[Paper Review] Quantum jumps in a two-level atom

Howard M. Wiseman, Gilman E. S. Toombes|ArXiv.org|Mar 5, 1999

Quantum Information and Cryptography4 references3 citations

TL;DR

This paper investigates quantum jump dynamics in a strongly-driven two-level atom, comparing the dressed atom model with the Teich-Mahler model of stochastic jumps between eigenstates. Using spectral detection and two adaptive homodyne schemes, the authors show that all three measurement methods closely reproduce the dressed state's jump behavior, with errors scaling as (γ/Ω)²/³ and (γ/Ω)², respectively, supporting the role of environment-induced superselection in explaining quantum jumps.

ABSTRACT

A strongly-driven ($Ω>> γ$) 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 $ρ$. 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 $ρ$. 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 $(3/4) (γ/Ω)^{2/3}$, $(1/4) (γ/Ω)^{2}$, and $(3/4) (γ/Ω)^{2}$ respectively. The significance of this result to the program of environmentally-induced superselection is discussed.

Motivation & Objective

• To resolve the contradiction between the dressed state model and the Teich-Mahler model of quantum jumps in a strongly-driven two-level atom.
• To test whether measurement schemes can reproduce the stochastic jump dynamics predicted by the dressed state theory.
• To assess the validity of the Teich-Mahler interpretation of the equilibrium state as an ensemble of individual atoms jumping between eigenstates.
• To evaluate the significance of these results for environmentally-induced superselection in open quantum systems.

Proposed method

• Employing spectral detection using optical filters to measure the emitted field and detect jump-like transitions.
• Implementing two-state jump detection via adaptive homodyne detection to track quantum jumps in real time.
• Applying an orthogonal jumps scheme using another adaptive homodyne method to compare jump dynamics.
• Analyzing the fidelity of each detection method to the idealized dressed state model using perturbative error estimates.
• Deriving error bounds of order (3/4)(γ/Ω)²/³, (1/4)(γ/Ω)², and (3/4)(γ/Ω)² for the three schemes, respectively.
• Using the dressed state basis as a reference to compare the stochastic jump behavior of individual atoms under different measurement protocols.

Experimental results

Research questions

• RQ1 Can spectral detection reproduce the quantum jump dynamics of the dressed state model in a strongly-driven two-level atom?
• RQ2 How accurately can adaptive homodyne detection schemes mimic the stochastic jumps predicted by the dressed state theory?
• RQ3 What is the quantitative error between the measured jump dynamics and the ideal dressed state model across different detection schemes?
• RQ4 Do the measurement schemes support the Teich-Mahler model's interpretation of the equilibrium state as an ensemble of jumping atoms?
• RQ5 What implications do these results have for the theory of environmentally-induced superselection in quantum measurement?

Key findings

• Spectral detection closely mimics the dressed state's jump dynamics with an error of order (3/4)(γ/Ω)²/³.
• The two-state jump adaptive homodyne scheme achieves an error of order (1/4)(γ/Ω)² in reproducing the dressed state jump behavior.
• The orthogonal jumps adaptive homodyne scheme also exhibits an error of order (3/4)(γ/Ω)², confirming consistency across detection methods.
• The results support the idea that the equilibrium state of a strongly-driven two-level atom can be understood as arising from continuous quantum jumps between eigenstates, consistent with the Teich-Mahler model.
• The small error terms indicate that measurement-induced backaction can effectively simulate the dynamics of the dressed state, reinforcing the role of environment-induced superselection in explaining quantum jumps.