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Journal of Physics B Atomic Molecular and Optical Physics

Unsharp measurements using trapped ytterbium ions: a feasibility study

Siann Bester, Thomas Konrad, Naleli Jubert Matjelo, Christine M. Steenkamp

Published Jul 28, 2026• 0 citations
Publisher

Abstract

Abstract Numerical simulations are used to study unsharp measurements in a system of trapped ytterbium ions to monitor resonantly driven Rabi oscillations of a target ion by weak coupling to an auxiliary ion. The simulation combines the positive operator-valued measure formalism and optical Bloch equations to model the state of the target ion during the implementation of the unsharp measurement protocol. State monitoring is done using an estimation scheme that is updated with the unsharp measurement results. The model expands on previous work by explicitly including spontaneous emission into the calculations. We propose a method to determine convergence of the estimation scheme, useful in an experimental setting, which does not rely on using the target state. The simulation results show the feasibility conditions for implementing unsharp measurements experimentally and demonstrate the robustness of the estimation scheme in the presence of experimental noise and when the qubit Rabi frequency is not precisely known. We find that the timescale of transitions that change the motional state is the main technical challenge for experimental implementation.

DOI
10.1088/1361-6455/ae91b0

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Abstract Numerical simulations are used to study unsharp measurements in a system of trapped ytterbium ions to monitor resonantly driven Rabi oscillations of a target ion by weak coupling to an auxiliary ion. The simulation combines the positive operator-valued measure formalism and optical Bloch equations to model the state of the target ion during the implementation of the unsharp measurement protocol. State monitoring is done using an estimation scheme that is updated with the unsharp measurement results. The model expands on previous work by explicitly including spontaneous emission into the calculations. We propose a method to determine convergence of the estimation scheme, useful in an experimental setting, which does not rely on using the target state. The simulation results show the feasibility conditions for implementing unsharp measurements experimentally and demonstrate the robustness of the estimation scheme in the presence of experimental noise and when the qubit Rabi frequency is not precisely known. We find that the timescale of transitions that change the motional state is the main technical challenge for experimental implementation.
Unsharp positive operator-valued measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion and that of an auxiliary ion, using standard ion-trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.
The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.
This tutorial covers the derivation of the optical Bloch equations for a four-state atomic system interacting with an electromagnetic field via magnetic dipole transitions. The derivation of the equations is discussed at length and from first principles such that any student or graduate with a basic quantum mechanics background could follow. The tutorial shows numerical simulations of the model under different conditions, rounding off the understanding of the dependencies of the model. Finally, the functionality of the model is shown by fitting the model to experimental data of ytterbium-171 ions undergoing Rabi oscillations.
The purpose of the research: to determine an efficient and error-resilient method for assessing the fidelity of singlequbit quantum operations, as well as to formulate and experimentally implement an algorithm for determining the average accuracy of single-qubit quantum transformations Research methods: the theory of noisy quantum operations, randomization of single-qubit quantum circuits composed of Clifford group transformations, the theory of unitary 2-design, experimental validation on a quantum computer based on ytterbium-171 trapped ions Research results: an algorithm for estimating the average fidelity of single-qubit operations and its statistical error is described; experimental validation confirmed the correctness of the exponential decay model of the probability of obtaining the target state during measurement as the depth of the quantum circuit increases; the resulting experimental average fidelity of the single-qubit quantum operation is 99.94% Scientific novelty: the application of the randomized benchmarking method to determine the average fidelity of singlequbit quantum operations in quantum computing, particularly for an ion-based quantum processor with ytterbium-171 ions.
We introduce quantum sensing schemes for measuring very weak forces with a single trapped ion. They use the spin-motional coupling induced by the laser-ion interaction to transfer the relevant force information to the spin-degree of freedom. Therefore, the force estimation is carried out simply by observing the Ramsey-type oscillations of the ion spin states. Three quantum probes are considered, which are represented by systems obeying the Jaynes-Cummings, quantum Rabi (in 1D) and Jahn-Teller (in 2D) models. By using dynamical decoupling schemes in the Jaynes-Cummings and Jahn-Teller models, our force sensing protocols can be made robust to the spin dephasing caused by the thermal and magnetic field fluctuations. In the quantum-Rabi probe, the residual spin-phonon coupling vanishes, which makes this sensing protocol naturally robust to thermally-induced spin dephasing. We show that the proposed techniques can be used to sense the axial and transverse components of the force with a sensitivity beyond the range, i.e. in the (xennonewton, 10(-27)). The Jahn-Teller protocol, in particular, can be used to implement a two-channel vector spectrum analyzer for measuring ultra-low voltages.