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arxiv:Condensed Matter::Quantum Gases, Condensed Matter::Other, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
This dissertation consists of a theoretical investigation into the transport and coherence properties of indirect excitons in coupled quantum wells (QWs) at helium temperatures. The motion of excitons along the quantum well plane is described through a quantum diffusion equation and the possibility of excitonic cloud formation is studied both due to the natural potential fluctuations and externally applied confining potentials. The photoluminescence (PL) of decaying excitons is used as a probe for their properties such as concentration, effective temperature and optical lifetime. The exciton thermalisation from an initial high energy to the lattice temperature is achieved within their lifetime due to a very effective coupling between the exciton states and a continuum of phonon states, a direct consequence of the relaxation of momentum conservation along the growth direction of a QW. Moreover, the natural spatial separation between electrons and holes prevents their recombination, resulting in long lifetimes. The dynamics of the system of excitons in optically-induced traps is also studied and the numerical solution of the quantum diffusion equation provides an insight into the extremely fast loading times of the trap with a highly degenerate exciton gas. The hierarchy of timescales in such a trap allows for the creation of a cold and dense gas confined within the trap, opening a new route towards the long sought Bose-Einstein Condensation (BEC) in solid state. Finally the issue of exciton spatial coherence is studied and an analytic expression for the coherence function, i.e., the measure of the coherence in a system, is derived. A direct comparison with large coherence lengths recently observed in systems of quantum well excitons and microcavity polaritons is attempted and interesting conclusions are drawn regarding the build up of spontaneous coherence in these systems.
5.1 Formation of Exciton Rings in Quantum W e l ls ................................................
5.2 Optical Trapping of Indirect Excitons ..............................................................
5.3 Spatial Coherence of E xcitons.............................................................................
5.4 Future Work ......................................................................................................... A D erivation of the generalised Einstein relation
A.0.1 The Einstein relation...............................................................................
A.0.2 The generalised Einstein re la tio n ......................................................... B Calculation of th e capture coefficient
B.0.3 The matrix element of the in te ra c tio n ................................................ 1.1 An idealised band structure of a direct-gap sem iconductor............................ 1.2 Energy band diagrams of a coupled quantum well s tr u c tu re ......................... 1.3 The photon and exciton dispersion relations..................................................... 1.4 A schematic diagram of the structure................................................................. 2.1 Spatial patterns of the indirect exciton PL intensity with increasing excitation
power [1]................................................................................................................. 34
2.2 Spatial profiles of the PL signal in the x -y and E -x plane [2] 35
2.3 The effective potential profile as a function of the distance from the current
filament c e n t r e ..................................................................................................... 39
2.4 Comparison between the quantum mass action law and the Saha formula for
the exciton concentration as a function of temperature.................................... 43
2.5 The concentration of electrons around the filament centre for four different
generation rates. At a distance of 10/mi the photogenerated carriers are
scarce and the electron density depends only on the electrically injected carriers. 46
2.6 The effective temperature as a function of the radial distance from the anti-
perature drops the exciton concentration reaches a maximum........................ 47
2.7 Experimental plots of the PL intensity and energy of indirect excitons around
the anti-trap. [3]..................................................................................................... 48
2.8 Theoretical plots of the PL intensity and energy of indirect excitons around
the anti-trap............................................................................................................ 49
2.9 A plot of the actual voltage drop across the QW active region as a function
of the total electric current flowing through the QW........................................ 50
3.1 The profile of the laser intensity used in optical tra p s ..................................... 3.2 Spatial profiles of the measured PL intensity from excitons created by a ring-
shaped laser excitation in the x -y and E x p la n e ........................................... 3.3 Time resolved images of laser-induced trapping of excitons............................ 3.4 Temporal evolution of the exciton density, PL intensity, diffusion coefficient
and ground state occupation number, after the creation of the optical trap. 3.5 Temporal evolution of the calculated exciton concentration in the x-y plane,
after the laser pulse is switched on...................................................................... 3.6 Temporal evolution of the exciton density, PL intensity, diffusion coefficient
and ground state occupation number, after removal of the optical trap. . . . 3.7 Temporal evolution of the calculated exciton concentration in the x-y plane,
after the laser pulse is switched off...................................................................... 3.8 The effective exciton temperature as a function of the radial coordinate for
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