Multilevel Holstein-Primakoff approximation and its application to atomic spin squeezing and ensemble quantum memories

TL;DR

This paper introduces a multilevel Holstein-Primakoff approximation for atomic ensembles, enabling efficient analysis of spin squeezing and quantum memories by describing atoms with collective oscillator modes.

Contribution

It develops a novel multilevel approximation method for atomic ensembles and explores its application to spin squeezing and quantum memory protocols.

Findings

Efficient description of d-level atomic ensembles using d-1 collective oscillators.

Analysis of spin squeezing without interatomic entanglement and via QND measurement.

Impact of squeezing order on final quantum state quality.

Abstract

We show that an ensemble of identical d-level atoms can be efficiently described by d-1 collective oscillator degrees of freedom in the vicinity of a product state with all atoms in the same, but otherwise arbitrary single-particle state. We apply our description to two different kinds of spin squeezing: (i) when each spin-F atom is individually squeezed without creating interatomic entanglement and (ii) when a particular collective atomic oscillator mode is squeezed via quantum non-demolition (QND) measurement and feedback. When combined in sequence, the order of the two methods is relevant in the final degree of squeezing. We also discuss the role of the two kinds of squeezing when multi-sublevel atoms are used as quantum memories for light.