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arXiv:1301.3242 · Physical Review A

Quantum-limited measurement of magnetic-field gradient with entangled atoms

H. T. Ng

Published Apr 4, 2013• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.043602

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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.
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 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 consider a two-component Bose-Einstein condensate in a double-well potential, where the atoms are magnetically coupled to a single mode of the microwave field inside a superconducting resonator. We find that the system has different dark-state subspaces in the strong- and weak-tunneling regimes. In the limit of weak tunnel coupling, steady-state entanglement between the two spatially separated condensates can be generated by evolving to a mixture of dark states via the dissipation of the photon field. We show that the entanglement can be faithfully indicated by an entanglement witness. Long-lived entangled states are useful for quantum-information processing with atom-chip devices.
Abstract We consider the interaction of a magnetically trapped Bose–Einstein condensate of Rubidium atoms with the stationary microwave radiation field sustained by a coplanar waveguide resonator. This coupling allows for the measurement of the magnetic field of the resonator by means of counting the atoms that fall out of the condensate due to hyperfine transitions to non-trapped states. We determine the quantum efficiency of this detection scheme and show that weak microwave fields at the single-photon level can be sensed.
We discuss how the nature of the relative phase between two entangled condensates differs depending on whether the entanglement is established by measurements or by coupling. In the former case, the limit of the resulting phase resolution scales inversely with the square root of the number of atoms. This limit can be surpassed, however, when the condensates are entangled by coupling and can reach the fundamental Heisenberg limit where the phase resolution scales inversely with the number of atoms involved.
We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles or particles in the two condensates get entangled due to quantum communication between the condensates via the probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables and depends strongly on the relative detuning of the two pumps and the relative atom-field coupling strengths of the two condensates. We present two methods of detecting the generated entanglement.