Why is superfluidity at 50 nanokelvin high-temperature superfluidity? Answer

Why can a superfluid not rotate as an ordinary object? Answer

Which were the crucial steps in realizing high-temperature superfluidity?  Answer

How do you show that something is superfluid?   Answer

Are Bose-Einstein condensation and superfluidity the same?    Answer

What is the BEC-BCS cross-over?     Answer

 

 High-Temperature Superfluidity

What matters for the phenomenon of superfluidity, is the temperature normalized by the density of the system.  More technically, the normalized temperature is the temperature divided by the so called Fermi temperature, which is proportional to the density to the power 3/2.  The normalized temperature is about the ratio of the binding energy of the fermion pairs to the kinetic energy of the atoms.

This table shows typical values for the normalized temperature for superconductors and superfluid helium-3.  The superfluidity in lithium-6 has a normalized transition temperature of around 0.3, much higher than any other Fermi system.
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Why rotating superfluids need vortices?

When you rotate a bucket with a normal fluid and a superfluid, you see a strikingly different behavior.  The normal fluid rotates like a rigid object (the only difference is the meniscus at the surface), whereas the superfluid forms an array of vortices.  Why?

A superfluid is one big wave.  All the particles are in one wavefunction.  When a wave rotates, it has to form a closed curve.  In other words, the number of de Broglie wavelengths on a circumference has to be an integer.

In a rotating normal fluid, the velocity increases smoothly from the origin to the outer boundary.  In a superfluid, it can only increase in discrete steps:  zero, one, two .. wavelengths per circumference.

It turns out that it is energetically more favorable, when the singularities of the velocity field don't form sheets, but lines.  Voila, these are the vortices.

Therefore, vortices are a direct way of observing that the liquid or gas behaves as a single wave.
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The quest for high-temperature superfluidity

 Here are some milestones in realizing high-temperature superfluidity

 1995 Observation of Bose-Einstein condensation in bosonic atoms

Around 1997, efforts started to apply the same techniques (laser cooling, magnetic trapping, evaporative cooling) to fermions

In addition to the now standard techniques how to make a BEC additional techniques were needed - they were developed with bosonic atoms in 1997 and 1998.
1997 Sympathetic cooling (Boulder)
1998 Realization of optical trapping of a Bose-Einstein condensate at MIT
1998 Feshbach resonances were discovered in (MIT, Texas)

All the techniques were now available to pursue the quest for superfluidity in fermionic gases and advances came quickly

1999 Degenerate fermions realized in a magnetic trap (Boulder)
2002 Feshbach resonances observed in fermions (Boulder, MIT, Duke, Innsbruck)

All the tools were now assembled:  Fermions in two hyperfine states in an optical trap near a Feshbach resonance

2003 Pairing of fermions to short-lived molecules (Boulder)

2003 Discovery that molecules near a Feshbach resonance are stable (Paris)

This was a key discovery and came unexpected, since in bosons, Feshbach resonances had always been accompanied by strong losses (At Rice, stable molecules were observed at the same time, but outside a narrow Feshbach resonance - this is not yet understood and has not been used in further studies).

November 2003 Bose-Einstein condensation of molecules consisting of weakly bound fermion pairs (Boulder , Innsbruck , MIT).

2004 Bose-Einstein condensation of atom pairs observed above the Feshbach resonance (Janaury, Boulder; March, MIT).  We know now that the properties of fermion pairs above and below the Feshbach resonance are very similar - it is a smooth cross over.  However, the sweep technique developed at Boulder has to be used to image atom pairs which form above the Feshbach resonance.

2004 and 2005:  Several studies of the strongly interacting Fermi gas including collective excitations, pair spectrum, and specific heat (Duke, Innsbruck, Boulder, Paris, Rice).  None of these studies observed a sudden change or singular behavior at the predicted phase transition, an unfortunate feature of the strongly interacting Fermi gas. Pairing, low damping and classical hydrodynamic flow are present already above the phase transition. Thus, none of these observations could provide a "smoking gun" or distinguishing feature of superfluidity,  but were consistent with the existence of superfluidity. So the previous evidence for superfluidity came from theory which predicted superfluidity in the parameter regime which had been experimentally explored by various techniques.

