lso

Choose between utilizing Lindblad superoperators or not.

Contents

Syntax

s.lso = boolean

Description

If boolean is set to true, the Lindblad superoperator is calculated and used in solving the Lindblad master equation. If boolean is set to false, calculations proceed via the Lindblad master equation in its conventional form.

Detailed Description

The Lindblad master equation,

$$\frac{\partial}{\partial t} \rho(t) = -\frac{i}{\hbar}[H(t),\rho(t)] +  \sum\limits_i \frac{1}{T_i} \left[ R_i \rho(t) R_i^{\dagger} - \frac{1}{2} R_i^{\dagger} R_i \rho(t) - \frac{1}{2} \rho(t) R_i^{\dagger}  R_i \right]$,

can be expressed in a superoperator form,

$$\frac{\partial}{\partial t} \rho(t) = -i \mathcal{L}_0 \rho(t) - \mathcal{L}_{\rm SO} \rho(t)$

with

$$\mathcal{L}_0 \rho(t) = \frac{1}{\hbar}\left[H(t),\rho(t)\right]$

and

$$\mathcal{L}_{\rm SO} \rho(t) = \sum\limits_i \frac{1}{T_i} \left[ R_i \rho(t) R_i^{\dagger} - \frac{1}{2} R_i^{\dagger} R_i \rho(t) - \frac{1}{2} \rho(t) R_i^{\dagger} R_i \right].$

With s.lso. = true, the Lindblad superoperator is precalculated at the beginning of a simulation and then reused for every external light field in the course of the simulation. This avoids calculating the Lindblad operators for every new external light field and thus increases computational speed.

Note: employing Lindblad superoperators significantly enhances the speed of a simulation with a large amount of external fields as they are present in simulating two-dimensional (2D) spectroscopy. However, there are cases where precalculating Linblad superoperators does not reduce computational cost such as in simulations with a single external light field. In these cases, s.lso should be set to false.