Ultrafast Quantum Kinetics of Time-Dependent RPA-Screened Coulomb Scattering

Bányai, L.; Vu, Q. T.; Mieck, B.; Haug, H.

doi:10.1103/physrevlett.81.882

Cited by 127 publications

(81 citation statements)

References 19 publications

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“…The intra-band scattering between quantum-well states is typically in the order of ≈ 100 fs [BIN92a,TRA92,CAM96,KAN96b,BAN98]. As long as this scattering is faster than the charge-carrier exchange between the quantum well and quantum-dots, the quantum well can be assumed to be in quasi-equilibrium with good accuracy:…”

Section: Detailed Balancementioning

confidence: 99%

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

Lingnau

2015

Springer Theses

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In this thesis the dynamics and performance of optoelectronic devices based on semiconductor quantum-dots are investigated.In the first part, the dynamics of quantum-dot lasers under external perturbations is discussed. Using a microscopically based balance equation model that incorporates detailed charge-carrier scattering dynamics and the possibility to describe nonequilibrium between intra-band electronic states, the relaxation oscillations of the quantum-dot laser are investigated. Three qualitatively different dynamic regimes are identified in dependence of the scattering rates -the "constantreservoir" regime for slow scattering, the "overdamped" regime, and the "synchronized" regime for high scattering -characterized by a varying degree of nonequilibrium between the quantum-dot and reservoir states.Important differences to conventional lasers are found in the modulation response and the dynamics in optical injection and feedback setups. Common theoretical models and approaches used to describe these applications are shown to yield inaccurate predictions, especially in the "constant-reservoir" and "overdamped" dynamic regimes. An important consequence is that the amplitude-phase coupling in quantum-dot lasers, commonly described by the α-factor, differs from conventional descriptions due to the desynchronization of gain and refractive index. While the α-factor describes bifurcations of fixed points accurately, it fails in describing dynamic solutions and overestimates the extent of complex dynamics. The observed low sensitivity to optical perturbations in quantum-dot lasers can therefore be attributed partly to the charge-carrier nonequilibrium. Three quantum-dot laser models on different levels of sophistication are presented that can accurately describe the quantum-dot nonequilibrium dynamics.In the second part of the thesis, the performance of quantum-dot semiconductor optical amplifiers is investigated, and two types of applications unique to quantum-dots as active medium are discussed. The ground and excited states of the quantum-dots allow an ultra-broad-band amplification of optical data streams. Amplified signals on the ground-state frequencies are shown to generally exhibit higher quality than on the excited state, due to a lower sensitivity of the groundstate to carrier-density variations. Nevertheless the quantum-dot amplifier is found to allow effective amplification on both frequency ranges. Furthermore, a parameter range is identified that allows for a simultaneous amplification of data signals on the ground and excited state in a counter-propagating setup.The long microscopically polarization dephasing times in quantum-dots are found to enable quantum-coherent interactions on a macroscopic scale at room-temperature. By comparison with experiments, the occurrence of Rabi-oscillations by amplification of ultra-short pulses is demonstrated. Quantum-dot based devices could therefore be used for future applications based on quantum-coherent effects.

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Section: Detailed Balancementioning

confidence: 99%

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

Lingnau

2015

Springer Theses

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“…Further relatively recent studies of nonequilibrium distributions in three dimensional quantum plasmas, both theoretical and experimental, were carried out by Lampin, et al [25] and Bonitz, et al [26], exhibiting enhanced carrier scattering and thermalization. Moreover, Huber, et al [27] observed the temporal development of the dielectric function in a laser-excited semiconductor experimentally, which was verified theoretically in a nonequilibrium extension of the RPA by Banyai, et al [28] In regard to the finite temperature dependence of RPA dielectric functions, there are good discussions in the relatively recent books of Kremp, et al [29], and of Bonitz [30]. This particular subject reaches back to the "grandfather" paper of Martin and Schwinger [5] (in which the temperature dependence is implicit in the Fermi/Bose distribution function) and, in the case of a magnetic field, to the early papers of Horing [9] for 3D Landau quantized solid state plasmas, and of Horing & Yildiz [16,17] for the corresponding 2D case.…”

Section: Discussionmentioning

confidence: 90%

Quantum Theory of Solid State Plasma Dielectric Response

Horing

2010

Contrib. Plasma Phys.

