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arXiv:2404.12429 · Physical Review Research

Effective light-induced Hamiltonian for atoms with large nuclear spin

D. Burba, Hubert Dunikowski, Martin Robert-De-Saint-Vincent, Emilia Witkowska, Gediminas Juzeliūnas

Published Sep 13, 2024• 2 citations
arXivHTMLPDF

Abstract

Ultracold fermionic atoms, having two valence electrons, exhibit a distinctive internal state structure, wherein the nuclear spin becomes decoupled from the electronic degrees of freedom in the ground electronic state. Consequently, the nuclear spin states are well isolated from the environment, rendering these atomic systems an opportune platform for quantum computation and quantum simulations. Coupling with off-resonance light is an essential tool to selectively and coherently manipulate the nuclear spin states. In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. The analysis has been carried out using the Green operator approach and solving the corresponding Dyson equation. Finally, we analyze different scenarios of light configurations which lead to the vector- and tensor-light shifts, as well as the pure spin-orbit coupling for the nuclear spin. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033293

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Ultracold fermionic atoms, having two valence electrons, exhibit a distinctive internal state structure, wherein the nuclear spin becomes decoupled from the electronic degrees of freedom in the ground electronic state. Consequently, the nuclear spin states are well isolated from the environment, rendering these atomic systems an opportune platform for quantum computation and quantum simulations. Coupling with off-resonance light is an essential tool to selectively and coherently manipulate the nuclear spin states. In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. The analysis has been carried out using the Green operator approach and solving the corresponding Dyson equation. Finally, we analyze different scenarios of light configurations which lead to the vector- and tensor-light shifts, as well as the pure spin-orbit coupling for the nuclear spin. Published by the American Physical Society 2024
Among the possible types of magnetic dipole interactions in molecular systems, couplings between nuclear motion and the nuclear spin have probably received the least attention in molecular spectroscopy. Although very small in comparison to effects related to electron spin, this type of hyperfine interaction plays an important role in the NMR spectroscopy of molecular systems. While measurement and prediction of spin-rotation tensors are a common place, vibrationally induced effects still lack a comprehensive description. In this article we develop a generic, theoretical framework that is well embedded in modern electronic structure theory and inspired by the Breit-Pauli Hamiltonian for electronic interactions, distinguishing between nuclear spin-orbit and spin-other-orbit contributions. We show that the interaction of nuclear spins with pseudorotational excitations of highly symmetric molecules may lead to experimentally accessible hyperfine splittings in NMR spectra, triggered by infrared light.
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We study laser induced spin-orbit (SO) coupling in cold atom systems where lasers couple three internal states to a pair of excited states, in a double tripod topology. Proper choice of laser amplitudes and phases produces a Hamiltonian with a doubly degenerate ground state separated from the remaining "excited" eigenstates by gaps determined by the Rabi frequencies of the atom-light coupling. After eliminating the excited states with a Born- Oppenheimer approximation, the Hamiltonian of the remaining two states includes Dresselhaus (or equivalently Rashba) SO coupling. Unlike earlier proposals, here the SO coupled states are the two lowest energy "dressed" spin states and are thus immune to collisional relaxation. Finally, we discuss a specific implementation of our system using Raman transitions between different hyperfine states within the electronic ground state manifold of nuclear spin I = 3/2 alkali atoms.
We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium-87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum simulation experiments with s u ( N ) -symmetric matter. By controlling the resonance conditions of Raman transitions with a tensor light shift, we can perform rotations within a restricted Hilbert space of two isolated spin states among the 2 F + 1 = 10 possible states. These manipulations correspond to engineering unitary operations derived from generators of the s u ( N ) algebra beyond what can be done by simple spin precession. We present Ramsey interferometers involving an isolated pair of Zeeman states with no measurable decoherence after 3 s. We also demonstrate that one can harness the large spin degrees of freedom as a qudit resource by implementing two interferometer schemes over four states. The first scheme senses in parallel multiple external fields acting on the atoms, and the second scheme simultaneously measures multiple observables of a collective atomic state—including noncommuting ones. Engineering unitary transformations of the large spin driven by other generators than the usual spin- F representation of the s u ( 2 ) group offers new possibilities from the point of view of quantum metrology and quantum many-body physics, notably for the quantum simulation of large-spin s u ( N ) -symmetric quantum magnetism with fermionic alkaline-earth atoms.
Abstract We derive the semiclassical evolution equations for a system consisting of helium-3 atoms in the 2 3 S metastable state interacting with a light field far-detuned from the 2 3 S − 2 3 P transition, in the presence of metastability exchange collisions with ground state helium atoms and a static magnetic field. For two configurations, each corresponding to a particular choice of atom–light detuning in which the contribution of either the metastable level F = 1 / 2 or F = 3 / 2 is dominant, we derive a simple model of three coupled collective spins from which we can analytically extract an effective coupling constant between the collective nuclear spin and light. In these two configurations, we compare the predictions of our simplified model with the full model.
Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.