# 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.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook