Abstract
We present a theoretical analysis of the coherent response of quantum wells to one or two short optical pulses. A bosonic description is used for the two physically different cases of undoped and doped systems. Coherent-control and optical beat experiments in intrinsic systems are studied in terms of the induced electrical polarisation associated with non-interacting excitons. In the case of a doped quantum well, we use a simple bosonisation procedure to show that the non-linear response presents exactly the same Fermi edge singularity as the well established one in linear response.
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If the probability density is approximated by a gaussian, \( {\left| {{c_{\xi,\alpha,M}}({{\mathbf{k}}_{\mathbf{L}}})} \right|^2}{{d\xi } \mathord{\left/ {\vphantom {{d\xi } {d{\omega _\xi }}}} \right. \kern-\nulldelimiterspace} {d{\omega _\xi }}} = {{{e^{ - {{[({\omega_{\xi,\alpha }} - {\omega _\alpha })/{\Gamma _\alpha }]}^2}}}} \mathord{\left/ {\vphantom {{{e^{ - {{[({\omega _{\xi,\alpha }} - {\omega _\alpha })/{\Gamma _\alpha }]}^2}}}} {\Gamma _\alpha ^2}}} \right. \kern-\nulldelimiterspace} {\Gamma _\alpha ^2}}, \) one obtains \( {A^G}({\mathbf{\tau }}) = {e^{ - {{({\tau \mathord{\left/ {\vphantom {\tau {{T_2}}}} \right. \kern-\nulldelimiterspace} {{T_2}}})}^2}}} \) Where \( {T_2} = \sqrt {2\Delta {t^2} + {4 \mathord{\left/ {\vphantom {4 {{\Gamma ^2}}}} \right. \kern-\nulldelimiterspace} {{\Gamma ^2}}}}. \)
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Fernández-Rossier, J., Porras, D., Tejedor, C., Merlin, R. (2000). Coherent Response to Optical Pulses in Quantum Wells. In: Sadowski, M.L., Potemski, M., Grynberg, M. (eds) Optical Properties of Semiconductor Nanostructures. NATO Science Series, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4158-1_15
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DOI: https://doi.org/10.1007/978-94-011-4158-1_15
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