Enhancement of activated decay of metastable states by resonant pumping

Abstract

We consider the effect of a high-frequency pumping ℰ cosωt on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequencyω(E) is assumed to be weak on the scale of thermal energy,ω′_E(0)T∼ω(0)T/V₀ ≪(0)[ω′_E(0) is the derivative ofω(E) atE= 0,V ₀ is the barrier height,V ₀ ≫ T]. The quadratic-in-ℰ contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, whenω = nω(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦ω-ω(0)¦ ∼γ and γ is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v≡ω′ _E (0)T/γ, and the resonance mismatch,δ ≡ [ω —ω(0)]/γ. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ⁻¹. In this regime, the dependence onδ is stepwise: the pumping contribution is large for vδ > 0 and small for vδ < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs ofδ andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.