In this paper we present a detailed analysis of the nuclear-spin manifolds associated with the $ns$ Rydberg levels of $^{87}\mathrm{Rb}$ atoms that interact with both magnetic and optical lattice fields. Eigenvalues and eigenkets for the Rydberg manifold are obtained and used to study the dynamics of phase-matched emission following illumination of an ensemble of cold atoms with excitation and readout laser pulses. By comparing the measured emission signal to predictions of a model that accounts for the quantized motion of atoms in a one-dimensional optical lattice potential, we are able to extract the Rydberg hyperfine and light shift contributions to the observed modulation frequencies. In this way the hyperfine splitting of Rydberg $ns$ levels is measured for $n$ in the range of 30 to 65. Our results should be relevant for realizations of high-fidelity Rydberg qubits confined in optical potentials.In this paper we present a detailed analysis of the nuclear-spin manifolds associated with the $ns$ Rydberg levels of $^{87}\mathrm{Rb}$ atoms that interact with both magnetic and optical lattice fields. Eigenvalues and eigenkets for the Rydberg manifold are obtained and used to study the dynamics of phase-matched emission following illumination of an ensemble of cold atoms with excitation and readout laser pulses. By comparing the measured emission signal to predictions of a model that accounts for the quantized motion of atoms in a one-dimensional optical lattice potential, we are able to extract the Rydberg hyperfine and light shift contributions to the observed modulation frequencies. In this way the hyperfine splitting of Rydberg $ns$ levels is measured for $n$ in the range of 30 to 65. Our results should be relevant for realizations of high-fidelity Rydberg qubits confined in optical potentials.

Physical Review ASep 18, 20195 citations

Modulation spectroscopy of Rydberg atoms in an optical lattice

Vladimir S. Malinovsky, Kaitlin Moore, Georg A. Raithel

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.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.

arXiv:1911.05671Physical Review AMar 25, 20209 citations

Quantum dynamics with strongly interacting Rydberg atoms

Jing Qian, Zhou Lü, Xing-Dong Zhao +1 more

Bulletin of the American Physical SocietyMar 3, 20140 citations

Excitation dynamics of interacting Rydberg atoms in small lattices

GR Wu, Markus Kurz, Benno Liebchen +1 more

Physics Letters ANov 18, 20141 citation

Tune-out wavelengths and landscape-modulated polarizabilities of alkali-metal Rydberg atoms in infrared optical lattices

Türker Topçu, Andrei Derevianko

Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO ${}_{2}$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the $ns$ , $np$ , and $nd$ Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the ${m}_{z}=0$ Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted $l=0$ states.Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO${}_{2}$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the $ns$, $np$, and $nd$ Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the ${m}_{z}=0$ Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted $l=0$ states.

arXiv:1308.6258Physical Review ANov 6, 201312 citations

In this paper we present a detailed analysis of the nuclear-spin manifolds associated with the

ns

Rydberg levels of

^{87}\mathrm{Rb}

atoms that interact with both magnetic and optical lattice fields. Eigenvalues and eigenkets for the Rydberg manifold are obtained and used to study the dynamics of phase-matched emission following illumination of an ensemble of cold atoms with excitation and readout laser pulses. By comparing the measured emission signal to predictions of a model that accounts for the quantized motion of atoms in a one-dimensional optical lattice potential, we are able to extract the Rydberg hyperfine and light shift contributions to the observed modulation frequencies. In this way the hyperfine splitting of Rydberg

ns

levels is measured for

n

in the range of 30 to 65. Our results should be relevant for realizations of high-fidelity Rydberg qubits confined in optical potentials.

{}_{2}

laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the

ns

np

, and

nd

Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the

{m}_{z}=0

Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted

l=0

states.