Partial secular BlochRedfield master equation for incoherent excitation of multilevel quantum systems
Abstract
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the BlochRedfield theory with a partial secular approximation for onephoton coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular BlochRedfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherencefree Paulitype master equation. The coherent regime requires nonorthogonal transition dipole moments in the energy basis and leads to the generation of noiseinduced quantum coherences and populationtocoherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe populationtocoherence transfer and the formation of nonequilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the Vtype system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] aremore »
 Authors:
 Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
 Publication Date:
 OSTI Identifier:
 22415494
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; DENSITY MATRIX; DIPOLE MOMENTS; ENERGY TRANSFER; EQUILIBRIUM; EXCITATION; EXCITED STATES; GROUND STATES; ILLUMINANCE; INTEGRODIFFERENTIAL EQUATIONS; MOLECULES; PHOTONS; QUANTUM SYSTEMS; VISIBLE RADIATION
Citation Formats
Tscherbul, Timur V., Email: ttscherb@chem.utoronto.ca, and Brumer, Paul. Partial secular BlochRedfield master equation for incoherent excitation of multilevel quantum systems. United States: N. p., 2015.
Web. doi:10.1063/1.4908130.
Tscherbul, Timur V., Email: ttscherb@chem.utoronto.ca, & Brumer, Paul. Partial secular BlochRedfield master equation for incoherent excitation of multilevel quantum systems. United States. doi:10.1063/1.4908130.
Tscherbul, Timur V., Email: ttscherb@chem.utoronto.ca, and Brumer, Paul. 2015.
"Partial secular BlochRedfield master equation for incoherent excitation of multilevel quantum systems". United States.
doi:10.1063/1.4908130.
@article{osti_22415494,
title = {Partial secular BlochRedfield master equation for incoherent excitation of multilevel quantum systems},
author = {Tscherbul, Timur V., Email: ttscherb@chem.utoronto.ca and Brumer, Paul},
abstractNote = {We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the BlochRedfield theory with a partial secular approximation for onephoton coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular BlochRedfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherencefree Paulitype master equation. The coherent regime requires nonorthogonal transition dipole moments in the energy basis and leads to the generation of noiseinduced quantum coherences and populationtocoherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe populationtocoherence transfer and the formation of nonequilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the Vtype system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excitedstate populations and coherences in both the small and largemolecule limits.},
doi = {10.1063/1.4908130},
journal = {Journal of Chemical Physics},
number = 10,
volume = 142,
place = {United States},
year = 2015,
month = 3
}

We present a new method for solving the Redfield equation, which describes the evolution of the reduced density matrix of a multilevel quantummechanical system interacting with a thermal bath. The method is based on a new decomposition of the Redfield relaxation tensor that makes possible its direct application to the density matrix without explicit construction of the full tensor. In the resulting expressions, only ordinary matrices are involved and so any quantum system whose Hamiltonian can be diagonalized can be treated with the full Redfield theory. To efficiently solve the equation of motion for the density matrix, we introduce amore »

Equivalence between Redfield and masterequation approaches for a timedependent quantum system and coherence control
We present a derivation of the Redfield formalism for treating the dissipative dynamics of a timedependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a timedependent spin1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T{sub 1} and T{sub 2} (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operatorsum representation and the equivalentmore » 
Criteria for the accuracy of small polaron quantum master equation in simulating excitation energy transfer dynamics
The small polaron quantum master equation (SPQME) proposed by Jang et al. [J. Chem. Phys. 129, 101104 (2008)] is a promising approach to describe coherent excitation energy transfer dynamics in complex molecular systems. To determine the applicable regime of the SPQME approach, we perform a comprehensive investigation of its accuracy by comparing its simulated population dynamics with numerically exact quasiadiabatic path integral calculations. We demonstrate that the SPQME method yields accurate dynamics in a wide parameter range. Furthermore, our results show that the accuracy of polaron theory depends strongly upon the degree of exciton delocalization and timescale of polaron formation.more » 
Multilevel MaxwellBlochequation description of ultrashort laser pulse amplification in inhomogeneously broadened XeCl media
Coherent amplification of shortpulse XeCl lasers is studied theoretically by using multilevel MaxwellBloch equations in which the vibrationalrotational structures of a XeCl gain spectrum are included. The model used considers 100 transitions each in the P and R branches for six different vibrational transitions of XeCl(B, v=0) {r arrow} XeCl(X, v{prime}=05). Coherence components between sublevels in the B and X states are also properly calculated. The model can successfully predict coherent effects such as a quantum beat caused by the spectrum overlap of the several vibrationalrotational transitions involved in a shortpulse laser spectrum. During amplification, laser pulses experience some nonlinearmore » 
Quantumstateselective twophoton excitation of multilevel systems assisted by the Stark shift
Starkchirped rapid adiabatic passage [T. Rickes et al., J. Chem. Phys. 113, 534 (2000); A. A. Rangelov et al. Phys. Rev. A 72, 053403 (2005)] has been proposed as a laser scheme that allows the optical excitation of atoms or molecules with high quantum yields. The laser control proceeds via adiabatic passage assisted by dynamic Stark shifts. We propose several extensions of the scheme with alternative sequences, by frequency tuning or by repeating the pulse sequences, in order to achieve fine state selectivity within multilevel structures and adiabatic passage of quantum superposition states. The efficiency and selectivity of the schemesmore »