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arXiv:0704.0340

Phonon-mediated decay of an atom in a surface-induced potential

Fam Le Kien, Subhasish Dutta Gupta, K. Hakuta

Published Apr 3, 2007• 0 citations
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Abstract

We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with temperature in the range from 100 $μ$K to 400 $μ$K in the vicinity of a silica surface with temperature of 300 K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.

DOI
10.48550/arxiv.0704.0340

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We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with temperature in the range from 100 μμμK to 400 μμμK in the vicinity of a silica surface with temperature of 300 K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.
We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with a temperature in the range from $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}400\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in the vicinity of a silica surface with a temperature of 300K300\phantom{\rule{0.3em}{0ex}}\mathrm{K}300K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.
We study spontaneous radiative decay of translational levels of an atom in the vicinity of a semi-infinite dielectric. We systematically derive the microscopic dynamical equations for the spontaneous decay process. We calculate analytically and numerically the radiative linewidths and the spontaneous transition rates for the translational levels. The roles of the interference between the emitted and reflected fields and of the transmission into the evanescent modes are clearly identified. Our numerical calculations for the silica-cesium interaction show that the radiative linewidths of the bound excited levels with large enough but not too large vibrational quantum numbers are moderately enhanced by the emission into the evanescent modes and those for the deep bound levels are substantially reduced by the surface-induced redshift of the transition frequency.
Using the Dirac–Frenkel variational principle, a time-dependent description of the dynamics of a two-level system coupled to a bosonic bath is formulated. The method is applied to the case of a gas of cold atoms adsorbing to an elastic membrane at a finite temperature via phonon creation. The time-dependence of the system state is analytically calculated using Laplace transform methods, and a closed-form expression for the transition rate is obtained. Atoms in the gas transition to the adsorbed state through a resonance that has contributions from a distribution of vibrational modes of the membrane. The resonance can decay with the creation of a phonon to complete the adsorption process. The adsorption rate at low membrane temperatures agrees with the golden rule estimate to the lowest order in the coupling constant for values greater than a critical coupling strength. Below this critical coupling strength, the adsorption rate is exponentially suppressed by a phonon reduction factor whose exponent diverges with increasing adsorbent size. The rate changes discontinuously with coupling strength for low temperature membranes, and the magnitude of the discontinuity decreases with increasing temperature. These variational results suggest the quantum adsorption model may contain a first-order quantum phase transition.
Adsorbed atoms on the surface of a harmonic lattice are immersed in a strong laser field. The optical Bloch equations are derived, which include the thermal relaxation and the coherent excitation of the adbond. This is accomplished by a transformation to dressed states, which diagonalizes the interaction with the laser. The single-phonon couplings are then understood as transitions between dressed states. The radiative contributions for arbitrarily strong fields are obtained in the master equation, and it is shown that the coherences with respect to the dressed states decay exponentially, due to the phonon relaxation. General properties of the competing phonon-induced redistribution and optical excitation of the level populations are presented, and exemplified by an explicit elaboration of a three-level system. The results are amenable to analytical evaluation once the interaction potential is prescribed, and extensions of the approach to include multiphonon processes are straightforward.
An atom, bounded to the surface of a crystal; absorbs photons from a strong incident laser field and subsequently emits phonons into the solid. In this paper we study the influence of the laser linewidth on this photon–phonon conversion process. The appearance of coherences obscures the interpretation of the equation of motion in terms of transition rates and prohibits the derivation of a master equation in the transient region. The absorbed energy from the driving field, which is assumed to be resonant with a set of two levels only, results from the work done by the external field on the transition dipole. In the steady state, the energy absorption from the radiation field equals the energy emission in the phonon field. It is shown that in this long-time limit the coherences can be expressed in terms of the populations, and hence the system is again described by a masterlike equation. Specific aspects of the finite laser bandwidth are pointed out.
Results from four different approximations to the phonon-assisted quantum adsorption rate for cold atoms on a 2D material are compared and contrasted: (1) a loop expansion (LE) based on the atom-phonon coupling, (2) non-crossing approximation (NCA), (3) independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). The SPR method treats the adsorbed atom as a surface polaron where the phonon cloud accompanying the bound atom is a phonon coherent state. We conclude that, of the four approximations considered, only the SPR method gives a divergence-free result in the large membrane regime at finite temperature. The other three methods give an adsorption rate that diverges in the limit of an infinite surface.