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Entanglement enhanced precision test of local Lorentz invariance

E. Megidish, Joseph Broz, Nicole Greene, Hartmut Häffner

Published Sep 26, 2018• 1 citation
OpenAlex

Abstract

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this paper we study how entangled states can be leveraged to enhance a precision test of local Lorentz invariance of the electron. Employing high-fidelity entanglement of a pair of trapped Ca-ions, we find that the sensitivity can be improved by a factor of two. The sensitivity of our measurements nearly reaches the projection noise limit set by quantum mechanics. Our measurements improve the previous best limit for local Lorentz invariance of the electron using Ca-ions by factor of two to about $5\times10^{-19}$.

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The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this paper we study how entangled states can be leveraged to enhance a precision test of local Lorentz invariance of the electron. Employing high-fidelity entanglement of a pair of trapped Ca-ions, we find that the sensitivity can be improved by a factor of two. The sensitivity of our measurements nearly reaches the projection noise limit set by quantum mechanics. Our measurements improve the previous best limit for local Lorentz invariance of the electron using Ca-ions by factor of two to about 5×10−195\times10^{-19}5×10−19.
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.
A recent proposal for testing Lorentz-symmetry violation (LSV) presents a formulation where the effect of violation is described as a local interaction [R. Shaniv et al., Phys. Rev. Lett. 120, 103202 (2018)]. An entangled ion pair in a decoherence free subspace (DFS) is shown to double the signal-to-noise ratio (SNR) of one ion, while (even)-N/2N/2N/2 such DFS pairs in a collective entangled state improve SNR by NNN times, provided the state parity or the even or odd numbers of ions can be measured. It remains to find out, however, how such fiducial entangled states can be prepared at nonexponentially small success rates. This work suggests two types of many-particle entangled states for testing LSV: the maximally entangled NOON state, which can achieve Heisenberg limited precision; and the balanced spin-1 Dicke state, which is readily available in deterministic fashion. We show that the latter also lives in a DFS and is immune to stray magnetic fields. It can achieve classical precision limit or the standard quantum limit (SQL) based on collective population measurement without individual atom resolution. Given the high interests in LSV and in entanglement assisted quantum metrology, our observation offers additional incentives for pursuing practical applications of many-atom entangled states.
Entangled states hold the promise of improving the precision and accuracy of quantum sensors. We experimentally demonstrate that spectroscopy of an optical clock transition using entangled states can outperform its classical counterpart. Two ^{40}Ca^{+} ions are entangled in a quantum state with vanishing first-order magnetic field sensitivity, extending the coherence time of the atoms and enabling near-lifetime-limited probe times of up to 550 ms. In our protocol, entangled ions reach the same instability as uncorrelated ions, but at half the probe time, enabling faster cycle times of the clock. We run two entangled ^{40}Ca^{+} ions as an optical clock and compare its frequency instability with a ^{87}Sr lattice clock. The instability of the entangled ion clock is below a clock operated with classically correlated states for all probe times. We observe instabilities below the theoretically expected quantum projection noise limit of two uncorrelated ions for interrogation times below 100 ms. The lowest fractional frequency instability of 7×10^{-16}/sqrt[τ/1 s] is reached for 250 ms probe time, limited by residual phase noise of the probe laser. This represents the lowest instability reported to date for a ^{40}Ca^{+} ion clock.
Quantum entanglement of atoms enables precision measurement and frequency metrology beyond the standard quantum limit that is imposed by the quantum projection noise. Here we propose employing entangled atoms in the synchronous differential measurement to enhance the detection sensitivity of spatially dependent frequency shift. Two ways of engineering entangled atoms are studied. The synchronous comparison between two pixels within an entangled atomic cloud leads to a sensitivity enhancement factor of 1.4 over the standard quantum limit. The sensitivity enhancement becomes saturated for a large number of atoms. In contrast, the synchronous comparison between two independent pixels that are individually composed of entangled atoms allows for a strong sensitivity enhancement by a factor of, for example, about 10 with 103{10}^{3}103 entangled atoms in each pixel, corresponding to a reduction of the averaging time by a factor of about 102{10}^{2}102. A large atom number may further elevate the sensitivity. Our work paves the way towards the entanglement-enhanced detection of gravitational redshift by means of the in situ imaging spectroscopy.
This paper explores the potential of quantum metrology, specifically utilizing entangled photon pairs, to significantly enhance the precision of measurement systems. Traditional metrology is often limited by the fundamental precision constraints imposed by classical physics. Entanglement, a quantum mechanical phenomenon where two or more particles are linked in such a way that they share the same fate, regardless of the distance separating them, offers a pathway to overcome these limitations. This work details the theoretical framework for employing entangled photon pairs to minimize measurement noise and improve sensor accuracy. The core claim is that leveraging these correlations can provide a measurable advantage over classical techniques. The proposed mechanism focuses on reducing uncertainties associated with the measurement process by exploiting the inherent correlations between the entangled photons. The research targets applications like gravitational wave detection and biological imaging, where high precision is paramount. The paper presents a comprehensive overview of the theoretical concepts and potential advancements offered by this approach, laying the groundwork for future experimental investigations.
Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter κ via an ensemble of spinor atoms. By employing an N -atom multimode GHZ state, the test precision can attain the Heisenberg limit Δκ∝1/(F2N) with the spin length F and the atom number N . We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin- 1 atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter κ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter κ can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.