Quantum jumps in a two-level atom

TL;DR

This paper investigates three measurement schemes to observe quantum jumps in a strongly-driven two-level atom, demonstrating their effectiveness in mimicking dressed state dynamics and discussing implications for environment-induced superselection.

Contribution

The study compares three measurement methods for quantum jumps, showing they closely replicate dressed state behavior with quantifiable errors, advancing understanding of quantum measurement dynamics.

Findings

Spectral detection mimics dressed state jumps with error ~ (3/4)(γ/Ω)^{2/3}

Adaptive homodyne detection shows errors ~ (1/4)(γ/Ω)^2

All schemes effectively reproduce quantum jump behavior with small errors

Abstract

A strongly-driven ($\Omega >> \gamma$) two level atom relaxes towards an equilibrium state rho which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $\rho$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed atom theory is also supposed to describe the quantum jumps of an individual atom due to photo-emissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $\rho$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are: spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection) and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed state model, with errors of order $(3/4) (\gamma/\Omega)^{2/3}$, $(1/4) (\gamma/\Omega)^{2}$, and $(3/4) (\gamma/\Omega)^{2}$ respectively. The significance of this result to the program of environmentally-induced superselection is discussed.