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arXiv:1904.02646 · Physical Review A

Lattice quantum magnetometry

Luca Razzoli, Luca Ghirardi, Ilaria Siloi, Paolo Bordone, Matteo G. A. Paris

Published Jun 24, 2019• 24 citations
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Abstract

We put forward the idea of lattice quantum magnetometry, i.e., quantum sensing of magnetic fields by a charged (spinless) particle placed on a finite two-dimensional lattice. In particular, we focus on the detection of a locally static transverse magnetic field, either homogeneous or inhomogeneous, by performing ground-state measurements. The system turns out to be of interest as a quantum magnetometer, since it provides non-negligible quantum Fisher information (QFI) in a large range of configurations. Moreover, the QFI shows some relevant peaks, determined by the spectral properties of the Hamiltonian, suggesting that certain values of the magnetic fields may be estimated better than others, depending on the value of other tunable parameters. We also assess the performance of coarse-grained position measurement, showing that it may be employed to realize nearly optimal estimation strategies.

DOI
10.1103/physreva.99.062330

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We put forward the idea of lattice quantum magnetometry, i.e., quantum sensing of magnetic fields by a charged (spinless) particle placed on a finite two-dimensional lattice. In particular, we focus on the detection of a locally static transverse magnetic field, either homogeneous or inhomogeneous, by performing ground-state measurements. The system turns out to be of interest as a quantum magnetometer, since it provides non-negligible quantum Fisher information (QFI) in a large range of configurations. Moreover, the QFI shows some relevant peaks, determined by the spectral properties of the Hamiltonian, suggesting that certain values of the magnetic fields may be estimated better than others, depending on the value of other tunable parameters. We also assess the performance of coarse-grained position measurement, showing that it may be employed to realize nearly optimal estimation strategies.
Quantum magnetometry uses quantum resources to measure magnetic fields with a precision and accuracy that cannot be achieved by its classical counterparts. In this paper, we propose a scheme for quantum magnetometry using discrete-time quantum walk (DTQW) where multipath interference plays a central role. The dynamics of a spin-half particle implementing DTQW on a one-dimensional lattice gets affected by magnetic fields and the controlled dynamics of DTQW help in estimating the fields' strength. To gauge the effects of the field, we study the variance of the particle's position probability distribution (PD) and use it to determine the direction of the magnetic field maximally affecting the quantum walk. We then employ statistical tools like quantum Fisher information (QFI) and Fisher information (FI) of the particle's position and spin measurements to assess the system's sensitivity to the magnetic fields. We find that one can use the position and spin measurements to estimate the strengths of the magnetic fields. Calculations for an electron implementing quantum walk of 50 time steps show that the estimate has a root-mean-square error of the order of 0.1 picoTesla. Moreover, the sensitivity of our system can be tuned to measure any desired magnetic field. Our results indicate that the system can be used as a tool for optimal quantum magnetometry.
Abstract A central qubit coupled to an Ising ring of N qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of N values.
We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, a simultaneous measurement is needed, as the homogeneous field must also be estimated. We prove that for the cases studied in this paper, such a measurement is feasible. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles. We also consider a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions. While in most of the discussion we consider an ensemble of localized particles that are classical with respect to their spatial degree of freedom, we also discuss the case of gradient metrology with a single Bose-Einstein condensate.
We study the performance of quantum sensors composed of four qubits arranged in different geometries for magnetometry and thermometry. The qubits interact via the transverse-field Ising model with both ferromagnetic and antiferromagnetic couplings, maintained in thermal equilibrium with a heat bath under an external magnetic field. Using quantum Fisher information, we evaluate the metrological precision of these sensors. For ferromagnetic couplings, weakly connected graphs (e.g., the chain graph, P_4) perform optimally in estimating weak magnetic fields, whereas highly connected graphs (e.g., the complete graph, K_4) excel at strong fields. Conversely, K_4 achieves the highest sensitivity for temperature estimation in the weak-field regime. In the antiferromagnetic case, we uncover a fundamental trade-off dictated by spectral degeneracy: configurations with non-degenerate energy spectra - such as the pan-like graph (three qubits in a triangle with the fourth attached) - exhibit strong magnetic field sensitivity due to their pronounced response to perturbations. In contrast, symmetric structures like the square graph, featuring degenerate energy levels (particularly ground-state degeneracy), are better suited for precise thermometry. Notably, our four-qubit sensors achieve peak precision in the low-temperature, weak-field regime. Finally, we introduce a spectral sensitivity measure that quantifies energy spectrum deformations under small perturbations, providing a simple heuristic indicator of metrological sensitivity.
We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of NNN particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the offset field determining the level splitting of the particles and results in collective dephasing. In this work, we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states, allowing the estimation of gradients with maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow us to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states, we find simple and feasible measurements saturating the quantum Cram\'er-Rao bound.
This study examines a quantum sensor consisting of two qubits modeled in an XXZ Heisenberg spin chain under a homogeneous magnetic field, for use in quantum thermometry and magnetometry. The sensor is subjected to a common classical environment driven by static noise and is in thermal equilibrium with a heat bath. We analyze the impact of spin–spin, Dzyaloshinskii–Moriya, and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions, as well as the static noise characterized by the disorder parameter, on the sensor's time-evolved state. We also assess the influence of magnetic field homogeneity on performance. Employing quantum Fisher information criteria, we determine the sensor's metrological precision. The performance of the proposed sensor in estimating the external magnetic field and temperature in weak and strong field regimes is different over time with temperature variations. In the strong magnetic field regime, static noise reduces the sensitivity of quantum sensing, while in the weak field regime, this effect is negligible. Our sensor achieves optimal sensitivity and precision for temperature and magnetic field estimation in the presence of static noise and in the weak magnetic field and low temperature regime. Finally, we demonstrate that the quantum sensor achieves a stable sensitivity and precision in its performance over time in quantum magnetometry and thermometry, which can be very valuable in quantum sensing. Moreover, we propose some experimental platforms for the realization of our quantum sensor.