May 2005 Observations of vortices at MIT established superfluidity in a fermionic gas.
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How do you show that a gas or liquid is superfluid?

The phenomenological observation of superfluidity and superconductivity (which is superfluidity for charged particles)  is the sudden disappearance of friction and dissipation below the superfluid transition temperature.  A superconducting wire sudden completely loses its resistance and currents can circulate for ever without generating any heat and dissipating any energy.  The prime example for a superfluid is helium-4.  At 2.2 Kelvin, the viscosity of the fluid drops dramatically.  Films of helium-4 can creep up containers, and helium-4 can flow through small orifices.  Similar experiments are very difficult in atomic gases because the atom clouds are small. Furthermore, they can't be kept for more than a few seconds or up to a minute because of unavoidable heating and loss processes.

The microscopic picture behind both superfluidity and superconductivity are particles marching in lockstep, when they form one big (quantum mechanical) wave.  Being one big wave implies phase coherence.  Therefore, to observe the long-range coherence is direct manifestation of superfluidity.  The superfluid velocity is proportional to the spatial variation of the phase.  In atomic Bose-Einstein condensates, the phase coherence was shown in the MIT interference experiment in 1997.  There is only on system, which is phase coherent, but not superfluid, and this is the ideal gas.  The reason is that this system has a critical velocity of zero, i.e. the superfluidity is destroyed by any kind of motion.  Therefore, superfluidity in atomic Bose-Einstein condensates was clinched by the observation of vortex arrays (Paris 2000, MIT 2001).  A regular lattice of vortices shows that the gas is phase-coherent, each vortex core showing a wrap-around of the phase by 2 Pi.  In that sense, observation of a vortex lattice is equivalent to observing phase-coherence (as in an interference experiment) and establishing at the same time that the gas remains phase coherent while it is rotating.  This directly implies a finite critical velocity below which the gas can move without friction.
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Are Bose-Einstein condensation and superfluidity the same?

In most cases, BEC and superfluidity occur together.  However, there are known examples where superfluidity occurred without Bose-Einstein condensation (1D and 2D systems) and where a Bose-Einstein condensed system doesn't show superfluidity (ideal gas, disordered systems).  Experimentally, the condensation phenomenon is observed as a narrow spike in the particles' velocity distribution.  However, due to repulsive forces between atoms and finite experimental resolution, the peak is much wider than the velocity distribution of the ground state wavefunction.  As a result, one doesn't know whether the observed "condensate" is phase-coherent.  One only knows that there is fraction of the particles which have very low energy.  It is only the observation of phase coherence or superfluid flow which established superfluidity.
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The BEC-BCS crossover

When atoms form a Bose-Einstein condensate, it is the condensation of bosonic particles which are composed of fermions, since electrons, protons and neutrons are fermions.  Usually, the binding energy of those fermions is quite high, much higher than the temperature at which the bosons condense, and one can regard the bosonic atoms as single (and not composite) particles.  This is the situation of normal Bose-Einstein condensation.  When fermion pairs condense, the pairs usually form only right at the transition temperature, and their binding energy is comparable to the transition temperature.  The nature of the pairs is not simply a two-body bound state, but includes all the other particles around --- a genuine many-body effect.  The ratio of the binding energy of the pairs to the Fermi temperature is usually very small.

Once can now imagine to smoothly vary the binding energy of the fermions and smoothly cross-over from a Bose-Einstein condensate of compact fermion pairs to a condensate of pairs which are only weakly bound by many-body effects.  The latter is called the BCS state, named after the physicists Bardeen, Cooper and Schrieffer, who discovered it

Until now superfluidity in a BEC and BCS state were two very different phenomena.  The normalized binding energy of the pairs was much larger than one in the BEC case, and much smaller in the BCS case.

With the ultracold Fermi gases, it is now possible to study superfluidity in the BEC-BCS crossover where the normalized binding energy of the pairs is around one.  It is in this regime that high-temperature superfluidity was realized.
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