Variational approach to atom-membrane dynamics

Dennis Clougherty University of Vermont

The adsorption of cold atoms to a surface differs in many ways from the adsorption of atoms at higher energies. It has been established both theoretically [1] and experimentally [2] that the adsorption rate of cold atoms can be dramatically suppressed in comparison to rates at higher energies by two quantum mechanical effects: (1) quantum reflection of the cold atoms away from the surface, and (2) a phonon orthogonality catastrophe [3] resulting from the surface displacement that accompanies adsorption. The first effect is a single particle phenomenon that depends on the wave mechanics of the cold atoms; the second effect is a many-body phenomenon that results from the behavior of the phonon matrix element between the initial and final states of the surface. In the most extreme case of adsorption on a 2D material, it has been proposed that this phonon reduction factor can completely suppress cold atom adsorption [4].

A time-dependent, nonperturbative description of phonon-assisted cold atom adsorption on a membrane will be presented. Using the Dirac-Frenkel variational principle, closed-form expressions for adsorption rates can be obtained. One strength of this method is that the case of intermediate atom-phonon coupling can be treated where the adsorption rate is found to change discontinuously with atom-phonon coupling strength at low membrane temperatures. The framework presented can be customized in a straightforward way to describe a variety of reactions in the quantum regime. Possible applications of these results to emerging quantum technologies will also be discussed.

[1] Dennis P. Clougherty and W. Kohn, Phys. Rev. B, 46, 4921 (1992).

[2] I. A. Yu, J. M. Doyle, J. C. Sandberg, C. L. Cesar, D. Kleppner, and T. J. Greytak, Phys. Rev. Lett. 71, 1589 (1993).

[3] Dennis P. Clougherty and Yanting Zhang, Phys. Rev. Lett. 109, 120401 (2012).

[4] Dennis P. Clougherty, Phys. Rev. B, 96, 235404 (2017); Sanghita Sengupta and Dennis P. Clougherty, J. Phys.: Conf. Ser., 1148, 012007 (2018).