Abstract
We develop and study quantum and semiclassical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in other spectroscopic schemes, 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 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 semiclassical 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.
Highlights
The interaction of an electron with an electromagnetic field consists of a term eA · p /m and a term e2A 2/(2m), with electron mass m, elementary charge e, the field’s vector potential A (r), and electron position and momentum operators rand p, respectively [1,2]
The combination of the aforementioned features enables high-precision spectroscopy on long-lived circular-state Rydberg atoms trapped in optical lattices [35], utilizing a scheme in which the transition frequency between the circular Rydberg levels is measured via resonant ponderomotive optical lattice (POL)-modulation at microwave frequencies
VI B we show that these facts enable a type of sub-Doppler method that is realized automatically in modulated-POL spectroscopy
Summary
The interaction of an electron with an electromagnetic field consists of a term eA · p /m and a term e2A 2/(2m), with electron mass m, elementary charge e, the field’s vector potential A (r), and electron position and momentum operators rand p , respectively [1,2]. The combination of the aforementioned features enables high-precision spectroscopy on long-lived circular-state Rydberg atoms trapped in optical lattices [35], utilizing a scheme in which the transition frequency between the circular Rydberg levels is measured via resonant POL-modulation at microwave frequencies. This experimental platform may be useful for quantum simulators [36] that are based on circular-state Rydberg-atom arrays. In the present paper we develop such models, investigate quantum-classical correspondence in POL modulation spectroscopy, and exhibit the quantum features in the spectra
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