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arXiv:2311.13736

Multi-ion frequency reference using dynamical decoupling

Lennart Pelzer, Kai Dietze, V. J. Martínez-Lahuerta, Ludwig Krinner, Kramer, Johannes, Fabian Dawel, Nicolas Spethmann, Klemens Hammerer, Piet O. Schmidt

Published Nov 22, 2023• 0 citations
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Abstract

We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on $^{40}\mathrm{Ca}^+$. By near-resonant magnetic coupling of the $^2\mathrm{S}_{1/2}$ and $^2\mathrm{D}_{5/2}$ Zeeman sub-levels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2\textsuperscript{nd}-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to $3(2)\,\text{mHz}/μm^2$ and coherence times of $290(20)\,\text{ms}$ on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.

DOI
10.48550/arxiv.2311.13736

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We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Ca+^{40}\mathrm{Ca}^+40Ca+. By near-resonant magnetic coupling of the 2S1/2^2\mathrm{S}_{1/2}2S1/2​ and 2D5/2^2\mathrm{D}_{5/2}2D5/2​ Zeeman sub-levels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2\textsuperscript{nd}-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm23(2)\,\text{mHz}/μm^23(2)mHz/μm2 and coherence times of 290(20) ms290(20)\,\text{ms}290(20)ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.
We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on ^{40}Ca^{+}. By near-resonant magnetic coupling of the ^{2}S_{1/2} and ^{2}D_{5/2} Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm^{2} and coherence times of 290(20) ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.
We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Caþ. By near-resonant magnetic coupling of the 2S1=2 and 2D5=2 Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3ð2Þ mHz=μm2 and coherence times of 290(20) ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.
Abstract We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic field shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions, such as 40 Ca + , 88 Sr + , 138 Ba + and 176 Lu + . Taking a spherically symmetric Coulomb crystal formed by 400 40 Ca + ions as an example, we show through numerical simulations that the inhomogeneous linewidth of tens of Hertz in such a crystal together with linear Zeeman shifts of order 10 MHz are reduced to form a linewidth of around 1 Hz. We estimate a two-order-of-magnitude reduction in averaging time compared to state-of-the art single ion frequency references, assuming a probe laser fractional instability of 10 − 15 . Furthermore, a statistical uncertainty reaching 2.9 × 10−16 in 1 s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an 27 Al + clock.
Dynamical decoupling techniques are a versatile tool for engineering quantum states with tailored properties. In trapped ions, nested layers of continuous dynamical decoupling by means of radio-frequency field dressing can cancel dominant magnetic and electric shifts and therefore provide highly prolonged coherence times of electronic states. Exploiting this enhancement for frequency metrology, quantum simulation or quantum computation, poses the challenge to combine the decoupling with laser-ion interactions for the quantum control of electronic and motional states of trapped ions. Ultimately, this will require running quantum gates on qubits from dressed decoupled states. We provide here a compact representation of nested continuous dynamical decoupling in trapped ions, and apply it to electronic SSS and DDD states and optical quadrupole transitions. Our treatment provides all effective transition frequencies and Rabi rates, as well as the effective selection rules of these transitions. On this basis, we discuss the possibility of combining continuous dynamical decoupling and Mølmer-Sørensen gates.
We study and characterize a quasicontinuous dynamical decoupling scheme that effectively suppresses dominant frequency shifts in a multi-ion optical clock. Addressing the challenge of inhomogeneous frequency shifts in such systems, our scheme mitigates primary contributors, namely, the electric quadrupole and the linear Zeeman shifts. Based on ^{88}Sr^{+} ions, we implement the scheme in linear chains of up to 7 ions and demonstrate a significant suppression of the shift by more than 3 orders of magnitude, leading to relative frequency inhomogeneity below 7×10^{-17}. Additionally, we evaluate the associated systematic shift arising from the radio-frequency drive used in the QCDD scheme, showing that, in the presented realization, its contribution to the systematic relative frequency uncertainty is below 10^{-17}, with the potential for further improvement. These results provide a promising avenue toward implementing multi-ion clocks exhibiting an order of magnitude or more improvement in stability while maintaining a similar high degree of accuracy to that of single-ion clocks.