[Paper Review] Strongly enhanced effects of Lorentz symmetry violation in entangled Yb+ ions

V. A. Dzuba, V. V. Flambaum+5 more|arXiv (Cornell University)|Jul 22, 2015

Quantum Mechanics and Applications17 references3 citations

TL;DR

This paper proposes using entangled Ytterbium-1+ (Yb+) ions to achieve unprecedented sensitivity in testing Lorentz symmetry violation (LSV) in the electron-photon sector. By exploiting the long-lived metastable $^{2}\text{F}_{7/2}$ state and high theoretical and experimental control in Yb+ ions, the study predicts a sensitivity of $1.5 \times 10^{-23}$ for $c_{JK}$ parameters—over 100,000 times more sensitive than current limits—enabling the first probe of minimally suppressed LSV at low energies.

ABSTRACT

Lorentz symmetry is one of the cornerstones of modern physics. However, a number of theories aiming at unifying gravity with the other fundamental interactions including string field theory suggest violation of Lorentz symmetry [1-4]. While the energy scale of such strongly Lorentz symmetry-violating physics is much higher than that currently attainable by particle accelerators, Lorentz violation may nevertheless be detectable via precision measurements at low energies [2]. Here, we carry out a systematic theoretical investigation of the sensitivity of a wide range of atomic systems to violation of local Lorentz invariance (LLI). Aim of these studies is to identify which atom shows the biggest promise to detect violation of Lorentz symmetry. We identify the Yb+ ion as an ideal system with high sensitivity as well as excellent experimental controllability. By applying quantum information inspired technology to Yb+, we expect tests of LLI violating physics in the electron-photon sector to reach levels of $10^{-23}$, five orders of magnitude more sensitive than the current best bounds [5-7]. Most importantly, the projected sensitivity of $10^{-23}$ for the Yb+ ion tests will allow for the first time to probe whether Lorentz violation is minimally suppressed at low energies for photons and electrons.

Motivation & Objective

• To identify atomic systems with maximal sensitivity to Lorentz symmetry violation (LSV) in the electron-photon sector.
• To evaluate the feasibility of using Yb+ ions for high-precision LSV tests using quantum control techniques.
• To project the ultimate sensitivity of LSV measurements in Yb+ ions and compare it with current experimental bounds.
• To establish general selection rules for atomic systems that maximize LSV sensitivity based on electronic structure and matrix element enhancement.

Proposed method

• Theoretical analysis of the Standard Model Extension (SME) Lagrangian, focusing on the $c_{\mu\nu}$ tensor term that describes LSV in the electron-photon sector.
• Calculation of reduced matrix elements for the $T^{(2)}$ operator, which couples to the LSV interaction, using relativistic many-body methods.
• Identification of the $4f^{13}6s^2 \, ^2\text{F}_{7/2}$ metastable state in Yb+ as optimal due to deep electron localization and long lifetime (~10 years).
• Estimation of systematic effects, including differential black-body radiation (BBR) shifts, which are projected to limit sensitivity at ~$6 \times 10^{-24}$.
• Use of quantum information-inspired techniques to coherently manipulate and measure Zeeman sublevels in Yb+ ions to detect LSV-induced energy shifts.
• Comparison of LSV sensitivity across multiple ions (Yb+, Tm+, Th3+) to identify the most favorable candidate based on matrix element magnitude and experimental feasibility.

Experimental results

Research questions

• RQ1 What atomic system exhibits the highest theoretical sensitivity to Lorentz symmetry violation in the electron-photon sector?
• RQ2 How does electron localization in $4f$-hole configurations enhance the matrix elements responsible for LSV detection?
• RQ3 Can the $^{2}\text{F}_{7/2}$ metastable state in Yb+ ions enable LSV tests at sensitivities below $10^{-23}$?
• RQ4 What are the dominant systematic effects limiting the sensitivity of such experiments, and can they be mitigated?
• RQ5 Is it possible to probe whether Lorentz violation is minimally suppressed at low energies for electrons and photons?

Key findings

• The $4f^{13}6s^2 \, ^2\text{F}_{7/2}$ metastable state in Yb+ ions exhibits an exceptionally long lifetime of approximately 10 years, enabling high-precision measurements.
• The reduced matrix elements for the $T^{(2)}$ operator in Yb+ are enhanced due to deep localization of the $4f$ hole electrons, with $\langle r \rangle \lesssim 0.8$ a.u. being a key indicator of high sensitivity.
• The projected sensitivity for $c_{JK}$ parameters in Yb+ ions reaches $1.5 \times 10^{-23}$, exceeding current best bounds by more than five orders of magnitude.
• Systematic effects from differential black-body radiation (BBR) shifts are estimated at $\sim 1~\mu\text{Hz}$, limiting sensitivity to the $6 \times 10^{-24}$ level.
• The $T^{(2)}$ matrix element in Yb+ is more than three times larger than in Th3+ due to deeper $4f$-hole localization compared to $5f$ valence electrons.
• The study identifies general rules for enhancing LSV sensitivity: deeper electron localization and $4f$-hole configurations maximize matrix elements, with higher ionization levels further increasing sensitivity.