Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Dynamical model of coherent circularly polarized optical pulse interactions with two-level quantum systems

Gabriela M. Slavcheva, Ortwin G. Hess

Published Nov 3, 2005• 19 citations
Publisher

Abstract

We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.

DOI
10.1103/physreva.72.053804

Related papers

All-Optical Coherent Control of Spin Dynamics in Semiconductor Quantum Dots

Gabriela M. Slavcheva, Ortwin G. Hess

A new model for rigorous theoretical description of circularly (elliptically) polarized ultrashort optical pulse interactions with singly charged quantum dots embedded in semiconductor optical waveguides and microcavities is proposed. The method is based on self-consistent solution in the time domain of the vector Maxwell equations coupled via microscopic polarization to the coherent time-evolution equations of a discrete N-level quantum system in terms of the real pseudospin (coherence) vector. The model is applied to a 4-level system describing the optical dipole transitions of the trion state in a singly charged quantum dot. Selective optical excitation of specific spin states by predefined helicity of the optical field and an onset of self-induced transparency and polarized soliton formation in the nonlinear regime are numerically demonstrated

International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)•Sep 1, 2006•0 citations

Spin‐dependent dynamics of ultrafast polarised optical pulse propagation in coherent semiconductor quantum systems

Gabriela M. Slavcheva, Ortwin G. Hess

Abstract A new model for rigorous theoretical description of circularly (elliptically) polarised ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides is proposed. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations coupled via microscopic polarisation to the coherent time‐evolution equations of a discrete N‐level quantum system in terms of the real pseudospin (coherence) vector. The model is initially applied to a generic two‐level quantum system and subsequently to a 4‐level system describing the heavy‐hole excitonic transitions in low‐dimensional semiconductor systems, such as quantum wells and quantum dots. Selective optical excitation of specific spin states by predefined helicity of the optical field in the linear regime and an onset of self‐induced transparency and polarised soliton formation in the nonlinear regime are numerically demonstrated in both discrete‐level systems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•Jul 5, 2006•6 citations

Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: Finite-difference time-domain study

Gabriela M. Slavcheva, John M. Arnold, Iain D. Wallace +1 more

We extend to more than one spatial dimension the semiclassical full-wave vector Maxwell-Bloch equations for the purpose of achieving an adequate and rigorous description of ultrashort pulse propagation in optical waveguides containing resonant nonlinearities. Our considerations are based on the generalized pseudospin formalism introduced by Hioe and Eberly [Phys. Rev. Lett. 47, 838 (1981)] for treatment of the resonant coherent interactions of ultrashort light pulses with discrete-multilevel systems. A self-consistent set of coupled curl Maxwell-pseudospin equations in two spatial dimensions and time for the special case of a degenerate three-level system of quantum absorbers is originally derived. Maxwell's curl equations are considered to be coupled via macroscopic medium polarization to the three-level atom model for the resonant medium. Two distinct sets of pseudospin equations are obtained corresponding to the TE- and TM-polarized optical waves. For the case of TM polarization, the electromagnetic wave is polarized in a general direction in the plane of incidence inducing two dipole transitions in a degenerate three-level system by each E-field component along the propagation axis and in transverse direction. We introduce a dipole-coupling interaction Hamiltonian allowing Rabi flopping of the population difference along and perpendicular to the propagation axis with frequencies depending on the corresponding field components. The relationship between the induced polarization and the state vector components that describe the evolution of the discrete-level system is derived in order to couple the quantum system equations to the Maxwell's curl equations. The pseudospin equations are phenomenologically extended to include relaxation effects by introducing nonuniform decay times corresponding to the various dipole transitions occurring in a three-level system. The system has been discretized using finite differences on a Yee grid and solved numerically by an iterative predictor-corrector finite-difference time-domain method. Self-induced transparency soliton propagation through a degenerate three-level quantum system of absorbers in two spatial dimensions and time is demonstrated in planar parallel-mirror waveguide geometries.

Physical Review A•Dec 31, 2002•60 citations

All-optical quantum coherent control of electron spin in semiconductor quantum dots

Gabriela M. Slavcheva, Ortwin G. Hess

We develop and apply a new dynamical model for rigorous description of circularly (elliptically) polarized ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations for electromagnetic wave propagation coupled via macroscopic polarization to the coherent time‐evolution equations of a discrete N‐level system in terms of the real pseudospin (coherence) vector. We investigate theoretically the optically‐induced ultrafast resonant coherent spin dynamics in a singly charged semiconductor quantum dot. Onset of Rabi oscillations at sufficiently high excitation intensities is demonstrated numerically resulting in suppression of the spin relaxation and a longer decay time of the polarized photoluminescence.

Open Research (University of Surrey)•Jan 1, 2006•0 citations

All-optical Quantum Coherent Control of Electron Spin in Semiconductor Quantum Dots

Gabriela M. Slavcheva, Ortwin G. Hess

We develop and apply a new dynamical model for rigorous description of circularly (elliptically) polarized ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations for electromagnetic wave propagation coupled via macroscopic polarization to the coherent time‐evolution equations of a discrete N‐level system in terms of the real pseudospin (coherence) vector. We investigate theoretically the optically‐induced ultrafast resonant coherent spin dynamics in a singly charged semiconductor quantum dot. Onset of Rabi oscillations at sufficiently high excitation intensities is demonstrated numerically resulting in suppression of the spin relaxation and a longer decay time of the polarized photoluminescence.

