Calculation of quantum escape rates from a metastable well

Alex Edison, Anupam Garg

The Wentzel–Kramers–Brillouin and bounce (path integral) answers for the rate of escape from the ground state of a metastable potential well are both reduced to an expression involving only functionals of the potential, without the need for solving any auxiliary problems. The results are extended to low-lying excited states, and they are applied to the classic cubic parabola and other model potentials. A numerical calculation is done of the escape rate from the ground state of the cubic parabolic well for a variety of barrier heights, and is found to compare well with the WKB result.

Seiji Miyashita

Sudarson Sekhar Sinha, Arnab Ghosh, Deb Shankar Ray

We derive the quantum mechanical description of overdamped Brownian motion of a particle in a spin bath of two-level atoms. The resulting Smoluchowski equation is used to calculate the rate of escape of the particle from a metastable state. At 0 K the decay rate is finite. We show that while quantization enhances the decay rate, higher temperatures induce thermal saturation, resulting in effective a reduction of the system-bath coupling. The role of coherence is examined.

Antonio Defendi, M. Roncadelli

T. Colbert, Bernard L. Wexler

We develop a radiation diffusion equation for an infinite slab geometry where the slab may have different reflectivities on either surface, and for conditions where complete frequency redistribution is valid. Additionally we consider the effect of two competing trapped transitions. Specifically we consider the emission from the thallium 7 $^{2}$${\mathit{S}}_{1/2}$ state to either the 6 $^{2}$${\mathit{P}}_{3/2}$ (metastable state) at 535 nm or 6 $^{2}$${\mathit{P}}_{1/2}$ (ground state) at 378 nm. High densities of the long-lived metastable level can be produced in a number of ways. The escape factors (which are simply related to the decay rates) and excited-atom spatial profiles are calculated for a variety of conditions for the first several natural modes of the system. The spatial modes for this system are asymmetric. The asymmetry can vary dramatically with only small changes in either of the two lower-state densities. The correct description of the spatial modes is critical in order to determine the overall excited-atom profile accurately. For the simpler systems (i.e., a single transition and nonreflective boundaries) usually considered the mode profiles do not change appreciably as the optical depth is changed (given conditions of high optical depth and a single-line broadening mechanism). The fundamental mode decay rate is shown for a fixed metastable-state density as a function of the ground-state density.The dependence of the fundamental mode escape factor for the first resonance transition on the optical depth (or ground-state density) is in general more complicated than for the case of a single trapped transition. For conditions considered here a simple power rule cannot be used to scale the decay rates as a function of line-center optical depth. Also shown is the fundamental mode escape factor as a function of buffer gas pressure for fixed ground- and metastable-state densities. The calculations presented here allow us to model the narrow-bandwidth thallium fluorescence filter. This filter will be discussed in more detail in a separate paper. A thorough review of atomic resonance filters was done by Gelbwachs [IEEE J. Quantum Electron. 24, 1266 (1988)]. We have considered a much broader range of ground- and metastable-state densities than would be practical for efficient filter operation. This is done to illustrate several aspects of the radiation trapping processes.

Roberto Cristiano, Luigi Frunzio, Yurii N. Ovchinnikov +1 more