# What is the minumum arrangement to cause decoherence?

1. Apr 30, 2012

### precisionart

In principle, what is the absolute simplest arrangement to cause decoherence? In other words what constitutes a measurement? Clearly gravitational interaction is not sufficient.

2. May 1, 2012

### Staff: Mentor

Anything which can change the phase of the thing you want to disturb by a significant (comparable to pi) and not predictable (by the experimental setup) amount.

3. May 1, 2012

### TrickyDicky

Why would a simple phase shift cause decoherence? I woul rather say a frequency or speed change in the wave enough to prevent interference.

4. May 1, 2012

### precisionart

This raises a couple more questions for me:

1. Is phase the only property that can be entangled?
2. Can two particles become entangled just by circumstantial phase alignment? For example, no immediate common cause of phase alignment.
3. What is the least action necessary to force particle-like behavior (localization)?

5. May 1, 2012

### Dali

What is needed is any coupling to any environment (i.e. degrees of freedom that are not measured) in such a way that the various states of the studied subsystem gives rise to different time-evolution of that environment.
It is clear that all normal measurements fulfill this. The measurement apparatus is then be necessity coupled to the studied subsystem in such a way that the end-state of the macroscopical apparatus depends on wich state the system was in (or rather, decohered to). Otherwise it would not have been a measurement!
But decoherence always takes place as soon as anything is coupled to the system in question in such a way that different states of the system gives rise to different time-evolution of that environment.
For example, if the system to study is a free particle in a superposition of two (or more) positions and a single photon interacts with the particle, the particle superposition will decohere if the photon is affected in ever-so-slightly different ways depending on the position of the particle. Say that particle position 1 bounces the photon sligtly to the left, whereas particle position 2 bounces it more to the right. What happens is that the photon will time-evolve into a superposition of going left and going right. Since we don't measure the bouncing photon, we have to take the average over both possibilities to get a prediction for what the particle (i.e. the studied subsystem) does. This averaging makes all off-diagonal elements of the density matrix describing the studied particle to be suppressed by the overlap between a left-going and right-going photon. That overlap will decrease exponentially as the two photon paths diverge. This means any interference effects between the two superpositions of the particle are killed off exponentially, leaving the particle in a mixed state corresponding to the classical probability mixture of position 1 and position 2, i.e it has been localized.

I don't think it is possible to state in more general terms which interactions that cause decoherence. It depends on the states of the system in study. If the coupling makes something outside the studied system behave differently, it will irrevocably decohere that system.

6. May 1, 2012

### Delta Kilo

Zurek in one of his papers had a toy model of a qubit coupled to about 50 or so other qubits making up the "environment". There were some interesting results of computer simulations. The paper is out there on arxiv but I don't remember which one, sorry.

7. May 2, 2012

### Demystifier

I think the crucial property needed for decoherence (measurement) is that the environment (interacting with the measured system) contains a large number of effective degrees of freedom.

8. May 2, 2012

### Staff: Mentor

Imagine a photon wave going through two slits.
1) If you don't do anything, you get the nice interference pattern.
2) If you add a delay of 1/2 wavelength at one slit, you get the opposite pattern (high intensity at the points of minimum intensity in (1)).
3) If you disturb the photon depending on the position of some electron, or scatter is somewhere in material or whatever, you couple your electron/material to the photon and add a phase shift to the photon which somehow depends on this coupling. You lose interference.

The difference between 2 and 3 is what I meant with "predictable". A single phase shift alone does not give decoherence. But if you couple it to some material with a lot of relevant degrees of freedom (see Demystified), it gives decoherence.

9. May 2, 2012

### f95toli

Indeed. The usual "toy system" for decoherence is a bath of two-level systems (or something that can be parametrized as such) with a white frequency spectrum (i.e. there are always plenty of systems resonant with the system you are trying to measure) that is coupled with some energy g to the (two-level) system you are trying to measure.

if you go through the math you will find that the decoherence can then be characterized by some time constant T1 and you have T2=2*T1.

10. May 2, 2012

### TrickyDicky

Ok, but I thought this coupling was more often explained in terms of momentum perturbation.