addDissipation

Implements a dissipation process via the Lindblad master equation in a specified subsystem.

Contents

Syntax

Description

Detailed Description and Examples

Dissipation between different levels within one subsystem is realised by the Lindblad master equation. The Liouville von Neumann Equation is expanded by an additional term, resulting in:

$$\rho' = [H,\rho] +  \sum\limits_i \frac{1}{T_i} (R_i \rho R_i^{\dagger}  - \frac{1}{2} R_i^{\dagger} R_i \rho - \frac{1}{2} \rho R_i^{\dagger}  R_i)$$

where $R_i$ denotes the jumping operator. If $R_i$ takes on the form of the lowering operator, the Lindblad equation models a dissipative process between the different levels of a subsystem. This loss progresses with a lifetime of $T_i$. If the dissipation levels are not specified, dissipation is simulated between adjacent levels.

Example of a qbit coupled to a lightfield.

s = System;
s.addEntity(Nlevel(1),'qbit');
s.addEntity(Qoscillator(3,1),'lightfield');
s.addCoupling('qbit','lightfield',0.05);
s.addDissipation('qbit',40);
s.addExternalField(Gausspulse(0.04,50,15,1),'qbit');
s.setTimestep(0.1);
s.simulate();

%plot the gained data
plot(s.time, s.getEnergy('qbit'));
hold on;
plot(s.time, s.getEnergy('lightfield'));
plot(s.time, s.getOpValue(s.H));
s.plotEfields;
xlabel('Time');
ylabel('Energy');
title('Qbit Coupled to a Lightfield');
thelegend = legend('qbit' ,'lightfield','total','laserpuls','Location','northeast');
set(thelegend,'FontSize',16);