Quickstart

This package provides tools to compute full-counting-statistics cumulants from a Liouvillian.

Installation

To install the package, in the Julia REPL,

using Pkg 
Pkg.add("QuantumFCS")

Quickstart example

We model a quantum dot heat engine as a single mode coupled to two reservoirs (hot and cold) in the large bias limit ($n_c = 0,~ n_h = 1$).

using QuantumOptics 
using QuantumFCS
# Basis for the single quantum dot
b = FockBasis(1)
# Operators 
d = destroy(b)
d_dag = create(b)
# Parameters
ϵd = 1.0;                            # Energy level of the quantum dot
κc = 0.1;                            # Coupling strength to cold reservoir
κh = 0.5;                            # Coupling strength to hot reservoir
# Hamiltonian and jump operators
H = ϵd * d_dag * d;                  
Jcloss = sqrt(κc) * d;               # Jumps into the cold reservoir 
Jhgain = sqrt(κh) * d_dag;           # Jumps from the hot reservoir
J = [Jcloss, Jhgain];
# Steady state
ρss = steadystate.iterative(H, J)
# Weight vector 
nu = [1];
# Monitored jump operator (particles entering the cold reservoir)
mJ = [Jcloss];
# Calculating the first two cumulants
c1, c2 = fcscumulants_recursive(H, J, mJ, 2, ρss, nu);
println("\nFull Counting Statistics:")
println("First cumulant : $c1")
println("Second cumulant : $c2")