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Physical Review A

Differential nuclear-spin-dependent light shifts and state mixing of Rydberg atoms

Huy Minh Nguyen, Jacob Lampen, P. R. Berman, A. Kuzmich

Published Sep 18, 2019• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.100.033412

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In this paper we present a detailed analysis of the nuclear-spin manifolds associated with the nsnsns Rydberg levels of 87Rb^{87}\mathrm{Rb}87Rb 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 nsnsns levels is measured for nnn in the range of 30 to 65. Our results should be relevant for realizations of high-fidelity Rydberg qubits confined in optical potentials.
Rydberg ensembles have many diverse and important applications for quantum information and quantum optics. For example, Rydberg ensembles can generate non-classical states of light which would be useful in a quantum network, and they could be used as qubits in a future quantum computer. For this reason, this thesis will present investigations of light-matter interactions in Rydberg ensembles. Non-classical states of light, such as single-photon states, are important for many quantum communication protocols. We have performed an experiment that demonstrates the generation of single-photon states from a Rydberg ensemble. We then studied the second-order correlations between this single-photon state of light and an incident coherent field. Under these conditions, we observed Hanbury Brown Twiss interference between the emission from a driven super-atom and a coherent field in the absence of stimulated emission. For a universal quantum computing architecture, coherence times must be much longer than gate operations. We observe ground-Rydberg coherence times in excess of 20 microseconds by using a "magic-wavelength" optical lattice to confine the atoms. Using this coherence time, we measured the differential nuclear-spin-dependent light shifts for principal quantum numbers, n, between n = 30 and n = 65, which is relevant for future high-fidelity Rydberg qubits in optical potentials. Also, we measured the hyperfine constant for atomic Rb to be 35.71 GHz with an uncertainty of 0.18 GHz.
In this dissertation, I explore several aspects of Rydberg physics with laser spectroscopy. The experiments center around the use of a very deep, cavity-generated, one-dimensional optical lattice in a cold atom sample. The optical lattice produces elongated clouds of dense, cold atoms via dipole trapping and is able to generate extreme light shifts in the atoms due to its high intensity. I describe experiments which may be divided into two main classes. In the first, I use the dipole trap to prepare a dense sample of atoms for photoassociation of Rb atom pairs into diatomic Rydberg molecules. The Rydberg molecules are formed by low-energy scattering of the Rydberg electron of one atom from the other atom, which is a ground-state atom. This novel binding mechanism also has relevance for chemical physics. I present binding energy measurements for eight different cases of Rydberg molecules. The binding energies reveal information about electron-atom collisions, such as their scattering lengths, and about the spin couplings present within the molecular system. In the second class of experiments, I introduce two proposed measurements in which the optical lattice is ramped to very high intensity during the laser excitation, creating AC Stark shifts in the transition frequencies. In one measurement, low-lying atomic states are probed. Measurements of the light shifts are expected to yield data on the dynamic polarizability and the photoionization cross section of the 5D3/2D_{3/2}D3/2​-state in rubidium in a 1064-nm light field. I show corresponding preliminary experimental data. The polarizability and photo-ionization cross-section measurements will provide tests of atomic structure theory, which is important both at a fundamental level and for applications such as atomic clocks. In another proposed measurement, Rydberg atoms in the lattice experience ponderomotive shifts and strong mixing of their angular-momentum states, allowing direct optical excitation of the lattice-mixed high-angular-momentum states. I describe the theoretical basis and experimental preparation for spectroscopically characterizing the lattice-mixed states. The ability to optically excite selected high-angular-momentum states without the use of static or RF fields may be useful for quantum information processing and simulation.
We have performed high resolution photoassociation spectroscopy of rubidium ultralong-range Rydberg molecules in the vicinity of the 25P state. Because of the hyperfine interaction in the ground state perturber atom, the emerging mixed singlet-triplet potentials contain contributions from both hyperfine states. We show that this can be used to induce remote spin flips in the perturber atom upon excitation of a Rydberg molecule. Furthermore, when the spin-orbit splitting of the Rydberg state is comparable to the hyperfine splitting in the ground state, the orbital angular momentum of the Rydberg electron is entangled with the nuclear spin of the perturber atom. Our results open new possibilities for the implementation of spin-dependent interactions for ultracold atoms in bulk systems and in optical lattices.
We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition and the differential ggg factor between the two clock states for alkaline-earth-metal(-like) atoms, using 87Sr^{87}\mathrm{Sr}87Sr as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential ggg factor in 87Sr^{87}\mathrm{Sr}87Sr is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below ${10}^{\ensuremath{-}17}$ in lattice clocks.
We present experimental results on the influence of magnetic fields and laser polarization on electromagnetically induced transparency (EIT) using Rydberg levels of ^{87} 87 Rb atoms. The measurements are performed in a room temperature vapor cell with two counter-propagating laser beams at 480 m and 780 m in a ladder-type energy level scheme. We measure the EIT spectrum of a range of ns_{1/2} n s 1 / 2 Rydberg states for n=19-27 n = 19 − 27 , where the hyperfine structure can still be resolved. Our measurements span the range of magnetic fields from the low field linear Zeeman regime to the high field Paschen-Back regimes. The observed spectra are very sensitive to small changes in magnetic fields and the polarization of the laser beams. We model our observations using optical Bloch equations that take into account the full multi-level structure of the atomic states involved and the decoupling of the electronic J J and nuclear I I angular momenta in the Breit-Rabi regime. The numerical model yields excellent agreement with the observations. In addition to EIT related experiments, our results are relevant for experiments involving coherent excitation to Rydberg levels in the presence of magnetic fields.
Rydberg interactions of trapped alkali-metal atoms are used widely to facilitate quantum gate operations in quantum processors and repeaters. In most laboratory realizations using this protocol, the Rydberg states are repelled by the trapping laser fields, requiring that the fields be turned off during gate operations. Here we create a quasi-two-level system in a regime of Rydberg excitation blockade for a mesoscopic Rb ensemble of several hundred atoms confined in a magic-wavelength optical lattice. We observe many-body Rabi oscillations between the ground and collective Rydberg state. In addition we use Ramsey interference techniques to obtain the light shifts of both the lower and upper states of the collective qubit. Whereas the coupling producing the Rabi oscillations is enhanced by a factor of sqrt[N], there is no corresponding enhancement for the light shifts. We derive an effective two-level model which is in good agreement with our observations. Trapped Rydberg qubits and an effective two-level description are expected to have broad applicability for studies of quantum simulation and networking using collective encoding in ensembles of neutral atoms.