Critical quantum metrology with fully-connected models: from Heisenberg to Kibble–Zurek scaling

Abstract

Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum mechanics, in the limit of large probe number and long measurement time. Due to the critical slowing down, the protocol duration time is of utmost relevance in critical quantum metrology. However, how the long-time limit is reached remains in general an open question. So far, only two dichotomic approaches have been considered, based on either static or dynamical properties of critical quantum systems. Here, we provide a comprehensive analysis of the scaling of the quantum Fisher information for different families of protocols that create a continuous connection between static and dynamical approaches. In particular, we consider fully-connected models, a broad class of quantum critical systems of high experimental relevance. Our analysis unveils the existence of universal precision-scaling regimes. These regimes remain valid even for finite-time protocols and finite-size systems. We also frame these results in a general theoretical perspective, by deriving a precision bound for arbitrary time-dependent quadratic Hamiltonians.

Spin squeezing from bilinear spin-spin interactions: Two simple theorems

“…The H 0 ∼ P 2 Hamiltonian evolves the initial vacuum statewhich in the position eigenbasis is a Gaussian wavepacket corresponding to the ground state of a harmonic oscillator -via an indefinite free expansion. The latter leads to squeezing of a quadrature of the field [45], intermediate between P and X = (b 0 + b † 0 )/ √ 2 ≈ J y / √ N S, corresponding to the squeezing of one collective-spin component in the yz plane. This is expected as H 0 is the quadratic approximation to the OAT Hamiltonian.…”

Critical parametric quantum sensing

“…Notice that here we focused on the scaling with respect to the number of photons, which is the most relevant figure for the relevant regime of parameters. However, even if the Gaussian model presents a critical slowing down, the Heisenberg scaling can in principle be achieved also with respect to time 17,19 . We notice also that the divergence rate I ω /N 2 is maximal at ω = Γ.…”

“…A promising approach to quantum sensing exploits quantum fluctuations in the proximity of the criticality to improve the measurement precision. Despite a critical slowing down at the phase transition, theoretical analyses of many-body systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] show that critical quantum sensors can achieve the optimal scaling of precision 18 , both in the number of probes and in the measurement time 8,17 . Furthermore, it has been shown 19 that finite-component phase transitions [20][21][22][23][24] -where the thermodynamic limit is replaced by a scaling of the system parameters [25][26][27][28][29] -can also be applied in sensing protocols.…”

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

“…However, the dynamical approach can achieve a constant factor advantage over static protocols [ 36 ], and it can allow super-Heisenberg scaling in collective light–matter interaction models [ 51 ]. For fully connected models, it has recently been shown that a continuous connection [ 54 ] can be drawn between the static and dynamical approaches, identifying universal time-scaling regimes.…”