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European Frequency and Time Forum

Precision frequency measurements with entangled ions

Christian F. Roos, Michael Chwalla, Mark Riebe, Gavin P. T. Lancaster, Christoph Becher, Hartmut Häffner, W. Hänsel, Ferdinand Schmidt‐Kaler, R. Blatt

Published Jan 1, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1049/cp:20040937

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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.
We demonstrate how quantum entanglement can be used for precision frequency measurements with trapped ions. In particular, we show how to suppress linear Zeeman shifts in optical frequency measurements by using maximally entangled states of two ions even if the individual ions do not have any field-independent transition. In addition, this technique allows for an accurate measurement of small external field frequency shifts such as the electric quadrupole shift which are important for ion clock experiments.
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.
We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.
Experiments with two entangled trapped 9Be+ ions are discussed. In one type of experiments we used entanglement to increase the precision of rotation angle measurements. For “spin-squeezed" and maximally entangled states we observed a reduction in uncertainty of rotation angle below the standard quantum limit. In a second experiment we demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace of two ions, we protect it from environment-induced dephasing. We increased the storage time by up to an order of magnitude compared to an unprotected qubit.
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
We report an experimental determination of the ground-state hyperfine constant AAA of the 25Mg+^{25}\mathrm{Mg}^{+}25Mg+ ions by measuring the $|{S}_{1/2},F=2,m=0\ensuremath{\rangle}$ to $|{S}_{1/2},F=3,m=0\ensuremath{\rangle}$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=\ensuremath{-}596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.