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We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired "second quantized" creation and annhilation field operators of interacting quantum many-body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron-hole pair excitations and plasmons.

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“…This has resulted in a simple analytic formula for the time dependence of the dielectric function. Subtracting this gross feature from the data allows one to extract the effects which are due to higher-order correlations and which have to be simulated by quantum kinetic theory [7,8,9,10] and response functions with approximations beyond the mean field [17]. These treatments are numerically demanding such that analytic expressions for the time dependence of some variables [18] are useful for controlling the numerics.…”

Section: (T T − T ) (15)mentioning

confidence: 99%

“…For an overview over theoretical and experimental work see [5,6]. Such ultrafast excitations in semiconductors have been satisfactorily described by calculating nonequilibrium Green's functions [7,8]. This approach allows one to describe the formation of collective modes [3,9] and even exciton population inversions [10].…”

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confidence: 99%

Femtosecond formation of collective modes due to mean-field fluctuations

2005

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Starting from a quantum kinetic equation including the mean field and a conserving relaxationtime approximation we derive an analytic formula which describes the time dependence of the dielectric function in a plasma created by a short intense laser pulse. This formula reproduces universal features of the formation of collective modes seen in recent experimental data of femtosecond spectroscopy. The presented formula offers a tremendous simplification for the description of the formation of quasiparticle features in interacting systems. Numerical demanding treatments can now be focused on effects beyond these gross features found here to be describable analytically.PACS numbers: 71.45. Gm, 78.47.+p, 42.65.Re, 82.53.Mj The last ten years have been characterized by an enormous activity about ultrafast excitations in semiconductors, clusters, or plasmas by ultrashort laser pulses. The femtosecond spectroscopy has opened the exciting possibility to observe directly the formation of collective modes and quasiparticles in interacting many-body systems. This formation is reflected in the time dependence of the dielectric function [1, 2, 3] or terahertz emission [4]. For an overview over theoretical and experimental work see [5,6]. Such ultrafast excitations in semiconductors have been satisfactorily described by calculating nonequilibrium Green's functions [7,8]. This approach allows one to describe the formation of collective modes [3,9] and even exciton population inversions [10].The experimental data in semiconductors like GaAs [2] or InP [3] reveal similar features. These features are explained by several numerically demanding calculations. Since some common features are robust, i.e., independent of the actual used material parameters, it should be possible to describe them by a simple theory. The origin of such robust features likely rests in the short-or transienttime behavior itself. At short times higher-order correlations have no time yet to develop, therefore the dynamics is controlled exclusively by mean-field forces.Based on the mean-field character of the short-time evolution we intend to derive a time-dependent response function from the mean-field linear response. We will start from a conserving relaxation-time approximation which dates back to an idea of Mermin [11,12]. Our aim is a simple analytic formula suitable for fits of experimental data.The electron motion is controlled by the kinetic energŷ E, the external perturbationV ext and the induced meanfield potentialV ind . The corresponding kinetic equation for the one-particle reduced density matrixρ readṡwith the relaxation time τ and a local equilibrium density matrixρ l.e. determined in the following. We will calculate the response in the momentum representationwhere |p is an eigenstate of momentum p. For interpretations it is more convenient to transform the reduced density matrix to the Wigner distribution in phase spacewhere R is the spatial coordinate. The relaxation process in Eq.(1) tends to establish a local equilibrium. Following Mermin...

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Ultrafast Quantum Kinetics of Time-Dependent RPA-Screened Coulomb Scattering

Cited by 127 publications

References 19 publications

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

Quantum Theory of Solid State Plasma Dielectric Response

Femtosecond formation of collective modes due to mean-field fluctuations

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