AIP conference proceedings•Jan 1, 2007•0 citations

Circularly polarized few-optical-cycle solitons in the short-wave-approximation regime

Hervé Leblond, Houria Triki, DUMITRU BOGDAN MIHALACHE

We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.

Physical Review A•Aug 18, 2011•12 citations
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference (\ensuremathΔJz=\ifmmode±\else\textpm\fi1)(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)(\ensuremathΔJz​=\ifmmode±\else\textpm\fi1) excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.
A new model for rigorous theoretical description of circularly (elliptically) polarized ultrashort optical pulse interactions with singly charged quantum dots embedded in semiconductor optical waveguides and microcavities is proposed. The method is based on self-consistent solution in the time domain of the vector Maxwell equations coupled via microscopic polarization to the coherent time-evolution equations of a discrete N-level quantum system in terms of the real pseudospin (coherence) vector. The model is applied to a 4-level system describing the optical dipole transitions of the trion state in a singly charged quantum dot. Selective optical excitation of specific spin states by predefined helicity of the optical field and an onset of self-induced transparency and polarized soliton formation in the nonlinear regime are numerically demonstrated
Abstract A new model for rigorous theoretical description of circularly (elliptically) polarised ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides is proposed. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations coupled via microscopic polarisation to the coherent time‐evolution equations of a discrete N‐level quantum system in terms of the real pseudospin (coherence) vector. The model is initially applied to a generic two‐level quantum system and subsequently to a 4‐level system describing the heavy‐hole excitonic transitions in low‐dimensional semiconductor systems, such as quantum wells and quantum dots. Selective optical excitation of specific spin states by predefined helicity of the optical field in the linear regime and an onset of self‐induced transparency and polarised soliton formation in the nonlinear regime are numerically demonstrated in both discrete‐level systems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We extend to more than one spatial dimension the semiclassical full-wave vector Maxwell-Bloch equations for the purpose of achieving an adequate and rigorous description of ultrashort pulse propagation in optical waveguides containing resonant nonlinearities. Our considerations are based on the generalized pseudospin formalism introduced by Hioe and Eberly [Phys. Rev. Lett. 47, 838 (1981)] for treatment of the resonant coherent interactions of ultrashort light pulses with discrete-multilevel systems. A self-consistent set of coupled curl Maxwell-pseudospin equations in two spatial dimensions and time for the special case of a degenerate three-level system of quantum absorbers is originally derived. Maxwell's curl equations are considered to be coupled via macroscopic medium polarization to the three-level atom model for the resonant medium. Two distinct sets of pseudospin equations are obtained corresponding to the TE- and TM-polarized optical waves. For the case of TM polarization, the electromagnetic wave is polarized in a general direction in the plane of incidence inducing two dipole transitions in a degenerate three-level system by each E-field component along the propagation axis and in transverse direction. We introduce a dipole-coupling interaction Hamiltonian allowing Rabi flopping of the population difference along and perpendicular to the propagation axis with frequencies depending on the corresponding field components. The relationship between the induced polarization and the state vector components that describe the evolution of the discrete-level system is derived in order to couple the quantum system equations to the Maxwell's curl equations. The pseudospin equations are phenomenologically extended to include relaxation effects by introducing nonuniform decay times corresponding to the various dipole transitions occurring in a three-level system. The system has been discretized using finite differences on a Yee grid and solved numerically by an iterative predictor-corrector finite-difference time-domain method. Self-induced transparency soliton propagation through a degenerate three-level quantum system of absorbers in two spatial dimensions and time is demonstrated in planar parallel-mirror waveguide geometries.
We develop and apply a new dynamical model for rigorous description of circularly (elliptically) polarized ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations for electromagnetic wave propagation coupled via macroscopic polarization to the coherent time‐evolution equations of a discrete N‐level system in terms of the real pseudospin (coherence) vector. We investigate theoretically the optically‐induced ultrafast resonant coherent spin dynamics in a singly charged semiconductor quantum dot. Onset of Rabi oscillations at sufficiently high excitation intensities is demonstrated numerically resulting in suppression of the spin relaxation and a longer decay time of the polarized photoluminescence.
We develop and apply a new dynamical model for rigorous description of circularly (elliptically) polarized ultrashort optical pulse interactions with the resonant nonlinearities in semiconductor optical waveguides. The method is based on self‐consistent solution in the time domain of the vector Maxwell equations for electromagnetic wave propagation coupled via macroscopic polarization to the coherent time‐evolution equations of a discrete N‐level system in terms of the real pseudospin (coherence) vector. We investigate theoretically the optically‐induced ultrafast resonant coherent spin dynamics in a singly charged semiconductor quantum dot. Onset of Rabi oscillations at sufficiently high excitation intensities is demonstrated numerically resulting in suppression of the spin relaxation and a longer decay time of the polarized photoluminescence.
We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.