Is There a Bose Condensate in Supersolid Helium?

Is there a Bose condensate in Supersolid helium?

Collaborators

• M. A. Adams (ISIS) • O. Kirichek (ISIS)

• R. B. E. Down (ISIS)

“Measurement of the kinetic energy and lattice constant • in hcp solid helium at temperatures 0.07-0.4 K” M. A. Adams, J. Mayers, O. Kirichek and R.B.E. Down

• Phys. Rev. Lett. 98 085301 Feb 2007

Experimental evidence

E. L. Andronikashvili, (1946) E. Kim and M. H. W. Chan Science 305 2004

ρS

Liquid He4 is 100% superfluid at T=0 Solid He4 is ~2% superfluid at T=0

Bose –Einstein Condensation

Momentum distribution

2 dn ∫∫ Ψ= ).exp(),()( di rrpsrsp

r=r1 s=r2..rN

Fractional weight of condensate peak = f

(a)Ψ(r,s) is a non zero function of r over length scales ~ L

(b) Ψ(r,s) has phase correlations over distances ~L Ground state of liquid 4He

Ψ(r,s) Non-zero over length scales ~L

1 Phase correlations over distances ~L

Ψ(r,s) is connected over macroscopic 2 length scales between phase coherent points e.g. 1 and 2 Single valued wave function

nh ).( dv rr = ∫ m

Mass flow must be quantised over macroscopic length scales Loops in Ψ(r,s) over macroscopic (cm) length scales

Normal viscous processes cannot occur → zero viscosity at T=0 Ψ(r,s) in solid

Can still be connected over macro length scales if enough vacancies are present

Solid can “flow” if

(a) Flow conserves mass density

(b) wave function is connected

At least ~10% vacancies →~10% condensate fraction If BEC of atoms is the origin of supersolidity, reducing T should

• Decrease kinetic energy.

• Increase vacancy concentration.

VESUVIO Measurement

Cylinder of solid He4 in O Dilution fridge Rotating Au Foil

92 Back scattering detectors

Beam Direction

he can can

He4

Binned data from 92 detectors Binned data after can subtraction. Dotted line is resolution function

solid σ

O single crystal high purity He4 X polycrystal high purity He4 □ 10ppm He3 polycrystal

3 σ 22 KE = h 22 M liquid

J. Mayers, F. Albergamo, D. Timms Physica B 276 (2000) 811

Measured hcp lattice spacings T (K) (101) (002) (100)

0.070 2.758 (7) 3.1055 (300) Single Crystal Pure He4 0.115 2.759 (7) 3.1055 (300)

0.150 2.758 (7) 3.1056 (300)

0.400 2.759 (7) 3.1055 (300)

Powder 0.075 2.758 (2) 2.934 (4) 3.131 (2) Pure He4

0.075 2.757 (3) 2.940(3) 3.128 (2) Powder He4+ 10ppm He3 Conclusions

• No change in KE, no change in vacancy concentration through SS transition.

• Implies SS transition quite different to SF transition in liquid.

• Probably not BEC in crystalline helium.

Recent Experiments

S. O. Diallo,J.V. Pearce, R. T. Azuah, O. Kirichek, J.W. Taylor, and H. R. Glyde PRL 98, 205301 May 2007 n0 = 0:10 ± 1:20% at T 80 mK n0 = 0:08 ± 0:78% at T 120 mK

A S Ritner, J D Reppy PRL 98, 175302 May 2007

Supersolid fraction reduced by annealing.

Glassy phase? Proposed experiment (POLARIS)

Perform in situ NCRIF experiment

Measure diffraction with and without supersolidity