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arXiv:1010.0564 · Physical Review A

Quantum metrology to probe atomic parity nonconservation

P. Mandal, Manas Mukherjee

Published Nov 23, 2010• 12 citations
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Abstract

An entangled state prepared in a decoherence-free subspace, together with a Ramsey-type measurement, can probe parity violation in heavy alkali-metal ions such as Ba${}^{+}$ or Ra${}^{+}$. Here we propose an experiment with Ba${}^{+}$ as an example to measure the small parity-violating effect in this system. It has been shown that a measurement on a maximally correlated system will reduce the uncertainty as compared to that on a single ion measurement, and also provides a feasible solution to measure the nuclear-spin-dependent part of the total parity-violating light shift in an ionic system.

DOI
10.1103/physreva.82.050101

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An entangled state prepared in a decoherence-free subspace, together with a Ramsey-type measurement, can probe parity violation in heavy alkali-metal ions such as Ba+{}^{+}+ or Ra+{}^{+}+. Here we propose an experiment with Ba+{}^{+}+ as an example to measure the small parity-violating effect in this system. It has been shown that a measurement on a maximally correlated system will reduce the uncertainty as compared to that on a single ion measurement, and also provides a feasible solution to measure the nuclear-spin-dependent part of the total parity-violating light shift in an ionic system.
Atomic parity violation (APV) provides a low-energy probe of the weak interaction between electrons and nuclei, complementary to collider tests of the Standard Model. Isotope-chain measurements are especially attractive because they test weak-charge scaling while reducing dependence on absolute atomic-structure theory. We review the APV mechanism, the state of the art in Cs and Yb, and recent trapped-ion, optical-lattice, and molecular proposals. Motivated by progress in coherent control of atoms, ions, and molecules, we ask a metrological question: given N probes distributed over an isotope chain, what quantum strategy optimally measures a deviation from Standard Model weak-charge scaling? The optimum is a particular form of a cross-isotope cat state protocol. We compare this protocol with the standard quantum limit, squeezed-array, same-isotope cat, and discuss extension to recently suggested decoherence-free subspace protocols. We show that entanglement can strongly accelerate statistical averaging, but the ultimate precision is set by APV-specific systematic floors which require careful studies.
Motivated by the challenges and limitation of existing experimental techniques, this work elaborates our recent proposal for the precision measurement of atomic parity nonconservation by quantum metrology with an entangled pair of trapped ions. Although the technique is fundamentally based on an existing proposal, it can potentially reach a figure of merit twice as high for an exceedingly tiny observable, yet to be measured in any ion trap experiment. The systematic of the technique have been shown to be better controlled as compared to other experiments. Since the goal of the experiment is to test the Standard Model of physics, the measured parity violating transitional dipole matrix element has to be compared with the theory of competitive precision. The choice of the element therefore plays an important role for the success of the experiment. Barium and radium ions have been compared from this perspective. The work presents the theoretical study on nuclear spin dependent atomic parity nonconservation and nuclear anapole moment in different isotopes of these ions and proposes specific transitions that are experimentally feasible.
This paper proposes a scheme to measure atomic parity violation (APV) in barium ions at <0.1% precision. The scheme is based on using multi-ion entangled states to common-mode reject parity-conserving systematic shifts and selectively detect a parity-violating vector light shift. This measurement protocol eliminates the need to suppress a leading systematic by 11 orders of magnitude, as is required in the single-ion measurement scheme [N. Fortson, Phys. Rev. Lett. 70, 2383 (1993)]. Furthermore, the protocol can be combined with the use of integrated photonic waveguides in an architecture that is scalable to large ion numbers, with a proportional increase in measurement precision.
Experiments with two entangled trapped 9Be+ ions are discussed. In one type of experiments we used entanglement to increase the precision of rotation angle measurements. For “spin-squeezed" and maximally entangled states we observed a reduction in uncertainty of rotation angle below the standard quantum limit. In a second experiment we demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace of two ions, we protect it from environment-induced dephasing. We increased the storage time by up to an order of magnitude compared to an unprotected qubit.
We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods that have been demonstrated experimentally.