# What's “bimodal” about BEC velocity distributions?

I was just reviewing some papers discussing Bose-einstein condensation, specifically "Creation of a Bose-condensed gas of 87Rb by laser cooling" by Hu et al., and I saw repeated references to the emergence of a "bimodal" velocity distribution being a hallmark of the BEC transition. However, I realized that none of the distributions look remotely bimodal, i.e. having two modes, i.e. prominent peaks or local maxima (See figure 2 here).

Trying to track this down a bit better, I realized that Wolfgang Ketterle's original paper also called their measured BEC velocity distribution bimodal (in the abstract no less!) (see figure 3 here).

As far as I can tell, with any reasonable reference to the normal definition of a "mode", all these distributions unambiguously have exactly 1 mode (at zero velocity), and are not bimodal. I get that the distribution is non-gaussian and that to fit the distribution they typically have a sum of two distributions, and maybe this is what they are trying to get at, but I feel that I'm missing something. What's "bimodal" about BEC velocity distributions?

## 2 Answers

Bimodal refers to the fact that the velocity distribution is described by the sum of two terms, a Gaussian, which captures the behavior of the non-condensed fraction which looks thermal (follows Maxwell-Boltzmann distribution for velocity, hence the Gaussian velocity distribution) and a second component which is much more sharply peaked and captures the behavior of the macroscopic condensed fraction of atoms in the ground state of the trap.

One striking feature of the velocity distributions is as follows. Consider thermal (non-condensed) atoms in a non-isotropic trap. For long time of flight the thermal expansion will be isotropic since the velocity distrbutions in the three dimensions are thermalized together. Thus, you will see a spherical cloud even for an oblong trap. However, for the condensed BEC in the ground state you will observe anisotropy of the velocity distribution after long time of flight because the ground state has anisotropic velocity distribution.

Thus the two modes directly refer to the two different behaviors: Gaussian and thermal on the one hand and sharply peaked/condensed on the other hand.

• and the anisotropic velocity distribution comes in the condensed phase because spread in momentum ~ 1/(trap width) (uncertainty principle) and usually the trap geometries achieved are more cigar-like than spherical in aspect ratio. – wcc Mar 11 at 1:40
• Doesn't a "mode" usually refer to an eigenmode in physics? There's no "thermal eigenmode"... – aquirdturtle Mar 11 at 8:19
• I'll agree with you that yes "mode" usually refers to an eigenmode of something and your confusion is justified since that is what your thinking. But then next I'm going to stretch the definition of "mode" to show how what I describe in my answer could be seen to be a mode. In mechanics "modes" are best defined as "patterns of motion". In the BEC we see two patterns of motion: thermal and ground state/condensed. I agree its a stretch and isn't quite the same as "eigenmode" (though the ground state is an eigenmode) but I wouldn't go so far as to criticize the use of the term. – jgerber Mar 11 at 8:32

I am afraid 'bimodal' originates from the fits used to characterise a BEC, like the ones below (from my experiment): The Bose-condensed atoms and the thermal fraction have different spatial distribution functions, and by fitting both functions at the same time you can compute the numbers of both.