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Physical Review B

Two-dimensional Fourier spectroscopy applied to electron-phonon correlations in quantum well intersubband systems

Thi Uyen-Khanh Dang, Carsten Weber, Sebastian Eiser, Andreas Knorr, Marten Richter

Published Oct 9, 2012• 6 citations
Publisher

Abstract

Two-dimensional photon echo spectroscopy allows one to track relaxation and correlation processes in optically excited nanostructures. We analyze such spectra for intersubband transitions in an $n$-doped GaAs/Al${}_{0.35}$Ga${}_{0.65}$As single quantum well. Focusing on electron-longitudinal optical phonon interaction in a non-Markovian treatment, the carrier dynamics in the conduction subbands are investigated in the low density regime. Our results provide detailed information about the temporal evolution of electron-phonon correlations in the two-dimensional frequency spectrum.

DOI
10.1103/physrevb.86.155306

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Two-dimensional photon echo spectroscopy allows one to track relaxation and correlation processes in optically excited nanostructures. We analyze such spectra for intersubband transitions in an nnn-doped GaAs/Al0.35{}_{0.35}0.35​Ga0.65{}_{0.65}0.65​As single quantum well. Focusing on electron-longitudinal optical phonon interaction in a non-Markovian treatment, the carrier dynamics in the conduction subbands are investigated in the low density regime. Our results provide detailed information about the temporal evolution of electron-phonon correlations in the two-dimensional frequency spectrum.
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo-dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and the importance of coherence for Rabi oscillations is investigated. The optically induced charge dynamics is discussed with respect to coherent effects. Calculations of the electronic density and pump-probe signals within a microscopic theory of dephasing show coherent transport effects such as gain oscillations, in agreement with recent experimental results.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.
We present results for two coherent control schemes in semiconductor heterostructures obtained within Boltzmann- Bloch equations. The latter are obtained from Dyson's equation within the Keldysh nonequilibrium Green's function approach and allow a microscopic analysis of coherent control schemes in semiconductors. Here we focus on the coherent control of optical gain and longitudinal optical photon emission rates in intersubband transitions in a three-subband model of a biased asymmetric double well. We show that by coupling the two energetically close subbands with a coherent microwave field, we can induce coherence into the carriers in the double well, thus manipulating intersubband transitions. By adjusting the phase of the microwave field, we can achieve significant modification to the gain spectra for light pulses shorter than the period of the low frequency intersubband polarization. Similarly, LO- phonon induced intersubband transitions can be controlled due to quantum interference between electron-lattice and electron-light interactions.
Electronic structure and dynamics are captured by optical 2D-Fourier-transform (2DFT) spectroscopy, which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. These Fourier-transformed spectra separate and isolate overlapping and competing contributions to the coherent response. We have developed an ultra-stable platform consisting of nested interferometers with active phase control, allowing for exploration of single- and two-quantum coherences. Phase-resolved spectra are retrieved by all-optical determination of experimental phase ambiguities. GaAs quantum wells show suppression of many-body interactions in cross-linear polarized 2DFT spectra and many-body two-quantum coherences. Potassium vapor also shows unexpected two-quantum coherences.