Magnetic field sensing subject to correlated noise with a ring spin chain

Li-Sha Guo,Bin Shao,Bao-Ming Xu,Jian Zou

doi:10.1038/srep33254

Li-Sha Guo, Bin Shao + Show 2 more

Open Access

https://doi.org/10.1038/srep33254

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Abstract

In this paper, we focus on the magnetic field sensing subject to a correlated noise. We use a ring spin chain with only the nearest neighbor interactions as our probe to estimate both the intensity B and the direction θ of the magnetic field when the probe reaches its steady state. We numerically calculate the quantum Fisher information (QFI) to characterize the estimation precision. On the one hand, for estimating B, we find that the coupling between spins in the probe plays an important role in the precision, and the largest value of the QFI can be achieved when θ = π/2 together with an optimal coupling. Moreover, for any direction, the precision scaling can be better than the Heisenberg-limit (HL) with a proper coupling. On the other hand, for estimating θ, we find that our probe can perform a high precision detection for θ ~ π/2, with the QFI much larger than that for any other directions, especially when the coupling is tuned to the optimal value. And we find that the precision scaling for θ ~ π/2 can be better than the HL, but for other directions, the precision scaling is only limited to the standard quantum limit (SQL). Due to the computational complexity we restrict the number of spins in the probe to 60.

Highlights

Any real quantum system is inevitably affected by its surrounding environment which impairs the metrological capabilities, reducing the quadratic improvement drastically. It has been shown in the seminal work on noisy quantum metrology that for the uncorrelated Markovian dephasing noise the product and maximally entangled states become asymptotically equivalent, and even the optimal partially entangled states with a highly symmetry can only improve the quantum enhancement to a constant factor, and bound the precision scaling to the standard quantum limit SQL1
We use a ring spin chain consisting of N spins, with only the nearest neighbor interactions, as our probe to estimate the intensity B and the direction θ of an external magnetic field when the probe reaches its steady state
We use a ring spin chain consisting of N spins, with only the nearest neighbor interactions, as our probe to estimate an unknown magnetic field in the presence of correlated dissipative Markovian noise

Summary

Introduction

Quantum metrology is a fundamental and important subject in physics, which uses entanglement to increase the precision of parameter estimation by quantum measurements beyond the limit of its classical counterpart, with its widely applications in quantum frequency standards[1,2], optical phase estimation[3,4,5,6,7,8,9], atomic clocks[10,11,12,13,14], atomic interferometers[15], and magnetic field sensing[16,17]. Any real quantum system is inevitably affected by its surrounding environment which impairs the metrological capabilities, reducing the quadratic improvement drastically It has been shown in the seminal work on noisy quantum metrology that for the uncorrelated Markovian dephasing noise the product and maximally entangled states become asymptotically equivalent, and even the optimal partially entangled states with a highly symmetry can only improve the quantum enhancement to a constant factor, and bound the precision scaling to the standard quantum limit SQL1. Has investigated the QFI of a steady state of two qubits in the presence of a local dephasing noise with a reset machanism, and has shown that by choosing a proper coupling strength, the QFI scaling can be larger than the SQL at a certain value of the reset and decoherence parameters. When θ ~ π/2, the scaling can be better than the HL, but when θ is not equal or not close to π/2, the scaling is just constrained near the SQL, no matter what the value of coupling is

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