Optical reconstruction of collective density matrix of qutrit

TL;DR

This paper introduces an optical method for reconstructing the collective density matrix of atomic ensembles with a ground state of F=1, enabling practical quantum state determination in room-temperature vapors for quantum information applications.

Contribution

The paper presents a novel optical reconstruction technique for the collective density matrix of F=1 atomic ensembles, with explicit formulas and robustness analysis.

Findings

Fidelity exceeds 0.95 under noisy conditions

Method effectively relates optical signals to density matrix elements

Supports practical quantum state reconstruction in real systems

Abstract

Reconstruction of a quantum state is of prime importance for quantum-information science. Specifically, means of efficient determination of a state of atoms of room-temperature vapor may enable applications in quantum computations and cryptography. To step toward such applications, here we present a method of reconstruction of a collective density matrix of an atomic ensemble, consisting of atoms with an $F=1$ ground state. Such a long-lived state is often encountered in real systems (e.g., potassium, sodium, rubidium) and hence may be practically utilized. Our theoretical treatment enables derivation of explicit formulas relating optical signals (polarization rotation and ellipticity change) with specific density-matrix elements. The analysis are supported with numerical simulations, which allows to evaluate fidelity and robustness of the algorithm. The tests show that our algorithm allows to obtain the fidelity exceeded 0.95 even at noisy environment and/or significant atomic manipulation imperfections.