insight into the Heisenberg limit in quantum metrology, and shed new light on improving the precision of practical metrological and sensing tasks in realistic quantum systems.
Abstract Critical quantum metrology, which exploits quantum critical systems as probes to estimate a physical parameter, has gained increasing attention recently. However, the critical quantum metrology with a continuous quantum phase transition (QPT) is experimentally challenging since a continuous QPT only occurs at the thermodynamic limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with a first-order QPT. By introducing a small transverse magnetic field, we can not only encode an unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. Moreover, we experimentally implement the critical quantum metrology scheme using nuclear magnetic resonance techniques and show that at the critical point the precision achieves the Heisenberg scaling as 1/ T . As a theoretical proposal and experimental implementation of the adiabatic scheme of critical quantum metrology and its advantages of easy implementation, inherent robustness against decays and tunable energy gap, our adiabatic scheme is promising for exploring potential applications of critical quantum metrology on various physical systems.
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.