Effective light-induced Hamiltonian for atoms with large nuclear spin

TL;DR

This paper derives an effective Hamiltonian for nuclear spin states in ultra-cold fermionic atoms under off-resonance light, enabling precise control of nuclear spins for quantum applications.

Contribution

It provides a systematic derivation of the effective Hamiltonian including scalar, vector, and tensor light shifts, using the Green operator approach.

Findings

Derived compact expressions for light shifts including hyperfine contributions

Analyzed scenarios leading to vector and tensor light shifts

Explored pure spin-orbit coupling effects on nuclear spins

Abstract

Ultra-cold 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 ultra-cold 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.