Optical nonlinear waves in semiconductor quantum dots: Solitons and breathers

Adamashvili, G. T.; Weber, Carsten; Knorr, Andreas; Adamashvili, N. T.

doi:10.1103/physreva.75.063808

Cited by 29 publications

(18 citation statements)

References 36 publications

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“…The classical curve in Fig. 5 jumps abruptly from point (8,8) to point (10,6), with the same total energy. The quantum state corresponding to the classical separatrix is shown in Fig.…”

Section: B Comparison Of Qhd To Quantum Mechanicsmentioning

confidence: 92%

“…5 increase linearly up to the separatrix point around (8,8), then jump discontinuously to (10,6) and asymptotically approach the x axis. Before the separatrix, the system is in the normal mode regime.…”

Section: A Qhd Advantages Over Classical Dynamicsmentioning

confidence: 97%

“…After the point (8,8) the data jump to (10,6). Now the nonlinear effects dominate over the coupling and drive the system off resonance.…”

Section: A Qhd Advantages Over Classical Dynamicsmentioning

confidence: 97%

“…In quantum mechanics, the energy tunnels very slowly between lattice sites. Quantum breathers have been observed experimentally [5] in interacting Josephson junctions [7], Bose-Einstein condensates [8], crystals [9], quantum dots [10], molecules [11], and biological polymers [12]. Systems containing breathers are mostly nonintegrable, and, before the era of powerful computers, they were not accessible for theoretical analysis.…”

Section: Introductionmentioning

confidence: 99%

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Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Igumenshchev

Prezhdo

2011

Phys. Rev. E

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We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.

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“…The classical curve in Fig. 5 jumps abruptly from point (8,8) to point (10,6), with the same total energy. The quantum state corresponding to the classical separatrix is shown in Fig.…”

Section: B Comparison Of Qhd To Quantum Mechanicsmentioning

confidence: 92%

Section: A Qhd Advantages Over Classical Dynamicsmentioning

confidence: 97%

“…After the point (8,8) the data jump to (10,6). Now the nonlinear effects dominate over the coupling and drive the system off resonance.…”

Section: A Qhd Advantages Over Classical Dynamicsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Igumenshchev

Prezhdo

2011

Phys. Rev. E

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“…Understanding the mechanism of quantum discrete breathers (QDBs) is important for a number of application areas, including medicine [1], nano-materials [2][3][4] and quantum computers [5]. From the classical mechanics perspective, discrete breathers (DBs) is a fairly well understood phenomena, and occur when energy localizes in the system for an infinite amount of time.…”

Section: Introductionmentioning

confidence: 99%

Signatures of discrete breathers in coherent state quantum dynamics

Igumenshchev

Ovchinnikov

Maniadis

et al. 2013

The Journal of Chemical Physics

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In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.

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Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Jirauschek

Riesch

Tzenov

2019

Advcd Theory and Sims

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Due to their intuitiveness, flexibility, and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the 1D MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening, and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed. of a lower bandgap material than the adjacent layers, which restricts the free electron motion in that layer to the in-plane directions and gives rise to quantized energy states in growth direction. As a consequence of the further restriction of the energy spectrum and the even stronger carrier localization, additional improvement can be expected from 2D or 3D confinement, resulting in quantum wire/dash and quantum dot (QD) structures, respectively. Indeed, QD [1][2][3] and quantum dash [4] lasers and laser amplifiers have been shown to exhibit excellent characteristics. In Figure 1, the formation of quantized states in quantum wells, wires, and dots is schematically illustrated. The term quantum dash refers to an elongated nanostructure, that is, some kind of short quantum wire. By contrast, the term nanowire does not necessarily indicate strong quantum confinement. For example, in nanowire lasers, the nanowire geometry typically serves as a single-mode optical waveguide resonator, while the active region is based on a heterostructure or quantum well, as in a conventional laser diode. [5,6] Semiconductor optoelectronic devices usually rely on electron-hole recombination, that is, optical transitions between conduction and valence band states. The associated resonance wavelength is largely determined by the semiconductor bandgap, which establishes a lower bound on the transition energy. Thus, the coverage of a certain spectral region depends on the existence of suitable semiconductor materials, which for example restricts the availability of practical optoelectronic sources and detectors in the mid-infrared and terahertz regions. An alternative concept is based on intersubband devices, which employ so-called i...

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Optical nonlinear waves in semiconductor quantum dots: Solitons and breathers

Cited by 29 publications

References 36 publications

Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

Signatures of discrete breathers in coherent state quantum dynamics

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

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