Supersolids. Bose-Einstein Condensation in Quantum Solids Does it really exist?? W. J. Mullin

Transcription

1

2 Supersolids Bose-Einstein Condensation in Quantum Solids Does it really exist?? W. J. Mullin This is a lively controversy in condensed matter physics. Experiment says yes. Theory says no, or at best maybe. I. Superfluidity. Flow without friction. How does that occur? II. Bose-Einstein condensation. What is it? III. Quantum crystals. What makes them quantum? IV. Supersolids. Can superfluidity exist in a crystal?

3 Quantized Energies In QM a particle in a box has only certain allowed frequencies and energies Particles with short wavelengths (high energies) behave like marbles. Particles with long wavelengths (low energies) behave like waves Can t tell one from another. Quantum interference λ= Weird behavior. Energy Low T means long wavelength E 4 E 3 E 2 E 1 E 0 h < p > = h 2 2πmkT DeBroglie or thermal wavelength

4 Temperature Scales

5 The Cryostat -- a big thermos bottle.

6 Two kinds of particles in nature Fermions (Fermi-Dirac statistics) - all spin- particles e, n, p, µ, ν, quarks, and composites of an odd number of fermions Pauli principle- only one Fermion at a time allowed in each state Electrons in the atom, nuclei in the nucleus, white dwarf star Bosons (Bose-Einstein statistics) - all spin 0,1,... particles γ, π, w, z, gluons,.., composites of an even number of fermions. Bose principle -preference for occupation of the same state by more than one particle BEC in trapped gases and in liquid 4 He 1 2

7 2n 2p 4 He e e Superfluids Liquid 4 He first produced in 1908, superfluid studies in 30 s. Weird properties Liquid all the way to T=0K. (Solidifies only under pressure.) Excellent heat conductor (better than copper) Superleak T>2.2K T<2.2K 1n 2p 3 He e e Fictionless flow Persistent currents

8 Phase Diagram of Liquid Helium Andronikashvili's Experiment

9 Bose-Einstein Condensation Einstein (1925) found that at a certain temperature there was a phase transition in a collection of bosons in which a large number of particles fell into the lowest state. The number in that state grows as the temperature drops. Energy T>T c Energy T<T c E 4 E 3 E 2 E 1 E 0 E 4 E 3 E 2 E 1 E 0 N 0 particles N 0 Tc T Bitter theoretical debate between Landau and London over explanation via BEC (40 s, 50 s)

10 Explanation by BEC? Analogy: Bose effect in the laser (photons are bosons) Bosons like to be in the same state All photons have same frequency, same phase. Superfluid: Particles like to move all in the same way, as a group Energy gap gap object moves through liquid without being able to transfer energy no friction

11 Fermions and Superfluidity Superconductivity Metals that conduct electricity without resistance. Metals have transition T c at few Kelvin. Electrons pair up ( Cooper pairs ) coherently and cooperatively below T c. (Electron pairs are bosons, but this is not quite BEC.) Hi- T c superconductivity (>90K) discovered in ceramics. Superfluidity in liquid 3 He Superfluid transition at T=2 mk Three different superfluid phases Osheroff, Lee, and Richardson Nobel Prize in 1996.

12 Bose-Einstein Condensation of Trapped Atoms 7 Li, 23 Na, 87 Rb are Bosons Atoms are cooled to a transition temperature where they suddenly fall into the lowest energy state. Laser cooling plus magnetic evaporation. This is the phase transition predicted by Einstein in 1925! Cornell and Weiman* JILA, CU Rb 20,000 atoms, Tc= 0.2 µk July 95 Ketterle* MIT Na 50,000 to millions 2 µk August 95 Hulet Rice U Li 20,000 atoms 0.2 µk 1996 * Nobel Prize 2001

13 Theory is easy in a weakly interacting dilute gas; agreement with experiment is remarkable. Spectacular experimental possibilities Atom interference Atomic Laser! -- a coherent source of atomic matter waves

14 Quantum Crystals The lightest elements, hydrogen and helium, form crystals at low temperature. They show the effects of quantum mechanics, especially helium Zero-point energy: Particle in a box has a lowest energy E 0 h2 ml 2 N Particles confined in a crystal have smallest energy E N h2 ma 2 where a is interparticle separation.

15 Helium remains a liquid at T = 0 K unless one applies pressure (25 atm). Zero-point energy melts it. When it does form a crystal it is blown up by zero point motion by a factor of 2. Quantum tunneling: Particles easily exchange places. (Overlapping wave functions) Vacancy waves: All crystals have thermally activated vacancies. You have to heat the crystal to make them. Solid helium has vacancy waves. A vacancy is spread out over the whole crystal

16 All vacancies that have been observed directly in solid helium have been of the thermally activated kind. Zero-Point Vacancies??? Suppose delocalized vacancies existed in the crystal even at T = 0 K. Could the vacancies form a BEC and cause particle motion without friction? That would be a superfluid with solid ordering. Such a state was proposed theoretically in the 70 s. Several experiments looked for it but, never saw it.

17 Until last year! Probable observation of a supersolid helium phase E. Kim & M. H. W. Chan Nature 427, 225 (2004) Torsional oscillator--solid 4 He in vycor (hole-filled glass) annulus and without vycor Moses parts the Red Solid?

18 Measure the superfluid fraction ~2% by observing decrease in moment of inertia

19 New York Times article

20 Theory Old theories suggested supersolids in the first place. More recent work: One side: Supersolids cannot exist without zero-point vacancies, which are not observed. So it is something else. Other side: Superfluidity can be carried via exchange without vacancies. Large Monte Carlo simulations are involved on both sides of the argument. Other recent experiments have not found the same super flow as yet. So what have Kim and Chan found?