[Paper Review] Dynamical suppression of radiative decay via atomic deflection by a standing light wave

Maxim A. Efremov, М. В. Федоров+2 more|ArXiv.org|Sep 25, 2002

Quantum optics and atomic interactions5 references4 citations

TL;DR

This paper investigates radiative decay dynamics of atoms scattered by a resonant standing light wave under strong Rabi coupling and normal incidence. It demonstrates that scattering induces dynamical suppression of Rabi oscillations and leads to non-exponential, power-law decay of atomic populations due to position-dependent decay rate modulation, contrasting with standard exponential decay in two-level systems.

ABSTRACT

We consider the radiative decay of atoms scattered by a resonant standing light wave. Scattering is shown to suppress the Rabi oscillations and to slow down the atomic radiative decay giving rise to a power law behavior of the time-dependent level populations rather than the exponential one.

Motivation & Objective

• To investigate radiative decay dynamics of atoms in a resonant standing light wave under strong Rabi coupling and normal incidence, beyond the weak-scattering Bragg regime.
• To understand how scattering affects Rabi oscillations and decay kinetics in systems with a wide excited level decaying predominantly to nonresonant levels.
• To identify the mechanism behind non-exponential decay behavior and suppression of Rabi oscillations in the diffraction regime of atomic scattering.
• To establish a theoretical framework linking position-dependent decay rates and quasienergy level structure to the observed power-law decay tails.
• To compare the dynamics in a standing wave to a pure two-level system with doubled field strength, highlighting scattering-induced modifications.

Proposed method

• Formulate a two-component Schrödinger-like equation for the metastable and excited state wave functions, incorporating the standing light wave potential via the rotating wave approximation.
• Model the system as a time-dependent Hamiltonian with position-dependent Rabi coupling $ \Omega \cos(kx) $, leading to a quasienergy spectrum with spatially varying widths.
• Use a basis expansion in momentum states to describe the scattered atomic beams, decomposing the total population into contributions from different diffraction orders.
• Analyze the time evolution of total populations $ W_{\text{tot}}^{(m)}(t) $ and $ W_{\text{tot}}^{(e)}(t) $ by summing over individual diffraction channels, each with distinct oscillation frequencies.
• Derive asymptotic expressions for long-time decay behavior, showing power-law dependence $ \sim t^{-3} $ for the total populations.
• Interpret the suppression of Rabi oscillations as a result of inhomogeneous broadening from the summation of oscillations with different periods across diffraction beams.

Experimental results

Research questions

• RQ1 How does strong Rabi coupling in the normal-incidence diffraction regime alter the radiative decay dynamics of atoms in a standing light wave?
• RQ2 What causes the suppression of Rabi oscillations in scattered atoms compared to a pure two-level system?
• RQ3 Why does the total population of metastable and excited states exhibit power-law decay instead of exponential decay?
• RQ4 How does the position-dependent modulation of the decay rate by the standing wave influence the quasienergy level structure and decay kinetics?
• RQ5 Can the observed non-exponential decay be explained by the superposition of exponentially decaying components with spatially varying decay rates?

Key findings

• The total populations of both metastable and excited states decay as $ t^{-3} $ at long times, indicating a power-law behavior rather than the standard exponential decay.
• Rabi oscillations in the scattered atomic beam are strongly suppressed due to the incoherent summation of oscillations with different periods across multiple diffraction channels.
• The suppression of Rabi oscillations arises from an effective inhomogeneous broadening effect caused by the spatially varying coupling in the standing wave.
• The decay rate of quasienergy levels becomes position-dependent, with widths approaching zero at $ x = \pi/2k $, leading to non-exponential decay through superposition of $ x $-dependent exponential decays.
• The system exhibits a transition from discrete-level Rabi oscillations ($ \Gamma t \lesssim 1 $) to quasi-continuum decay ($ \Gamma t \gg 1 $), with the latter dominating at long times.
• The results are robust under strong Rabi coupling ($ |\Omega| \gg \Gamma $) and are consistent with experimental conditions similar to those in Ar* experiments, suggesting observability in current setups with modifications for normal incidence and strong coupling.