Collective Photon Assisted Dressing of Atomic Levels by the number $N$ of Correlated Atoms

TL;DR

This paper investigates how collective correlations among atoms, mediated by photon exchange in a cavity, can enhance quantum measurement sensitivities, potentially reaching the Heisenberg limit, through a novel operator describing photon-assisted excitation exchange.

Contribution

It introduces a new operator to describe photon-induced excitation exchange that accounts for energy conservation and collective effects in correlated atomic systems.

Findings

Photon exchange induces collective atomic correlations.

The new operator captures real and virtual photon-assisted interactions.

Potential to reach quantum noise limits in metrology.

Abstract

Enhancement of the sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices requires introducing new physical processes to improve on their present achievements. Many body collective correlations among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As these correlations introduce interference terms in the intensity of the scattering amplitudes, they may enhance the signal as $N(N-1)$ for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of $N^2$ and contribute to better sensitivity in quantum metrology. Moreover atomic correlation may provide quantum noise limit, Heisenberg limit. In the present communication excitation exchange induced by photons in a cavity between two atoms is calculated and clearly exhibits correlation and collective effects. A novel operator is introduced that expresses photon-induced excitation exchange that takes in account energy conservation, $V_{ij}=\hat{a}^\dag\sigma_i\sigma_j^\dag\hat{a}$, $\sigma_i=\left|g\right\rangle_{i}\left\langle e\right|_{i}$ is lowering operator of $i$-th atom, and $\hat{a}^\dag,\hat{a}$ are photon creation and annihilation operators. Here $i$ and $j$ stand for two atoms. This operator describes real or virtual photon assisted dipole-dipole interaction. Moreover, it conserves the total number of excitations in the joint em field and the quantum system. Experimental challenges are suggested.