Quantum control and measurement of atomic spins in polarization spectroscopy

TL;DR

This paper explores how polarization spectroscopy enables simultaneous quantum control and measurement of atomic spins, using light-shift interactions for continuous weak measurement and nonlinear spin dynamics.

Contribution

It introduces an irreducible tensor decomposition to connect light polarization with atomic spin moments, unifying control and measurement in atomic spin systems.

Findings

Polarization spectroscopy allows continuous weak measurement of atomic spins.

Light-shift interactions can induce nonlinear spin dynamics and generate unitary transformations.

A unified master equation describes spin dynamics with control, measurement, and photon scattering.

Abstract

Quantum control and measurement are two sides of the same coin. To affect a dynamical map, well-designed time-dependent control fields must be applied to the system of interest. To read out the quantum state, information about the system must be transferred to a probe field. We study a particular example of this dual action in the context of quantum control and measurement of atomic spins through the light-shift interaction with an off-resonant optical probe. By introducing an irreducible tensor decomposition, we identify the coupling of the Stokes vector of the light field with moments of the atomic spin state. This shows how polarization spectroscopy can be used for continuous weak measurement of atomic observables that evolve as a function of time. Simultaneously, the state-dependent light shift induced by the probe field can drive nonlinear dynamics of the spin, and can be used to generate arbitrary unitary transformations on the atoms. We revisit the derivation of the master equation in order to give a unified description of spin dynamics in the presence of both nonlinear dynamics and photon scattering. Based on this formalism, we review applications to quantum control, including the design of state-to-state mappings, and quantum-state reconstruction via continuous weak measurement on a dynamically controlled ensemble.