Joint Number state switching operator?

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Discussion Overview

The discussion revolves around the search for an operator that can switch between two joint Fock states in quantum mechanics, specifically transforming the state A|N,0> into A|0,N>. Participants explore potential operators, particularly the beam splitter operator, and discuss its applicability and limitations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about an operator that can switch joint Fock states, suggesting the beam splitter operator might be a candidate but expressing uncertainty about its effectiveness.
  • Another participant proposes a straightforward approach of destroying the first state and creating the second, implying a simple operator could achieve the desired transformation.
  • A third participant clarifies that the proposed transformation would require two different operators, A1 and A2, indicating that they are not equivalent.
  • One participant notes that the beam splitter operator can achieve the desired transformation with a specific phase setting (pi/2), but expresses a preference for a zero phase setting.
  • Another participant agrees that the beam splitter operator can work but highlights complications with the weightings of the input states and mentions alternative ideas that may not be physically realistic.

Areas of Agreement / Disagreement

Participants express differing views on the existence and nature of the operator in question. While some agree that the beam splitter operator can perform the transformation under certain conditions, there is no consensus on whether a single operator can achieve the desired effect without complications.

Contextual Notes

Limitations include the dependence on specific phase settings for the beam splitter operator and the unresolved nature of alternative operators proposed by participants.

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

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