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arXiv:2202.13681 · Physical Review A

Effect of micromotion and local stress in quantum simulations with trapped ions in optical tweezers

Liam J. Bond, Lisa Lenstra, R. Gerritsma, Arghavan Safavi-Naini

Published Oct 17, 2022• 9 citations
arXivHTMLPDF

Abstract

The ability to program and control interactions provides the key to implementing large-scale quantum simulation and computation in trapped-ion systems. Adding optical tweezers, which can tune the phonon spectrum and thus modify the phonon-mediated spin-spin interaction, was recently proposed as a way of programing quantum simulators for a broader range of spin models [Arias Espinoza et al., Phys. Rev. A 104, 013302 (2021)]. In this work we study the robustness of our findings in the presence of experimental imperfections: micromotion, local stress, and intensity noise. We show that the effects of micromotion can be easily circumvented when designing and optimizing tweezer patterns to generate a target interaction. Furthermore, while local stress, whereby the tweezers apply small forces on individual ions, may appear to enable further tuning of the spin-spin interactions, any additional flexibility is negligible. We conclude that optical tweezers are a useful method for controlling interactions in trapped-ion quantum simulators in the presence of micromotion and imperfections in the tweezer alignment, but require intensity stabilization on the subpercent level.

DOI
10.1103/physreva.106.042612

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The ability to program and control interactions provides the key to implementing large-scale quantum simulation and computation in trapped-ion systems. Adding optical tweezers, which can tune the phonon spectrum and thus modify the phonon-mediated spin-spin interaction, was recently proposed as a way of programing quantum simulators for a broader range of spin models [Arias Espinoza et al., Phys. Rev. A 104, 013302 (2021)]. In this work we study the robustness of our findings in the presence of experimental imperfections: micromotion, local stress, and intensity noise. We show that the effects of micromotion can be easily circumvented when designing and optimizing tweezer patterns to generate a target interaction. Furthermore, while local stress, whereby the tweezers apply small forces on individual ions, may appear to enable further tuning of the spin-spin interactions, any additional flexibility is negligible. We conclude that optical tweezers are a useful method for controlling interactions in trapped-ion quantum simulators in the presence of micromotion and imperfections in the tweezer alignment, but require intensity stabilization on the subpercent level.
We propose a method for generating programmable interactions in one- and two-dimensional trapped-ion quantum simulators. Here we consider the use of optical tweezers to engineer the sound-wave spectrum of trapped ion crystals. We show that this approach allows us to tune the interactions and connectivity of the ion qubits beyond the power-law interactions accessible in current setups. We demonstrate the experimental feasibility of our proposal using realistic tweezer settings and experimentally relevant trap parameters to generate the optimal tweezer patterns to create target spin-spin interaction patterns in both one- and two-dimensional crystals. Our approach will advance quantum simulation in trapped-ion platforms as it allows them to realize a broader family of quantum spin Hamiltonians.
This paper presents a routine to align an optical tweezer on a single trapped ion and use the ion as a probe to characterize the tweezer. We find a smallest tweezer waist of $2.3(2)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$, which is in agreement with the theoretical minimal attainable waist of $2.5(2)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ in our setup. We characterize the spatial dependence of the tweezer pattern in terms of its Rabi frequency on an optical transition in the ion. We find a peak Rabi frequency of 390(70)MHz390(70)\phantom{\rule{4pt}{0ex}}\mathrm{MHz}390(70)MHz in the center of the tweezer and a suppression factor of 19(3) in the immediate surrounding of the ion. We investigate the effects of optical forces and coherent population trapping on the ion. We show that the challenges posed by these forces can be overcome, and that the number of tweezers can be easily scaled up to reach several ions by using a spatial light modulator.
Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long 1D ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. We devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor these modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits enable to perform entangling gates on these subsets in parallel.
We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state-dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state-dependent forces generated by this effect are located on the plane perpendicular to the direction of propagation of the laser beams opening alternate ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground-state cooling of the ions although the waist of the tightly focused beam needs to be comparable to its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be implemented on both ground-state and magnetic-field-insensitive clock-state qubits without the need for counterpropagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular, a 30-nm tweezer alignment error, lead to an infidelity of $\ensuremath{\sim}{10}^{\ensuremath{-}3}$. In the absence of experimental imperfections and within the limits of the gate model explored in this paper the fidelity is predicted to be $\ensuremath{\sim}0.999\phantom{\rule{0.16em}{0ex}}88$ when using a Laguerre-Gaussian beam to suppress photon scattering errors.
Quantum Simulation of Spin Models with Trapped Ions C. Monroe, W. C. Campbell, E. E. Edwards, R. Islam, D. Kafri, S. Koren- blit, A. Lee, P. Richerme, C. Senko, and J. Smith Joint Quantum Institute University of Maryland Department of Physics College Park, MD 20742, USA Summary. — Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By ap- plying optical fields that exert optical dipole forces on the ions, their Coulomb inter- action can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theory behind this system, recent experimental data on the adiabatic prepration of complex ground states and dynamical studies with small collections of ions, and speculate on the near future when the system becomes so complex that its behavior cannot be modeled with conventional computers. PACS 03.67 – a. PACS 37.10 – Ty. PACS 75.25 – j. Introduction The advent of individual atomic control with external electromagnetic fields, both involving internal states through optical pumping and external states through laser cool- c Societ` a Italiana di Fisica
We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground-state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglement, and discuss the prospects of implementing the state-dependent tweezers in the laboratory.