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arXiv:2503.20003

An entanglement protocol to measure atomic parity violation at sub 0.1% precision

Diana Prado Lopes Aude Craik

Published Mar 25, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3929/ethz-c-000790453

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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.
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.
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.
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.
Summary form only given. The use of entangled states can provide an increased sensitivity in quantum-limited spectroscopic measurements, leading to an uncertainty that is inversely proportional to the number of particles instead of the usual square-law dependence. In this contribution, we show that spectroscopy with maximally entangled states of atoms also offers significant advantages over experiments done with single atoms. As a first example, we demonstrate that entanglement can be used to effectively eliminate first-order Zeeman shifts in spectroscopy with 40Ca+ even though there are no m=0 -> m=0 transitions. Secondly, we discuss how maximally correlated states of two 40Ca+ could be used for measuring tiny frequency shifts of the S1/2 - D5/2 transition arising from second-order Zeeman shifts and electric quadrupole shifts due to the trapping potential.
Quantum error correction requires the detection of errors by reliable measurements of suitable multi-qubit correlation operators. Here, we experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. An additional 'flag' qubit serves to detect errors occurring throughout the parity measurement, which would otherwise proliferate into uncorrectable weight-2 errors on the qubit register. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and phase-flip errors, we show that the fault-tolerant protocol is capable of reliably intercepting such faults. For holistic benchmarking of the parity measurement scheme, we use entanglement witnessing to show that the implemented circuit generates genuine six-qubit multi-partite entanglement. The fault-tolerant parity measurement scheme is an essential building block in a broad class of stabilizer quantum error correction protocols, including topological color codes. Our hardware platform is based on atomic ions stored in a segmented microchip ion trap. The qubit register is dynamically reconfigured via shuttling operations, enabling effective full connectivity without operational cross-talk, which provides key capabilities for scalable fault-tolerant quantum computing.
A scheme for entangling distant atoms is realized, as proposed in the seminal paper by [C. Cabrillo et al., Phys. Rev. A 59, 1025 (1999)]. The protocol is based on quantum interference and detection of a single photon scattered from two effectively one meter distant laser cooled and trapped atomic ions. The detection of a single photon heralds entanglement of two internal states of the trapped ions with high rate and with a fidelity limited mostly by atomic motion. Control of the entangled state phase is demonstrated by changing the path length of the single-photon interferometer.