Integrable quantum many-body sensors for AC field sensing

Abstract

Quantum sensing is inevitably an elegant example of supremacy of quantum technologies over their classical counterparts. One of the desired endeavor of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing.

Free-Fermionic Topological Quantum Sensors

“…From a fundamental point of view, our analysis indicates that gap closing, rather than long range correlation and spontaneous symmetry-breaking, is essential for obtaining quantum enhanced precision. This observation is consistent with recent discovery of quantum enhanced sensitivity at Floquet gap closing [7,29]…”

“…In such symmetry breaking transitions, the ground state reveals long-range correlations which lead to the scaling of F ∼ V 2/Dν , where V is the system size (volume), D is the dimension, and ν is the critical exponent with which the correlation length diverges near the criticality [3]. Recently, quantum enhanced sensing has also been observed in integrable Floquet systems [7,29] along the line that the Floquet gap vanishes. An important open question is what feature of a phase transition, e.g.…”

Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling

“…Note also the formal similarity of this expression with Eq. (18). Our expression includes explicitly the time-dependence of the number of probes, and the ordinary eigenstates of the Hamiltonian has been replaced by the eigenstates of the matrix M x , which are closely related to the notion of symplectic eigenvalues for Gaussian states [65,78].…”

“…In this context, the aim of critical quantum metrology is to exploit quantum fluctuations in proximity of a quantum phase transition (QPT) [5] to achieve quantum advantage in sensing protocols. In the last few years, a series of theoretical studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have shown that quantum critical sensors can in principle achieve the optimal limits of precision allowed by quantum mechanics [21]. For example, under standard assumptions, considering a system of N spins undergoing a QPT in the thermodynamic limit (N → ∞), the squared error in estimating physical parameters can scale as 1/(T 2 N 2 ), where T is the protocol duration time.…”

“…Critical quantum metrology protocols can be categorized in two main approaches, which we will label as static and dynamical. A) The static approach [6][7][8][9][10][11][12][13][14][15][16][17][18]22] exploits the susceptibility of equilibrium properties of critical systems. In a Hamiltonian settings, the static approach consists an adiabatic sweep that brings the system in close proximity of the critical point, to then measure an observable on the system ground state.…”