DOI: 10.4231/b7cm-vp26
title: Data for Photon-recoil and laser-focusing limits to Rydberg gate fidelity

description: &lt;p&gt;&lt;span dir="ltr" role="presentation" style="left: 186.611px; top: 355.627px; font-size: 14.944px; font-family: serif; transform: scaleX(1.02458);"&gt;Limits to Rydberg &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 186.611px; top: 355.627px; font-size: 14.944px; font-family: serif; transform: scaleX(1.02458);"&gt;gate fidelity that arise from the entanglement of internal states of neutral atoms with the &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 374.722px; font-size: 14.944px; font-family: serif; transform: scaleX(1.00912);"&gt;motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 393.818px; font-size: 14.944px; font-family: serif; transform: scaleX(1.03584);"&gt;This occurs when the atom is in a superposition of internal states but only one of these states is manipulated &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 412.913px; font-size: 14.944px; font-family: serif; transform: scaleX(1.00671);"&gt;by visible or UV photons. The Schr&ouml;dinger equation that describes this situation is presented and two cases are &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 432.008px; font-size: 14.944px; font-family: serif; transform: scaleX(1.00005);"&gt;explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 451.104px; font-size: 14.944px; font-family: serif; transform: scaleX(1.04939);"&gt;in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 470.199px; font-size: 14.944px; font-family: serif; transform: scaleX(1.05648);"&gt;can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 489.295px; font-size: 14.944px; font-family: serif; transform: scaleX(1.01565);"&gt;harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 508.39px; font-size: 14.944px; font-family: serif; transform: scaleX(0.995805);"&gt;the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 527.486px; font-size: 14.944px; font-family: serif; transform: scaleX(1.02222);"&gt;In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 546.581px; font-size: 14.944px; font-family: serif; transform: scaleX(0.993809);"&gt;emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 565.677px; font-size: 14.944px; font-family: serif; transform: scaleX(0.992372);"&gt;states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 584.772px; font-size: 14.944px; font-family: serif; transform: scaleX(1.05499);"&gt;can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 603.867px; font-size: 14.944px; font-family: serif; transform: scaleX(1.00304);"&gt;frequency, and the atomic mass. These limits on gate fidelity are studied for the standard&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 702.563px; top: 603.867px; font-size: 14.944px; font-family: serif;"&gt; &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 706.454px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt;&pi;&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 715.421px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt; &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 716.924px; top: 603.867px; font-size: 14.944px; font-family: serif; transform: scaleX(0.998187);"&gt;-2&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 729.435px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt;&pi;&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 738.401px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt; &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 739.905px; top: 603.867px; font-size: 14.944px; font-family: serif;"&gt;-&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 744.886px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt;&pi;&lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 753.852px; top: 603.739px; font-size: 14.944px; font-family: sans-serif;"&gt; &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 759.256px; top: 603.867px; font-size: 14.944px; font-family: serif; transform: scaleX(1.00923);"&gt;Rydberg gate &lt;/span&gt;&lt;span dir="ltr" role="presentation" style="left: 171.671px; top: 622.963px; font-size: 14.944px; font-family: serif; transform: scaleX(0.998645);"&gt;and a protocol based on a single adiabatic pulse with a Gaussian envelope.&lt;/span&gt;&lt;/p&gt;
description: Data used in the figures of Phys. Rev. A 103, 022424 (2021) with short information in FILE_INFO.txt. Also contains .eps files and gnuplot routines.