Photon-recoil and laser-focusing limits to Rydberg gate fidelity

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 Schrodinger 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 protocol based on a single adiabatic pulse with a Gaussian envelope.

Automated summary

This study quantifies the limits to Rydberg gate fidelity arising from entanglement between internal states and motion of neutral atoms due to photon absorption and re-emission. The Schrodinger equation is used to explore two cases, involving excitation and stimulated emission timings, as well as the effects of focused beam modes on gate fidelity. The decoherence can be expressed in simple analytic formulas considering factors such as photon momentum, atom temperature, harmonic oscillator frequency, laser waist, and atomic mass.