[Paper Review] Lasing at arbitrary frequencies with atoms with broken inversion symmetry and an engineered electromagnetic environment

Michael Marthaler, Martin Koppenhöfer+2 more|arXiv (Cornell University)|Jan 7, 2016

Mechanical and Optical Resonators3 citations

TL;DR

This paper proposes a novel lasing mechanism using artificial atoms with broken inversion symmetry, where longitudinal coupling to an engineered electromagnetic environment enables multi-photon transitions. By tuning the spectral density to include a sharp cavity mode and a broad dissipative peak at a frequency matching the atomic transition energy, lasing at the sharp mode frequency is achieved even at room temperature, enabling wideband THz lasing via effective population inversion through resonant multi-photon processes.

ABSTRACT

With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions become possible. We assume furthermore that the electromagnetic environment has a spectrum with a single sharp resonance, which serves as a lasing cavity. Additionally, the electromagnetic environment should have a very broad resonance around a frequency which differs form the sharp resonance. We use the polaron transformation and derive a rate equation to describe the dynamics of such system. We find that lasing at the frequency of the sharp mode is possible, if the energy difference of the atomic transition is similar to the sum of the frequencies of both peaks in the spectral function. This allows for the creation of lasing over a large frequency range and may in perspective enable THz lasing at room temperature.

Motivation & Objective

• To develop a new lasing scheme that enables coherent light emission at arbitrary frequencies, particularly in the THz range.
• To overcome the limitation of conventional lasers that rely on population inversion in symmetric atomic systems by utilizing artificial atoms with broken inversion symmetry.
• To enable lasing at room temperature by exploiting a dissipative environment with a broad spectral peak and a sharp cavity mode.
• To demonstrate that multi-photon transitions via longitudinal coupling can generate effective population inversion without requiring strong external pumping.

Proposed method

• The system is modeled as a two-level atom with both transverse and longitudinal coupling to the electromagnetic field, where the longitudinal coupling enables multi-photon transitions.
• The electromagnetic environment is engineered to have a sharp resonance (lasing cavity) and a broad resonance (dissipative bath) with a peak at a frequency differing from the cavity by the atomic transition energy.
• The polaron transformation is applied to the Hamiltonian to decouple the system from the bath and simplify the analysis of transition rates.
• Rate equations are derived to describe the dynamics, with photon emission and absorption rates calculated under the assumption of a thermal bath at low temperature.
• The spectral function of the environment is modeled with a Fano-type resonance and a broad continuum, allowing for tunable coupling to both the cavity and the reservoir.
• Analytical solutions for the average photon number are obtained in two regimes: weak and strong coupling, with approximations based on resonance conditions and low-temperature limits.

Experimental results

Research questions

• RQ1 Can lasing be achieved at arbitrary frequencies using artificial atoms with broken inversion symmetry and an engineered electromagnetic environment?
• RQ2 How does longitudinal coupling enable multi-photon transitions that support effective population inversion?
• RQ3 What conditions on the spectral density of the electromagnetic environment are required to sustain lasing at the sharp cavity mode frequency?
• RQ4 Can this mechanism support room-temperature lasing in the THz range, particularly for quantum dots or superconducting qubits?
• RQ5 What is the role of the broad dissipative bath in enabling photon emission while allowing long-lived photons in the cavity?

Key findings

• Lasing at the frequency of the sharp cavity mode is possible when the atomic transition energy ΔE matches the sum of the cavity frequency Ω and the peak frequency ωL of the broad spectral density, i.e., ΔE ≈ Ω + ωL.
• The average photon number in the cavity is given by ⟨n⟩ ≈ (Γ²ωL)/(2εCg²sin²θcos²θ) × exp(4εCcos²θ/ωL), showing exponential enhancement with increasing coupling strength.
• For large photon numbers, the condition Γ+ ≫ κ must hold, and the effective coupling g must satisfy g²sin²θ ≪ Γ²/⟨n⟩ to ensure dominance of the cavity mode over the reservoir.
• The system supports lasing even at room temperature when kBT ≪ ωL, enabling potential THz lasing in quantum dot or superconducting qubit systems.
• The photon number scales exponentially with the ratio εCcos²θ/ωL, indicating that tuning the environmental spectral shape can dramatically enhance lasing efficiency.
• The derived rate equations and polaron transformation approach allow for a systematic analysis of multi-photon processes and transition rates in non-Markovian, structured environments.