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I feel like the answer should be "no" since all superfluids are not strictly BEC since they can undergo a Kosterlitz–Thouless transition in 2D, for example. I believe the ideal gas isn't superfluid, but is there any experimental evidence of a BEC without superfluid properties? I've been searching with no luck.

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You can have superfluids that are not BECs and BECs that are not superfluid. Let me quote a text, "Bose-Einstein Condensation in Dilute Gases", Pethick & Smith, 2nd edition (2008), chapter 10:

Historically, the connection between superfluidity and the existence of a condensate, a macroscopically occupied quantum state, dates back to Fritz London's suggestion in 1938, as we have described in Chapter 1. However, the connection between Bose-Einstein condensation and superfluidity is a subtle one. A Bose-Einstein condensed system does not necessarily exhibit superfluidity, an example being the ideal Bose gas for which the critical velocity vanishes, as demonstrated in Sec. 10.1 below. Also lower-dimensional systems may exhibit superfluid behavior in the absence of a true condensate, as we shall see in Chapter 15.

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  • $\begingroup$ I really feel that my answer is a lose. I couldn't find any evidence either. I suspect it has to be done because it's such an important part of the "accepted wisdom" that goes into the leading textbook. The professor who I took the class from just left WSU for U Texas, Dallas, so he's not around to ask. :( $\endgroup$ – Carl Brannen Jul 3 '12 at 23:46
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    $\begingroup$ A BEC without any interactions is not a superfluid, which is the example described in the above passage. However, I do not think that condensation without superfluidity has been observed. Exotic condensates, like photon condensates, exist for which the concept of superfluidity might not makes sense. $\endgroup$ – emarti Dec 21 '12 at 23:06
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BEC exists in any Bose systems as long as temperature is lower than critical temperature. This can be explained from Bose statistics. As for superfluid, there must be interactions between two particles. That is, in ideal bose gas, it exists BEC, but not exists superfluid. As far as I know, there are still no robust proof of relations between BEC and superfluid.

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  • $\begingroup$ "BEC exists in any Bose systems as long as temperature is lower than critical temperature" is completely untrue. There are many bosonic systems which never exhibit BEC even at zero temperature. $\endgroup$ – Alex Aug 12 '18 at 6:30
  • $\begingroup$ To @Alex , BEC has been proved in Bose statistics. As for whether one can find BEC in any Bose systems, that's an another issue. For example, can experimentalists reach temperature under critical temperature? Or could you share any references that there doesn't exist BEC in Bose systems? I would appreciate it. $\endgroup$ – Hsuan Hao Fan Sep 1 '18 at 0:45
  • $\begingroup$ Your comment says that it exists in any Bose system, this is not true. For example, a 1D ideal Bose gas will never be in a BEC, and in 2D the critical temperature is exactly zero. Another example is the Bose-Hubbard model, where the system does not exhibit BEC even at zero temperature if the bosons are tightly bound to a lattice. See: P. C. Hohenberg. Existence of long-range order in one and two dimensions. Phys. Rev., 158:383–386, 1967 and M. P. A. Fisher et al. Phys. Rev. B 40, 546, 1989 $\endgroup$ – Alex Sep 5 '18 at 18:34

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