Different Fockbasis implementation

[amol2891]

I was trying to model the 50:50 beam splitter with input state |1,1,0,0> as the one, one photon at the input port and the 0,0 at the output port. For that I tried to create 4 different FockBasis for respective ports. But apparently even the creation and destruction operators of other FockBasis is giving non-zero results upon acted on other fockstates of different basis.

In the code attached even if a1d * i3, raises the photon number of i3 which is fockstate of fb3.

It would be really nice if someone please give an example of 50:50 beam splitter and the Hong-Ou-Mandel effect.

`#!/usr/bin/julia
using LinearAlgebra,QuantumOptics,Gnuplot

N = 2;
fb1 = FockBasis(N);
fb2 = FockBasis(N);
fb3 = FockBasis(N);
fb4 = FockBasis(N);

a1 = destroy(fb1);
a2 = destroy(fb2);
a3 = destroy(fb3);
a4 = destroy(fb4);

a1d = create(fb1);
a2d = create(fb2);
a3d = create(fb3);
a4d = create(fb4);

n1 = number(fb1);
n2 = number(fb2);
n3 = number(fb3);
n4 = number(fb4);

i1 = fockstate(fb1,1);
i2 = fockstate(fb2,1);
i3 = fockstate(fb3,0);
i4 = fockstate(fb4,0);

input = tensor(i1,i2,i3,i4);`

[a-eghrari]

QuantumOptics.jl implements a matrix representation of a given Fock basis, creation and annihilation operator. You will get the same matrix if you provide the create or destroy function with the Fock basis with the same $N$ . In other words, your a1,a2,a3, and a4 are equal (you can check it with a1 == a2), and the same for a1d, ... and n1, ... . what you should do instead is create the operators by tensoring everything as you did your states.

Something like this would work fine:

N = 2;
fb1 = FockBasis(N);
fb2 = FockBasis(N);
fb3 = FockBasis(N);
fb4 = FockBasis(N);

i1 = fockstate(fb1,1);
i2 = fockstate(fb2,1);
i3 = fockstate(fb3,0);
i4 = fockstate(fb4,0);
	
input = i1 ⊗ i2 ⊗ i3 ⊗ i4;

a1 = destroy(fb1) ⊗ identityoperator(fb2) ⊗ identityoperator(fb3) ⊗ identityoperator(fb4);
a2 = identityoperator(fb1) ⊗ destroy(fb2) ⊗ identityoperator(fb3) ⊗ identityoperator(fb4);
a3 = identityoperator(fb1) ⊗ identityoperator(fb2) ⊗ destroy(fb3) ⊗ identityoperator(fb4);
a4 = identityoperator(fb1) ⊗ identityoperator(fb2) ⊗identityoperator(fb3) ⊗ destroy(fb4);
		
a1d = create(fb1) ⊗ identityoperator(fb2) ⊗ identityoperator(fb3) ⊗ identityoperator(fb4);
a2d = identityoperator(fb1) ⊗ create(fb2) ⊗ identityoperator(fb3) ⊗ identityoperator(fb4);
a3d = identityoperator(fb1) ⊗ identityoperator(fb2) ⊗ create(fb3) ⊗ identityoperator(fb4);
a4d = identityoperator(fb1) ⊗ identityoperator(fb2) ⊗ identityoperator(fb3) ⊗ create(fb4);

If you want to keep $N=2$ for all the ports, then you can reduce your code to

N = 2;
fb = FockBasis(N);

i1 = fockstate(fb,1);
i2 = fockstate(fb,1);
i3 = fockstate(fb,0);
i4 = fockstate(fb,0);
	
input = i1 ⊗ i2 ⊗ i3 ⊗ i4;

a1 = destroy(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb);
a2 = identityoperator(fb) ⊗ destroy(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb);
a3 = identityoperator(fb) ⊗ identityoperator(fb) ⊗ destroy(fb) ⊗ identityoperator(fb);
a4 = identityoperator(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb) ⊗ destroy(fb);
		
a1d = create(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb);
a2d = identityoperator(fb) ⊗ create(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb);
a3d = identityoperator(fb) ⊗ identityoperator(fb) ⊗ create(fb) ⊗ identityoperator(fb);
a4d = identityoperator(fb) ⊗ identityoperator(fb) ⊗ identityoperator(fb) ⊗ create(fb);

About an example of a 50:50 beam splitter and the Hong-Ou-Mandel effect, I refer you to
https://www.mdpi.com/2227-7390/10/24/4794#:~:text=The%20beam%20splitter%20(BS)%20is,transmitted%20and%20a%20reflected%20beam.

[Krastanov]

Thanks for the answer, Ali! @amol2891 , I will close this issue as it seems it was answered, but please do not hesitate to reopen it.