Joint Number state switching operator?

1. Feb 23, 2014

Gwinterz

Hi,

I was just wondering if anyone know of an operator, which has some realistic analogue, that would perform the following action:

A|N,0> = A|0,N>

Where the ket's represent two joint fock states (i.e. two joint cavities) and A is the opeator I desire.

I thought that the beam splitter operator might perform this task with a proper selection of parameters, but I don't think it can.

Any ideas?

Thanks

2. Feb 24, 2014

ChrisVer

just destroy the 1st N, and then create the 2nd N.... that's the operator...

3. Feb 24, 2014

Gwinterz

That would be 2 different operators....

I.e.

A1|0,N> = |N,0>

A2 |N,0> = |0,N>

with A1 ≠ A2.

(Not what I looking for - see first post)

Edit:
It seems the beam splitter operator does do the trick with the right phase selected (pi/2), I was hoping I could set it to zero though so I missed that. Still, any alternatives would be nice to try.

Last edited: Feb 24, 2014
4. Feb 24, 2014

ChrisVer

Ah yes, sorry now I understand the question...
well due to the orthonormality of the states, you can have that only if A makes both states identical...
so I think there is not such operator.

5. Feb 24, 2014

Gwinterz

The beam splitter operator does do the trick,

It basically expands the state out into a superposition of each possible combinations of the joint fock states, the problem I was having is that the weightings were different for each of the two input states. My expression was a bit complicated so I didn't immediately see that a phase of pi/2 produced the results I require, and I was kind of hoping for the phase to be zero.

I have had a number of alternative ideas, however, most are not so physical.