# Partial secular Bloch-Redfield 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 Bloch-Redfield theory with a partial secular approximation for one-photon 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 Bloch-Redfield 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 coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence 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 population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type 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; INTEGRO-DIFFERENTIAL EQUATIONS; MOLECULES; PHOTONS; QUANTUM SYSTEMS; VISIBLE RADIATION

### Citation Formats

```
Tscherbul, Timur V., E-mail: ttscherb@chem.utoronto.ca, and Brumer, Paul.
```*Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems*. United States: N. p., 2015.
Web. doi:10.1063/1.4908130.

```
Tscherbul, Timur V., E-mail: ttscherb@chem.utoronto.ca, & Brumer, Paul.
```*Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems*. United States. doi:10.1063/1.4908130.

```
Tscherbul, Timur V., E-mail: ttscherb@chem.utoronto.ca, and Brumer, Paul. Sat .
"Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems". United States.
doi:10.1063/1.4908130.
```

```
@article{osti_22415494,
```

title = {Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems},

author = {Tscherbul, Timur V., E-mail: 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 Bloch-Redfield theory with a partial secular approximation for one-photon 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 Bloch-Redfield 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 coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence 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 population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.},

doi = {10.1063/1.4908130},

journal = {Journal of Chemical Physics},

number = 10,

volume = 142,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}