Can the Displacement Operator Rotate a Photonic State in Phase Space?

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Discussion Overview

The discussion revolves around the application and implementation of the displacement operator in the context of photonic states, particularly in relation to coherent states and their manipulation within a cavity. Participants explore theoretical aspects, experimental setups, and the implications of using the displacement operator to rotate states in phase space.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant seeks clarification on how the displacement operator can be implemented experimentally to displace a photonic state in a cavity.
  • Another participant notes that applying the displacement operator to the vacuum state results in a coherent state rather than a photon Fock state.
  • A participant expresses uncertainty about the specific experimental devices or interactions required to achieve the displacement of a state by a given parameter.
  • It is mentioned that lasers produce coherent states, but details on preparing specific coherent states are not provided.
  • A reference to Mandel & Wolf indicates that changing a time-dependent classical current can continuously change the state, akin to applying a displacement operator.
  • One participant proposes a scenario where a pulse displaces the vacuum to a Gaussian state in phase space, questioning whether applying the same pulse again would return the system to the vacuum state and how to determine the timing for this.

Areas of Agreement / Disagreement

Participants express various viewpoints on the theoretical implications and practical challenges of using the displacement operator, indicating that multiple competing views remain and the discussion is unresolved.

Contextual Notes

There are limitations regarding the specifics of experimental setups and the conditions under which the displacement operator can be effectively applied, as well as the dependence on the definitions of coherent states and the nature of the interactions involved.

naima
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Hi PF

I read the definition of the displacement operator:
##D(\lambda) = e^{\lambda a^\dagger - \lambda ^* a}##
but i did not find how this operator can be implemented say in a cavity with a photonic state inside.
Could you give me links?
thanks.
 
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Have a look at this:

http://en.wikipedia.org/wiki/Coherent_states

Note that the application of this "displacement operator" to the vacuum does not create a photon Fock state (i.e., a state with definite photon number) but a coherent state!
 
Danke Vanhees71
I read in this wiki
""...letting the unitary displacement operator D(α) operate..."
The problem is not to let it operate. The problem is to prepare a device which will enable an experimentalist to displace a sate by ##\alpha##
I read the external links at the end of the article but i did not find any device's
description. I think that it needs pulses but with which interaction?
 
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I only know that lasers produce coherent states. How you prepare a given coherent state in detail, I cannot say :-(.
 
Mandel & Wolf (sect. 11.13, p568) give a derivation of the field produced by a time-dependent classical current, and show (iiuc) that it's a coherent state. As the current changes, the state changes continuously, but it's always a coherent state. I.e., changing the current is equivalent (in that case) to acting with a ##D(\alpha)##--like operator.
 
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Thanks
I found the same in another book (Gerry and Knight)
http://qiqo.hznu.edu.cn/upLoad/down/month_1406/201406231000574799.pdf
Skip to "generating a coherent state" p52
 
Suppose that, using a pulse during t, i displace the vacuum to a gaussian centered around a point P in the phase space. This point will rotate in this plane. At a given moment the gaussian will be centerd around -P. If i apply the same pulse will the atom return to its vacuum?
If yes how can we know when we have to light the atom ?Edit
As i have many copies of the ground state |g> i can vary the ##\Delta t## between two pulses and for which it returms to |g> and know the rotation period.
 
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