WaveguideQED.jl

A Julia package for simulating quantum states of photon wavepackets using a discrete-time formalism Phys. Rev. A 101, 042322. The package works as an extension to QuantumOptics.jl where bases and operators from WaveguideQED.jl can be used together with operators and bases from QuantumOpics.jl.

Define a waveguide basis, containing a two-photon wavepacket for a time interval from 0 to 20 with timesteps of 0.2:

using WaveguideQED
times = 0:0.1:10
bw =  WaveguideBasis(2,times)

Define waveguide creation and annihilation operators from this basis:

w = destroy(bw)
wd = create(bw)

Combine with QuantumOptics.jl operators:

using QuantumOptics
bc = FockBasis(2)
a = destroy(bc)
ad = create(bc)
wda = a ⊗ wd
adw = ad ⊗ w

Finally, we can define an initial two-photon Gaussian wavepacket state with view_twophoton and zero photons in the cavity, a Hamiltonian, and simulate the evolution:

ξfun(t1,t2,σ1,σ2,t0) = sqrt(2/σ1) * (log(2)/pi)^(1/4)*exp(-2*log(2)*(t1-t0)^2/σ1^2)*sqrt(2/σ2)*(log(2)/pi)^(1/4)*exp(-2*log(2)*(t2-t0)^2/σ2^2)
ψ_cw = twophoton(bw,ξfun,1,1,5)
psi = fockstate(bc,0) ⊗ ψ_cw
dt = times[2] - times[1]
H = im*sqrt(1/dt)*(adw-wda)
ψ = waveguide_evolution(times, psi, H)

Plotting the two-photon state is also simple:

ψ_double = TwoPhotonView(ψ);
using PyPlot
fig,ax = subplots(1,1,figsize=(9,4.5))
plot_twophoton!(ax,ψ_double,times)