Effects of Non-idealities and Quantization of the Center of Mass Motion on Symmetric and Asymmetric Collective States in a Collective State Atomic Interferometer

TL;DR

This paper analyzes how non-idealities and quantization of atomic center of mass motion affect the behavior of collective states in a collective state atomic interferometer, aiding in its optimization and understanding.

Contribution

It formulates the properties of collective states under non-idealities and quantum center of mass motion, extending the understanding of COSAIN dynamics.

Findings

Generalized collective states can be constructed with localized atomic wave packets.

Non-idealities significantly influence the evolution of collective states.

Quantization of center of mass motion is compatible with collective state descriptions.

Abstract

We investigate the behavior of an ensemble of $N$ non-interacting, identical atoms, excited by a laser. In general, the $i$-th atom sees a Rabi frequency $\Omega_i$, an initial position dependent laser phase $\phi_i$, and a motion induced Doppler shift of $\delta_i$. When $\Omega_i$ or $\delta_i$ is distinct for each atom, the system evolves into a superposition of $2^N$ intercoupled states, of which there are $N+1$ symmetric and $(2^N-(N+1))$ asymmetric collective states. For a collective state atomic interferometer (COSAIN) we recently proposed, it is important to understand the behavior of all the collective states under various conditions. In this paper, we show how to formulate the properties of these states under various non-idealities, and use this formulation to understand the dynamics thereof. We also consider the effect of treating the center of mass degree of freedom of the atoms quantum mechanically on the description of the collective states, illustrating that it is indeed possible to construct a generalized collective state, as needed for the COSAIN, when each atom is assumed to be in a localized wave packet. The analysis presented in this paper is important for understanding the dynamics of the COSAIN, and will help advance the analysis and optimization of spin squeezing in the presence of practically unavoidable non-idealities as well as in the domain where the center of mass motion of the atoms is quantized.