[Paper Review] Rabi oscillation in a quantum cavity

Pierre-Olivier Guimond, Alexandre Roulet+2 more|arXiv (Cornell University)|May 29, 2015

Mechanical and Optical Resonators3 citations

TL;DR

This paper investigates Rabi oscillations in a quantum cavity where mirrors are formed by atomic chains in a one-dimensional waveguide, demonstrating that non-Markovian dynamics—accounting for finite photon travel time between mirrors—are essential for observing Rabi oscillations analogous to those in high-finesse classical cavities. The key result is that the cavity's Rabi frequency and photon loss rate depend critically on the delay-induced non-Markovian behavior.

ABSTRACT

We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the collective response of the atomic chain. Therefore, the delay must be taken into account and the dynamics of the problem is inherently non-Markovian. Parameters of interest such as the Rabi frequency and the cavity loss rate due to photon leakage through the mirrors are obtained.

Motivation & Objective

• To study Rabi oscillations in a quantum cavity with mirrors formed by atomic chains in a 1D waveguide.
• To identify the limitations of the Markov approximation in modeling such systems.
• To determine the conditions under which Rabi oscillations resemble those in high-finesse classical cavities.
• To derive key cavity parameters such as Rabi frequency and photon leakage rate in the non-Markovian regime.

Proposed method

• Model the cavity as a system where mirrors are formed by atomic chains trapped along a 1D waveguide.
• Use a non-Markovian approach to account for finite photon travel time between mirrors.
• Analyze the collective response of the atomic chains to light fields in the cavity.
• Derive expressions for the Rabi frequency and cavity loss rate from the non-Markovian dynamics.
• Compare results with the Markov approximation to highlight the necessity of delay effects.
• Employ quantum optical techniques to describe photon emission and scattering in the waveguide-mediated cavity.

Experimental results

Research questions

• RQ1 Under what conditions do Rabi oscillations in a waveguide-coupled cavity resemble those in high-finesse classical cavities?
• RQ2 How does the finite travel time of photons between mirrors affect the Rabi oscillation dynamics?
• RQ3 What is the role of the atomic chain's collective response in determining the cavity's effective parameters?
• RQ4 Why does the Markov approximation fail in describing this system's dynamics?
• RQ5 How do the Rabi frequency and photon leakage rate depend on non-Markovian effects?

Key findings

• Rabi oscillations resembling those in high-finesse classical cavities are only achieved when the photon round-trip time exceeds the timescale of the atomic chain's collective response.
• The dynamics are inherently non-Markovian, and neglecting the finite travel time of light leads to incorrect predictions.
• The Rabi frequency and cavity loss rate are derived from the non-Markovian framework, showing dependence on delay and collective atomic response.
• The Markov approximation fails to capture the correct oscillation behavior due to its neglect of time-delay effects.
• The system's behavior is governed by the interplay between atomic coherence and photon propagation delay in the waveguide.