# Difference between 1D lattice and 2D lattice on BEC

1. Jan 5, 2010

### Choi Si Youn

I studied in AMO physics. nowaday, I study about BEC.

I'm wonder, Difference between 1D lattice and 2D lattice on BEC.
In the web, they just explain what they do using that.

Maybe just short word, or sentence, give me a huge knowledge.

Thanks you, and Have a nice day!

2. Jan 11, 2010

### DrDu

I don't know exactly from which part of the "web" you have your information, so I just can guess:
In one dimensional systems, there is usually no phase transition (look for Wagner Mermin theorem), so also no BEC.

3. Jan 11, 2010

### Cthugha

The Wagner-Mermin theorem is valid for spatially homogeneous systems in the thermodynamic limit. Any real experimental situation necessarily includes spatially inhomogeneous systems, which therefore have finite size. While the thermodynamic limit is usually well justified in 3D, this is usually not the case in real 2D and 1D systems. Accordingly there are several realizations of BEC in lowdimensional structures. I do not know much about 1D, but I know there is a transition from "usual" BEC behaviour towards bosons, which mimic fermions, which is called Tonks-Girardeau gas (see Nature 429, 277-281 (2004) by Peredes et al.). If I remember correctly, also the dependence of the critical temperatur on the system size and particle number differ strongly in 1D and 2D.

4. Jan 12, 2010

### Choi Si Youn

Oh...'1D','2D' means "Optical lattice's dimension"////
and I found a difference what I wonder, Difference between 1D optical lattice and 2D optical lattice.
1D optical lattice is made by a pair of laser beams , and it makes interference of single standard wave. and 2D optical lattice's shape look like 1D but 2D's shape look like tube.

if that is wrong or something miss, please reply again.

5. Jan 12, 2010

### Cthugha

I am not an expert on that, but I think the easiest way to achieve a 1D lattice is to use 6 laser beams and therefore 3 standing wave patterns perpendicular to each other. This gives you a situation similar to a solid, where you have the equivalent of fixed lattice sites at the maxima of the standing waves of the crossing area, divided by some trapping potential (the minima of the standing waves). The atoms will be positioned at these intensity maxima. Now you can tune the strength of the trapping potential by varying the intensity of the standing waves. If the trapping potential in a dimension is large compared to the kinetic energy of the atoms, they will be trapped in this dimension. If you lower the trapping potential you will gradually reach the regime, where the atoms can move freely in that dimension.

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