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Edit and run



In [2]:

    
from qutip import *
from numpy import sqrt
from numpy import math
factorial = math.factorial



In [3]:

    
# from van Enk NotesBS.pdf
N = 5  # use a 5-dim space for now, enlarge as needed
a1 = tensor(destroy(N),qeye(N))  # a1 acts on photon 1
a2 = tensor(qeye(N),destroy(N))  # a2 acts on photon 2
a3 = (a1 + 1j*a2)/sqrt(2)  # output a3
a4 = (1j*a1 + a2)/sqrt(2)  # output a4



In [4]:

    
def input(n,m,N):
    an = a1.dag()
    am = a2.dag()
    psi_in = 1/sqrt(factorial(n)) * (an**n) * 1/sqrt(factorial(m)) * (am**m) * tensor(basis(N,0),basis(N,0))
    return psi_in.unit()



In [5]:

    
input(0,1,N)









    Out[5]:





Quantum object: dims = [[5, 5], [1, 1]], shape = [25, 1], type = ket\begin{equation*}\left(\begin{array}{*{11}c}0.0\\1.0\\0.0\\0.0\\0.0\\\vdots\\0.0\\0.0\\0.0\\0.0\\0.0\\\end{array}\right)\end{equation*}



In [131]:

    
a3 = tensor(destroy(N),identity(N))
a4 = tensor(identity(N),destroy(N))



In [132]:

    
def output(n,m,N):
    """Based on van Enk, NotesBS.pdf point 19"""
    an = (a3.dag() + 1j*a4.dag())/sqrt(2)
    am = (1j*a3.dag() + a4.dag())/sqrt(2)
    psi_out = 1/sqrt(factorial(n)) * (an**n) * 1/sqrt(factorial(m)) * (am**m) * tensor(basis(N,0),basis(N,0))
    return psi_out



In [133]:

    
psi01 = 1/sqrt(2)*(1j*tensor(basis(N,1),basis(N,0)) + tensor(basis(N,0),basis(N,1)))



In [134]:

    
psi01 == output(0,1,N)









    Out[134]:





True



In [135]:

    
psi11 = 1/sqrt(2)*(-1j*tensor(basis(N,2),basis(N,0)) - 1j*tensor(basis(N,0),basis(N,2)))

Oddly, this isn't right yet, but it's off by a sign error:



In [160]:

    
psi11 == -output(1,1,N)









    Out[160]:





True



In [163]:

    
test = 1/2 * (a3.dag() + 1j*a4.dag()) * (1j*a3.dag() + a4.dag()) * tensor(basis(N,0),basis(N,0))
test.full









    Out[163]:





<bound method Qobj.full of Quantum object: dims = [[5, 5], [1, 1]], shape = [25, 1], type = ket
Qobj data =
[[ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.70710678j]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.70710678j]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]
 [ 0.+0.j        ]]>



In [ ]: