Difference between 1D lattice and 2D lattice on BEC

In summary: This is the regime of the Tonks-Girardeau gas.In summary, the difference between 1D and 2D lattices in the context of Bose-Einstein condensation is that in 1D systems, there is usually no phase transition and therefore no BEC. In real experimental situations, the thermodynamic limit is not applicable in 2D and 1D systems, leading to different realizations of BEC. The critical temperature, system size, and particle number also differ greatly between 1D and 2D systems. Furthermore, 1D lattices are typically created using 6 laser beams while 2D lattices have a tube-like shape. By varying the trapping potential, the atoms
  • #1
Choi Si Youn
7
0
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!
 
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  • #2
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
DrDu said:
In one dimensional systems, there is usually no phase transition (look for Wagner Mermin theorem), so also no BEC.

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
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
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.
 

1. What is the difference between a 1D lattice and a 2D lattice in the context of Bose-Einstein condensates (BEC)?

A 1D lattice refers to a periodic potential that is present in one dimension, while a 2D lattice refers to a periodic potential present in two dimensions. In the case of BECs, these lattices are typically created using laser beams that trap the atoms in a periodic array, similar to an optical lattice.

2. How does the dimensionality of the lattice affect the behavior of the BEC?

The dimensionality of the lattice can significantly impact the properties of the BEC. In a 1D lattice, the BEC is confined to a single dimension and exhibits behaviors such as Anderson localization, where the atoms become localized in specific regions of the lattice. In a 2D lattice, the BEC has more freedom to move and can form extended states.

3. Can a BEC be created in both 1D and 2D lattices?

Yes, a BEC can be created in both 1D and 2D lattices. The creation of a BEC in a lattice depends on the balance between the trapping potential and the interatomic interactions. In 1D lattices, the interatomic interactions must be strong enough to counteract the confinement, while in 2D lattices, the interactions must be weak enough to allow the atoms to spread out and form extended states.

4. How does the number of atoms in the BEC affect the properties of the lattice?

The number of atoms in the BEC can affect the properties of the lattice in several ways. In 1D lattices, the number of atoms can affect the phase transition from a superfluid to a Mott insulator state. In 2D lattices, the number of atoms can impact the formation of vortices and the strength of the interatomic interactions.

5. Are there any practical applications for understanding the difference between 1D and 2D lattices on BEC?

Yes, understanding the difference between 1D and 2D lattices on BEC is crucial for a variety of applications. For example, the ability to control and manipulate BECs in lattices has potential applications in quantum computing, precision measurements, and simulating complex condensed matter systems. Additionally, the behavior of BECs in lattices can provide insights into fundamental quantum phenomena and aid in the development of new technologies.

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