Nonparaxial effects on laser-qubit operations

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mmultiscripts> <a:mi mathvariant="normal">S</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> <a:none/> <a:mprescripts/> <a:none/> <a:mn>2</a:mn> </a:mmultiscripts> <a:mo>→</a:mo> <a:mspace width="4pt"/> <a:mmultiscripts> <a:mi mathvariant="normal">D</a:mi> <a:mrow> <a:mn>5</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> <a:none/> <a:mprescripts/> <a:none/> <a:mn>2</a:mn> </a:mmultiscripts> </a:mrow> </a:math> transition in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Ca</e:mi> <e:none/> <e:mo>+</e:mo> <e:mprescripts/> <e:none/> <e:mn>40</e:mn> </e:mmultiscripts> </e:math> . 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.