Modulation spectroscopy of Rydberg atoms in an optical lattice

TL;DR

This paper introduces a comprehensive study of Rydberg-atom spectroscopy in amplitude-modulated optical lattices, revealing a novel sub-Doppler mechanism and comparing quantum, perturbative, and semi-classical models to understand spectral features.

Contribution

It develops and compares quantum, perturbative, and semi-classical models for Rydberg-atom spectroscopy in modulated optical lattices, highlighting a new sub-Doppler mechanism and quantum-classical correspondence.

Findings

Identification of a phase-locked, spatially periodic ponderomotive coupling.

Observation of spectral features from vibrational coherences and rotary-echo effects.

Validation of models through spectral analysis of Rydberg-state populations.

Abstract

We develop and study quantum and semi-classical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in any other spectroscopic scheme, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a novel type of sub-Doppler mechanism, which we explain in detail. In our exact quantum model, we solve the time-dependent Schr\"odinger equation in the product space of center-of-mass (COM) momentum states and the internal-state space. We also develop a perturbative model based on the band structure in the lattice and Fermi's golden rule, as well as a semi-classical trajectory model in which the COM is treated classically and the internal-state dynamics quantum-mechanically. In all models we obtain the spectrum of the target Rydberg-state population versus the lattice modulation frequency, averaged over the initial thermal COM momentum distribution of the atoms. We investigate the quantum-classical correspondence of the problem in several parameter regimes and exhibit spectral features that arise from vibrational COM coherences and rotary-echo effects. Applications in Rydberg-atom spectroscopy are discussed.