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April 11, 2017 15:42
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Compare timeevolution of coherent states created with analytic method and displacement method
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using QuantumOptics | |
using PyPlot | |
# Parameters | |
const ω = 1.89 # Frequency of driving laser | |
const ωc = 2.13 # Cavity frequency | |
const η = 0.76 # Pump strength | |
const κ = 0.34 # Decay rate | |
const δc = ωc - ω # Detuning | |
const T = [0, 10] | |
const α0 = 1.3 - 1.1im # Initial coherent state | |
const αT = (α0 + η/δc)*exp(-1im*δc*T[end]) - η/δc # Final coherent state | |
println("αT: ", αT) | |
# "Exact" solution at t=0 and t=T[end] | |
b_check = FockBasis(500) | |
psi_t0_check1 = coherentstate(b_check, α0) | |
psi_t0_check2 = displace(b_check, α0)*fockstate(b_check, 0) | |
println("Error of 'exact' solution at t=t0: ", norm(psi_t0_check1 - psi_t0_check2)) | |
@assert 1e-14 > norm(psi_t0_check1 - psi_t0_check2) | |
psi_t1_check1 = coherentstate(b_check, αT)*exp(1im*1.7149805399866265) | |
psi_t1_check2 = displace(b_check, αT)*fockstate(b_check, 0)*exp(1im*1.7149805399866265) | |
println("Error of 'exact' solution at t=T[end]: ", norm(psi_t1_check1 - psi_t1_check2)) | |
@assert 1e-14 > norm(psi_t1_check1 - psi_t1_check2) | |
psi_t0_check = (psi_t0_check1 + psi_t0_check2)/2 | |
psi_t1_check = (psi_t1_check1 + psi_t1_check2)/2 | |
# Difference between "exact" solution and solution obatined with a certain cutoff | |
function error(psi_large::Ket, psi_small::Ket) | |
psi_extended = Ket(b_check) | |
psi_extended.data[1:length(psi_small.data)] = psi_small.data | |
norm(psi_large - psi_extended) | |
end | |
error_analytic_t0 = Float64[] | |
error_analytic_t1 = Float64[] | |
error_displace_t0 = Float64[] | |
error_displace_t1 = Float64[] | |
function simulate(Ncutoff) | |
b = FockBasis(Ncutoff) | |
a = destroy(b) | |
at = create(b) | |
n = number(b) | |
Hint = δc*n + η*(a + at) | |
# Initial state | |
psi0_analytic = coherentstate(b, α0) | |
psi0_displace = displace(b, α0)*fockstate(b, 0) | |
# No decay | |
tout, psit_analytic = timeevolution.schroedinger(T, psi0_analytic, Hint, abstol=1e-10, reltol=1e-10) | |
tout, psit_displace = timeevolution.schroedinger(T, psi0_displace, Hint, abstol=1e-10, reltol=1e-10) | |
push!(error_analytic_t0, error(psi_t0_check, psit_analytic[1])) | |
push!(error_analytic_t1, error(psi_t1_check, psit_analytic[end])) | |
push!(error_displace_t0, error(psi_t0_check, psit_displace[1])) | |
push!(error_displace_t1, error(psi_t1_check, psit_displace[end])) | |
end | |
Ncutoffs = [1:1:200;] | |
for Ncutoff in Ncutoffs | |
simulate(Ncutoff) | |
end | |
println(error_analytic_t0) | |
println(error_analytic_t1) | |
println(error_displace_t0) | |
println(error_displace_t1) | |
# Visualization | |
subplot(2, 1, 1) | |
semilogy(Ncutoffs, error_analytic_t0, label="analytic") | |
semilogy(Ncutoffs, error_displace_t0, label="displace") | |
xlabel("cutoff") | |
ylabel("Error t=0") | |
legend() | |
grid() | |
subplot(2, 1, 2) | |
semilogy(Ncutoffs, error_analytic_t1, label="analytic") | |
semilogy(Ncutoffs, error_displace_t1, label="displace") | |
xlabel("cutoff") | |
ylabel("Error t=10") | |
legend() | |
grid() | |
tight_layout() | |
show() |
Author
bastikr
commented
Apr 11, 2017
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