Critical Quantum Metrology with a Finite-Component Quantum Phase Transition

Abstract

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 make use of 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 systems can lead to a quantum-enhanced time-scaling of the quantum Fisher information, and so of the measurement sensitivity.In a system close to a critical point, small variations of physical parameters may lead to dramatic changes in the equilibrium state properties. The possibility of exploiting this sensitivity for metrological purposes is well known, and it has already been applied in classical devices, e.g. in superconducting transition-edge sensor [1]. Besides, the development of quantum metrology has extensively shown that quantum states can outperform their classical counterparts for sensing tasks [2]. Therefore, a question naturally arises: what sensitivity can be achieved using interacting systems close to a quantum-critical point? In the last few years, this question has attracted growing interest and it has been addressed by different methods [3][4][5][6][7][8][9]. These studies may be roughly divided in two classes.The first approach, which we will call the "dynamical" paradigm [5,7], focus on the time evolution induced by a Hamiltonian close to a critical point. In this approach, one prepares a probe system in a suitably chosen state, lets it evolve according to the critical Hamiltonian, and finally measures it. This bear close similarity to the standard interferometric paradigm of quantum metrology [2]. On the other hand, the "static" approach [3, 6] is based on the equilibrium properties of the system. It consists in preparing and measuring the system ground state in the unitary case, or the system steady-state when open quantum systems are considered. In proximity of the phase transition the susceptibility of the equilibrium state diverges, and so it does the achievable measurement precision. Unfortunately, the time required to prepare the equilibrium state diverges as well, both in the unitary [10] and in the driven-dissipative case [11,12], a behavior called critical slowing down. Only very re-cently, it has been demonstrated that for a large class of spin models these two approaches are formally equivalent [9], and that they both make it possible to achieve the optimal scaling limit of precision with respect to system size and to measurement time. These results were obtained considering spin systems that undergo quantum phase transitions in the thermodynamic limit, where the numb...

Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

“…As a result the definition (5) is still valid for the case of first-order phase transition [31]. In addition, as discussed in [7,32], the QFI and the Bures metric correspondence is not broken provided that the rank of the GS density matrix is not changed at the critical region [33]. This also works for our case that the quantum state of the system remains pure with rank 1 in zero temperature and of rank 2 in the finite temperature case [7,32].…”

“…where the variance of the signalŜ is given by ∆ 2Ŝ = Ŝ 2 − Ŝ 2 . Not always the signal saturates the upper bound of sensitivity (7). Nevertheless, it has the advantage of being easier to be measured in a realistic experiments.…”

“…To date, the role of quantum criticality for parameter estimation has been investigated in the Lipkin-Meshkov-Glick [5], Dicke [6,7], bosonic Josephson junction [8] and many other quantum models [9]. While the majority of these works are devoted to examining the criticality around the second-order phase transitions, only a few works concern first-order ones [10][11][12].…”

Interplay of quantum phase transition and flat band in hybrid lattices

“…5. (a)-(c) Plots of the normal phase boundary E l nor (k, λ) = 0 (lower solid curves) and superradiant phase boundary E l sup (k, λ) = 0 (upper dash-dotted curves) for ζ (1) = 0.10ω, ζ (2) = 0.18ω, ζ (3) = 0.22ω, respectively. They intersect at the middle straight lines λ = λ (i) sc , where λ (i) sc = (ω A − 4ζ (i)2 /ω B )/2 (i = 1, 2, 3) are the critical points of QPT occurring in a single cell.…”

“…The quantum phase transition (QPT), driven by quantum fluctuations in many-body systems, is one of the most fundamental and significant concepts in physics since it can offer the important resources for quantum metrology [1][2][3] and quantum sensing [4][5][6]. For example, the generation of manybody entanglement through QPT enables precision metrology to reach the Heisenberg limit [7,8].…”