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arXiv:1207.0846 · Europhysics Letters (EPL)

Entangled states of trapped ions allow measuring the magnetic field gradient produced by a single atomic spin

F. Schmidt-Kaler, R. Gerritsma

Published Sep 1, 2012• 14 citations
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Abstract

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.

DOI
10.1209/0295-5075/99/53001

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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 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 a potential scheme to generate entangled photons by manipulating trapped ions embedded in two-mode microcavities assisted by a magnetic field gradient. By means of the spin-spin coupling due to the magnetic field gradient and the Coulomb repulsion between the ions, we show how to efficiently generate entangled photons by detecting the internal states of the trapped ions. We emphasize that our scheme is advantageous to create complete sets of entangled multiphoton states. The requirements and the experimental feasibility of our proposal are discussed in detail.
We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (h) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum computer.
We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 μm above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [J. Phys. B At. Mol. Opt. Phys. 42, 154009 (2009)]. We describe aspects where planar ion traps promise novel physics: spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schrödinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.
Applying a magnetic-field gradient to a trapped ion allows long-wavelength radiation to produce a mechanical force on the ion's motion when internal transitions are driven. We demonstrate such a coupling using a single trapped 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ ion and use it to produce entanglement between the spin and motional state, an essential step toward using such a field gradient to implement multiqubit operations.