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AIP conference proceedings

Precision Spectroscopy with Entangled States: Measurement of Electric Quadrupole Moments

Christian F. Roos, Michael Chwalla, K. Kim, Mark Riebe, R. Blatt

Published Jan 1, 2006• 1 citation
Publisher

Abstract

Entangled states of atoms prepared in a decoherence‐free subspace are shown to be useful for precision spectroscopy. Energy level shifts can be measured by using a pair of atoms in a Bell state for performing phase‐estimation by generalized Ramsey experiments. The immunity of decoherence‐free subspaces against certain sources of noise allows for long excitation times in the presence of noise that would render single‐atom experiments impossible. We employ this technique for a measurement of the electric quadrupole moment Θ of the meta‐stable 3D5/2 level of 40Ca+ which is found to be Θ(3d, 5/2) = 1.83(1)ea02.

DOI
10.1063/1.2400640

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Entangled states of atoms prepared in a decoherence‐free subspace are shown to be useful for precision spectroscopy. Energy level shifts can be measured by using a pair of atoms in a Bell state for performing phase‐estimation by generalized Ramsey experiments. The immunity of decoherence‐free subspaces against certain sources of noise allows for long excitation times in the presence of noise that would render single‐atom experiments impossible. We employ this technique for a measurement of the electric quadrupole moment Θ of the meta‐stable 3D5/2 level of 40Ca+ which is found to be Θ(3d, 5/2) = 1.83(1)ea02.
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.
The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of nnn two-level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays. Published by the American Physical Society 2024
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.
The precision of an atomic clock based on the standard Ramsey spectroscopy, involving the measurement of the population of the atomic excited state, essentially a measurement of energy, is determined by the free evolution time T between successive /2 pulses. The longer the time T, the narrower the Ramsey interference fringes and thus the greater the precision. The stability of an atomic clock is also increased with increased T. But there are practical limits to the degree to which T can be extended. The main approach so far has been through the introduction of the so-called atomic fountain clocks. In this talk we present alternative approach not based on extending T but based on collective atomic states where a non-classical observable, an observable having no classical counterpart, is to be measured. This is the collective atomic, or SU(2), parity for an ensemble of two-level atoms. We show that with this observable the corresponding Ramsey-like fringes can become remarkably narrower with an increasing number of atoms in the ensemble even when the atomics are not prepared in an entangled state. By preparing the atoms in an entangled state, such as a state known to be spin-squeezed, the precision can be further increased through atomic parity measurements. The issue of performing the required collective atomic parity measurements will be discussed.