Eliade Stefanescu - Master equation and conversion of environmental heat into coherent electromagnetic energy

Version 1

      Publication Details (including relevant citation   information):

      J. Prog. Quantum Electron. 34 (2010) 349-408


      We derive a non-Markovian master equation for the     long-time dynamics of a system of Fermions interacting with a   coherent   electromagnetic field, in an environment of   other Fermions, Bosons, and free   electromagnetic   field. This equation is applied to a superradiant   p–i–n   semiconductor heterostructure with quantum dots   in a Fabry–Perot cavity, we   recently proposed for   converting environmental heat into coherent     electromagnetic energy. While a current is injected in the   device, a   superradiant field is generated by quantum   transitions in quantum dots,   through the very thin   i-layers. Dissipation is described by correlated     transitions of the system and environment particles, transitions   of the system   particles induced by the thermal   fluctuations of the self-consistent field of   the   environment particles, and non-local in time effects of   these   fluctuations. We show that, for a finite   spectrum of states and a sufficiently   weak   dissipative coupling, this equation preserves the positivity of   the   density matrix during the whole evolution of the   system. The preservation of   the positivity is also   guaranteed in the rotating-wave approximation. For a     rather short fluctuation time on the scale of the system   dynamics, these   fluctuations tend to wash out the   non-Markovian integral in a long-time   evolution, this   integral remaining significant only during a rather   short   memory time. We derive explicit expressions of   the superradiant power for two   possible   configurations of the superradiant device: (1) a longitudinal   device,   with the superradiant mode propagating in the   direction of the injected   current, i.e.   perpendicularly to the semiconductor structure, and (2)   a   transversal device, with the superradiant mode   propagating perpendicularly to   the injected current,   i.e. in the plane of the semiconductor structure. The     active electrons, tunneling through the i-zone between the two   quantum dot   arrays, are coupled to a coherent   superradiant mode, and to a dissipative   environment   including four components, namely: (1) the quasi-free electrons   of   the conduction n-region, (2) the quasi-free holes   of the conduction p-region,   (3) the vibrations of the   crystal lattice, and (4) the free electromagnetic     field. To diminish the coupling of the active electrons to the   quasi-free   conduction electrons and holes, the   quantum dot arrays are separated from the   two n and p   conduction regions by potential barriers, which bound the   two-well   potential corresponding to these arrays. We   obtain analytical expressions of   the dissipation   coefficients, which include simple dependences on the     parameters of the semiconductor device, and are transparent to   physical   interpretations. We describe the dynamics of   the system by non-Markovian   optical equations with   additional terms for the current injection, the     radiation of the field, and the dissipative processes. We study   the dependence   of the dissipative coefficients on the   physical parameters of the system, and   the operation   performances as functions of these parameters. We show that   the   decay rate of the superradiant electrons due to   the coupling to the conduction   electrons and holes is   lower than the decay rate due to the coupling to the     crystal vibrations, while the decay due to the coupling to the   free   electromagnetic field is quite negligible.   According to the non-Markovian term   arising in the   optical equations, the system dynamics is   significantly   influenced by the thermal fluctuations   of the self- consistent field of the   quasi-free   electrons and holes in the conduction regions n and   p,   respectively. We study the dependence of the   superradiant power on the   injected current, and the   effects of the non-Markovian fluctuations. In     comparison with a longitudinal device, a transversal device has a   lower   increase of the superradiant power with the   injected current, but also a lower   threshold current   and a lesser sensitivity to thermal fluctuations.

      Address (URL): http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJD-50F8BPN-1&_user=1 0&_coverDate=11%2F30%2F2010&_rdoc=1&_fmt=high&_orig=browse&_origin=browse&_sort= d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=87f373b0658579 cf32ebc00dda577ef3