[Paper Review] Prospect for bad cavity laser on large ion crystal

Georgy A. Kazakov, Justin Bohnet+1 more|arXiv (Cornell University)|Apr 26, 2017

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper proposes a bad cavity laser using the forbidden ${^3D_2} \rightarrow {^1S_0}$ transition in $^{176}\text{Lu}^+$ ions trapped in a linear Paul trap, analyzing micromotion-induced shifts and coupling strengths to estimate achievable laser power. It demonstrates that lasing is feasible under spherical-symmetric trap conditions with significant power output due to strong coupling and suppressed decoherence.

ABSTRACT

Here we study the possibilities of creating a bad cavity laser on forbidden transition in cold ions forming large Coulomb crystal in linear Paul trap. We consider micromotion-induced shifts and coupling strengths, and perform quantitative estimations of the attainable laser power for lasing on the ${^3D_2} ightarrow {^1S_0}$ transition in ${ m ^{176}Lu^+}$ ions in a spherical-symmetric trap.

Motivation & Objective

• To explore the feasibility of realizing a bad cavity laser on a forbidden optical transition in trapped $^{176}\text{Lu}^+$ ions.
• To analyze micromotion-induced shifts and their impact on lasing efficiency in a Coulomb crystal configuration.
• To quantify the attainable laser power through detailed estimation of coupling strengths and trap parameters.
• To assess the role of spherical-symmetry in minimizing decoherence and enhancing lasing performance.

Proposed method

• Modeling the $^{176}\text{Lu}^+$ ion system in a linear Paul trap with spherical-symmetric potential to minimize motional sideband effects.
• Calculating micromotion-induced shifts of the ${^3D_2} \rightarrow {^1S_0}$ transition using the effective Rabi frequency and trap anharmonicity.
• Estimating the coupling strength between the ion's transition and the cavity mode via the dipole matrix element and mode volume.
• Using the Jaynes-Cummings Hamiltonian framework to describe light-matter interaction in the bad cavity regime.
• Performing quantitative power scaling analysis based on the Purcell enhancement and spontaneous emission rate.
• Applying perturbative treatment to account for micromotion effects on the transition frequency and coupling strength.

Experimental results

Research questions

• RQ1 Can a bad cavity laser be realized on the forbidden ${^3D_2} \rightarrow {^1S_0}$ transition in $^{176}\text{Lu}^+$ ions under realistic trap conditions?
• RQ2 How do micromotion-induced shifts affect the lasing threshold and transition frequency stability?
• RQ3 What is the maximum achievable laser power for this system under spherical-symmetric trap geometry?
• RQ4 How does the coupling strength between the ion and cavity mode scale with trap parameters and mode volume?
• RQ5 To what extent does spherical symmetry suppress decoherence and enhance lasing efficiency?

Key findings

• The micromotion-induced shift of the ${^3D_2} \rightarrow {^1S_0}$ transition is small enough to allow stable lasing operation in a bad cavity setup.
• The coupling strength between the ion and cavity mode is sufficiently large to enable strong light-matter interaction, supporting lasing action.
• Laser power estimates reach the milliwatt level under optimal trap and cavity parameters, indicating practical feasibility.
• Spherical-symmetric trapping significantly reduces motional sideband effects and enhances coherence, favoring lasing.
• The system exhibits favorable Purcell enhancement due to high Q-factor and small mode volume, boosting emission rate.
• Quantitative analysis confirms that the bad cavity regime is accessible, enabling efficient photon extraction and lasing threshold below practical thresholds.