Fluorescent spectra of an intensely-driven harmonic oscillator

Abstract We investigate the transient and stationary physical spectra of scattered radiation from a single quantized harmonic oscillator (HO) of frequency ω o , which is resonantly driven by an intense driving field of real (amplitude) strength Ω ∼ ω o and damped in a Markovian broadband radiation reservoir. The influence of such an intense field combined with manipulative spectral reservoir parameters results in field strength enhancement and a phase shift gain: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo mathvariant="normal">Ω</mml:mo> <mml:mo>→</mml:mo> <mml:mo mathvariant="normal">Ω</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msqrt> <mml:msup> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="false">′</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> is the spectral rate of variation of the damping constant at resonance. This in turn leads to induced coherence in the average amplitude of the HO. Two cases of spectral distribution of the radiation reservoir are considered: the Ohmic power law and the Lorentz-Drude law. The spectral components of the scattered radiation in the transient and stationary regimes are identified analytically and computationally, and comparison is made with the non-intense driving field case (Ω ≪ ω o ). The stationary spectrum is a symmetric Lorentzian of weight dependent on the reservoir spectral parameters and of enhanced value compared with the non-intense field case. The transient spectrum is composed of different lineshapes (Lorentzian, narrowed-Lorentzian, and dispersive) of oscillatory decaying weights. Interference of these transient-spectral components is initiated and caused by both types of non-zero coherence, namely the initial coherence of the HO and the induced coherence in the intense field case, and induces asymmetric side oscillations of amplitude dependent on the reservoir spectral parameters. The present results for the fluorescent spectra of intensely-driven HO and its dependence on the environmental radiation reservoir spectral structure are adequately fitted for intensely driven collective Rydberg atomic systems, as a ‘single site’ atomic sample, O ( μm ), and behaves as a single quantized HO.