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arXiv:2411.03301

State-dependent control of the motional modes of trapped ions using an integrated optical lattice

Alfredo Ricci Vásquez, Carmelo Mordini, Daniel Kienzler, Jonathan Home

Published Nov 5, 2024• 0 citations
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Abstract

In this work we study the interaction of trapped ions with a state-dependent, high-intensity optical lattice formed above an ion trap chip using integrated photonics. We use a single ion to map the optical potential landscape over many periods of the standing-wave field. For a single ion sitting in the centre of the lattice we observe a state-dependent trap-frequency shift of $2π\times 3.33(4)$ kHz, corresponding to a bare optical potential of $2π\times 76.8(5)$ kHz for the electronic ground state. We extend this to two ions, measuring state-dependent shifts of both axial modes. Additionally, using the internal-state dependence of the interaction, we perform a direct measurement of the energy distribution of the motion of a single ion using carrier spectroscopy. Improvements to the setup would allow to increase the state-dependent curvature by more than 50 times, providing a tool which can be utilised for motional state control, and multi-ion gates using optical potentials produced in a scalable fashion.

DOI
10.48550/arxiv.2411.03301

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In this work we study the interaction of trapped ions with a state-dependent, high-intensity optical lattice formed above an ion trap chip using integrated photonics. We use a single ion to map the optical potential landscape over many periods of the standing-wave field. For a single ion sitting in the centre of the lattice we observe a state-dependent trap-frequency shift of 2π×3.33(4)2π\times 3.33(4)2π×3.33(4) kHz, corresponding to a bare optical potential of 2π×76.8(5)2π\times 76.8(5)2π×76.8(5) kHz for the electronic ground state. We extend this to two ions, measuring state-dependent shifts of both axial modes. Additionally, using the internal-state dependence of the interaction, we perform a direct measurement of the energy distribution of the motion of a single ion using carrier spectroscopy. Improvements to the setup would allow to increase the state-dependent curvature by more than 50 times, providing a tool which can be utilised for motional state control, and multi-ion gates using optical potentials produced in a scalable fashion.
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Using a single calcium ion confined in a surface-electrode trap, we study the interaction of electric quadrupole transitions with a passively phase-stable optical standing wave field sourced by photonics integrated within the trap. We characterize the optical fields through spatial mapping of the Rabi frequencies of both carrier and motional sideband transitions as well as ac Stark shifts. Our measurements demonstrate the ability to engineer favorable combinations of sideband and carrier Rabi frequency as well as ac Stark shifts for specific tasks in quantum state control and metrology.
We control the relative coupling strength 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 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 ${180}^{\ensuremath{\circ}}$ 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 simulation and quantum control. Using the standing-wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.
We demonstrate a state-dependent Gaussian gate set on the motional modes of trapped 40^{40}40Ca+^++ ions, realized with an optical tweezer. Dynamic control of the tweezer intensity and position enables local displacement, squeezing, phase-space rotation, and beamsplitter operations, constituting a complete gate set. By varying the tweezer position relative to the ion, we show how the strength of each operation is set by the corresponding spatial derivative of the local optical potential. We further demonstrate the inherent dependence of each operation on the ion's internal state and use coherent spin-motion coupling provided by the tweezer to create a motional cat state. Our work establishes optical tweezers as a unified and local resource for continuous-variable quantum control in trapped ion systems.
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.