[Paper Review] Laser operation and Bose-Einstein condensation: analogies and differences

Alessio Chiocchetta, Andrea Gambassi+1 more|arXiv (Cornell University)|Mar 10, 2015

Strong Light-Matter Interactions4 citations

TL;DR

This paper proposes a quantitative criterion based on fluctuation-dissipation relations to distinguish equilibrium from non-equilibrium Bose-Einstein condensation (BEC), applying it to laser operation and photon/polariton BECs. It shows that non-equilibrium systems violate the KMS condition, while effective equilibrium emerges only when absorption-emission cycles are fast compared to losses, with experimental verification feasible via dynamical structure factors.

ABSTRACT

After reviewing the interpretation of laser operation as a non-equilibrium Bose-Einstein condensation phase transition, we illustrate the novel features arising from the non-equilibrium nature of photon and polariton Bose-Einstein condensates recently observed in experiments. We then proposea quantitative criterion to experimentally assess the equilibrium vs. non-equilibrium nature of a specific condensation process, based on fluctuation-dissipation relations. The power of this criterion is illustrated on two models which shows very different behaviours.

Motivation & Objective

• To clarify the conceptual and physical differences between equilibrium Bose-Einstein condensation and non-equilibrium condensation in lasers and photon/polariton systems.
• To develop a quantitative, experimentally accessible criterion to determine whether a condensate arises from equilibrium or non-equilibrium dynamics.
• To analyze how the interplay between pumping, losses, and thermalization rates determines the nature of the stationary state in condensates.
• To demonstrate the criterion’s utility through two model systems: a semi-classical laser model and a non-Markovian photon BEC model.

Proposed method

• Derives the KMS condition for non-equilibrium systems using the full quantum Langevin equation with colored noise and memory kernels.
• Introduces the effective inverse temperature β_eff(ω) from the ratio of structure factors S_bb†(ω)/S_b†b(−ω), which reduces to β in equilibrium.
• Applies the fluctuation-dissipation relation to the photon-cavity system with bath spectral functions ρ±(ω) modeling absorption and emission.
• Uses the Kennard-Stepanov relation to ensure consistency with thermal equilibrium when baths are in thermal contact.
• Analyzes the condition κ + ρ⁻(ω_BEC) = ρ⁺(−ω_BEC) for dynamical stability and KMS violation in the non-equilibrium regime.
• Demonstrates that β_eff(ω) approaches β only in the κ → 0 limit, indicating recovery of equilibrium behavior.

Experimental results

Research questions

• RQ1 Under what conditions does a non-equilibrium condensate in a laser or photon system exhibit effective thermal equilibrium?
• RQ2 How can the equilibrium vs. non-equilibrium nature of a condensate be experimentally diagnosed using dynamical response functions?
• RQ3 What role do repeated absorption-emission cycles play in establishing thermal equilibrium in a photon gas?
• RQ4 How does the violation of the KMS condition signal non-equilibrium dynamics in a condensate?
• RQ5 Can the effective inverse temperature β_eff(ω) serve as a reliable probe of the system's thermodynamic character?

Key findings

• The effective inverse temperature β_eff(ω) derived from structure factors deviates from β in non-equilibrium systems, with deviation vanishing only in the κ → 0 limit.
• The KMS condition is violated in general for non-equilibrium condensates, indicating a breakdown of detailed balance and thermal equilibrium.
• The criterion based on fluctuation-dissipation relations provides a measurable, experimentally feasible way to probe the equilibrium nature of a condensate via its dynamical response.
• In the limit of fast absorption-emission cycles (ρ⁻, ρ⁺ large), the photon gas inherits the thermal state of the dye molecules, recovering the KMS condition and effective equilibrium.
• The model shows that even with a finite loss rate κ, the system can appear thermal if the thermalization rate exceeds the loss rate, but this is not sufficient for full equilibrium.
• The proposed method allows distinguishing between static thermalization (momentum distribution) and dynamical thermalization (fluctuation-dissipation), with the latter being more stringent and experimentally accessible.