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Heisenberg-limited measurement of magnetic-field gradient with multipartite entangled states

H. T. Ng, Kihwan Kim

Published Sep 16, 2013• 0 citations
OpenAlex

Abstract

We propose a method to detect the magnetic-field gradient using an atomic spin chain. We consider to use W-states, which are a specific class of multipartite entangled states, for precision measurement. The magnetic-field gradient can be determined by measuring the coherence of the state. We find that the Heisenberg-limited measurement can be obtained even using imperfect W-states and in the presence of various types of noises, respectively. We discuss the implementations of the schemes with trapped ions and ultracold atoms in optical lattices. Our proposal can be realized by using an order of several tens of trapped ions with current technology. This robust method may be useful to the applications of magnetic resonance imaging.

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We propose a method to detect the magnetic-field gradient using an atomic spin chain. We consider to use W-states, which are a specific class of multipartite entangled states, for precision measurement. The magnetic-field gradient can be determined by measuring the coherence of the state. We find that the Heisenberg-limited measurement can be obtained even using imperfect W-states and in the presence of various types of noises, respectively. We discuss the implementations of the schemes with trapped ions and ultracold atoms in optical lattices. Our proposal can be realized by using an order of several tens of trapped ions with current technology. This robust method may be useful to the applications of magnetic resonance imaging.
We propose detecting the magnetic field gradient produced by the magnetic dipole moment of a single atom by using ions in an entangled state trapped a few μ m from the dipole. This requires measuring magnetic field gradients of order 10 −13 tesla/ μ m. We discuss applications in determining magnetic moments of a wide variety of ion species, for investigating the magnetic substructure of ions with level structures that are not suitable for laser cooling and detection, and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measuring spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques that are well established in ion trap quantum information processing, it is within reach of current technology.
We propose a method to detect the amplitude gradient of a microwave field by using a pair of entangled two-component Bose-Einstein condensates. We consider the two spatially separated condensates to be coupled to the two different magnetic fields. The magnetic-field gradient can be determined by measuring the variances of population differences and relative phases between the two-component condensates in two wells. The precision of measurement can reach the Heisenberg limit. We study the effects of one-body and two-body atom losses on the detection. We find that the entangled atoms can outperform the uncorrelated atoms in probing the magnetic fields in the presence of atom losses. The effect of atom-atom interactions is also discussed.
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
The generation and verification of large-scale entanglement are essential to the development of quantum technologies. In this paper, we present an efficient scheme to generate genuine multipartite entanglement of a large number of qubits by using the Heisenberg interaction. This method can be conveniently implemented in various physical platforms, including superconducting, trapped-ion, and cold-atom systems. In order to characterize the entanglement of the output quantum state, we generalize the stabilizer formalism and develop an entanglement witness method. In particular, we design a generic searching algorithm to optimize entanglement witness with a minimal number of measurement settings under a given noise level. From the perspective of practical applications, we numerically study the trade-off between the experiment efficiency and the detection robustness.
One of the most appealing quantum communication protocols is quantum teleportation, which involves sharing entanglement between the sender and receiver of the quantum state. We address the two-qubit quantum teleportation based on the Heisenberg XYZ chain with a magnetic-field gradient affected by intrinsic decoherence. An atomic spin chain is primarily coupled to the linear gradient of the magnetic field in the x-direction, with the assumption that the magnetic field varies linearly with the position of the atom. By using the concepts of fidelity and average fidelity in the presence of the magnetic field gradient and under the effect of intrinsic decoherence in the current model, and considering the variables of the system, an improved quantum teleportation can be achieved. In addition, using the concept of remote quantum estimation, we examine remote quantum sensing in this article, which is very useful in quantum communication.
We show that far-field diffraction images of spontaneously scattered Raman photons can be used for detection of spin entanglement and for metrology of field gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in the spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. The gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precession, which suggests a possibility for precision measurements beyond the standard quantum limit without entanglement. Monitoring of the temporal decay of the diffraction peak can also realize a nondemolition probe of the temperature and collisional interactions in trapped cold atomic gases. The approach can be readily generalized to cold molecules, trapped ions, and solid-state spin ensembles.