Photon recoil and laser focusing limits to Rydberg gate fidelity

TL;DR

This paper quantifies how photon recoil and laser focusing impose fundamental limits on the fidelity of Rydberg gates in neutral atom quantum computing, providing analytic formulas for decoherence effects in different experimental regimes.

Contribution

It introduces a detailed Schrödinger equation framework and derives simple analytic formulas to quantify photon recoil and focusing effects on Rydberg gate fidelity.

Findings

Decoherence due to photon recoil depends on atom temperature and trap frequency.

Focusing of laser beams causes position-dependent internal state changes.

Analytic formulas are provided for different pulse timing regimes.

Abstract

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schr\"odinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency and the atomic mass. These limits on gate fidelity are studied for the standard $\pi-2\pi-\pi$ Rydberg gate and a new protocol based on a single adiabatic pulse with Gaussian envelope.