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arXiv:2502.19345 · Physical Review Research

Nonparaxial effects on laser-qubit operations

L. P. H. Gallagher, M. Mazzanti, Z. E. D. Ackerman, Arghavan Safavi-Naini, R. Gerritsma, R. J. C. Spreeuw

Published Dec 17, 2025• 1 citation
arXivHTMLPDF

Abstract

Tightly focused laser beams, or optical tweezers, are essential for analog and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which is an insufficient description at the focus of tightly focused optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how nonparaxial effects will manifest in the next generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole S 1 / 2 2 → D 5 / 2 2 transition in Ca + 40 . Longitudinal field components in the beam center cause spatially dependent Rabi frequencies and ac Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where nonparaxial effects should be taken into account for high-precision quantum control, and highlight that the effects are potentially more severe for the case of neutral atom and molecule addressing.

DOI
10.1103/4ylp-h3qr

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Tightly focused laser beams, or optical tweezers, are essential for analog and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial approximation, which is an insufficient description at the focus of tightly focused optical tweezers. We develop an analytic model, which we use in tandem with numerical simulations, to quantify how nonparaxial effects will manifest in the next generation of scalable quantum hardware, where tightly focused beams are used for individual qubit control. In particular, we calculate the light potentials of Gaussian and Laguerre-Gaussian beams driving the quadrupole S 1 / 2 2 → D 5 / 2 2 transition in Ca + 40 . Longitudinal field components in the beam center cause spatially dependent Rabi frequencies and ac Stark shifts, leading to unexpected qubit-motion coupling. We characterize single- and two-qubit gate infidelities due to this effect with an analytic model and numerical simulation. We identify regimes where nonparaxial effects should be taken into account for high-precision quantum control, and highlight that the effects are potentially more severe for the case of neutral atom and molecule addressing.
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.
This article investigates the quadrupole excitation of a trapped atom exposed to the tightly focused Laguerre-Gaussian (LG) beams with parallel and antiparallel spin angular momentum (SAM) and orbital angular momentum (OAM) under nonparaxial conditions. The Rabi frequency profile of allowed quadrupole transition channels, modified by SAM and OAM interaction, in the focal plane is provided. In the case of antiparallel SAM and OAM, the excitation probability undergoes substantial modification due to the considerable contribution of longitudinal intensity variations in tightly focused condition. The findings offer insights into controlling localized atom transition, including OAM transfer, with potential applications in qudit-based technologies.
We examine the applicability and limitations of several established measures of paraxiality in the context of electric quadrupole interactions between light and trapped atoms. Focusing on Laguerre–Gaussian beams, we compare analytical predictions—particularly transition amplitudes and selection rules—derived under the paraxial assumption with full numerical solutions obtained via diffraction integrals that account for the complete vectorial field structure. This comparison allows us to assess the validity and relevance of these measures across a range of beam parameters. We also investigate the role of the power-series expansion in the paraxial parameter in bridging paraxial and nonparaxial regimes.
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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 live on the plane perpendicular to the direction of propagation of the laser beams opening new ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground state cooling of the ions and does not rely on the Lamb-Dicke approximation, although the waist of the tightly focused beam needs to be comparable with its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be performed on both ground state and magnetic field insensitive clock state qubits without the need for counter-propagating 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 pointing errors <30<30<30 nm in the tweezers reduce the gate fidelity from F≳0.99998\mathcal F\gtrsim 0.99998F≳0.99998 to ≳0.999\gtrsim 0.999≳0.999.
We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a 40^{40}40Ca+^++ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.