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

Liquid He4 is 100% superfluid

at T=0 Solid He4 is ~2% superfluid

at T=0

E. L. Andronikashvili, (1946) E. Kim and M. H. W. ChanScience 305

2004

ρS

0

1

2).exp(),()( ∫∫ Ψ= rrpsrsp didn

r=r1 s=r2

..rN

Bose –Einstein Condensation

(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

Fractional weight of condensate peak = f

Momentum distribution

Non-zero over length scales ~L

Ground state of liquid 4He

Phase correlations over distances ~L

Ψ(r,s) is connected over macroscopiclength scales between phase coherentpoints e.g. 1 and 2

2

1

Ψ(r,s)

Loops in Ψ(r,s)

over macroscopic (cm) length scales

Mass flow must be quantisedover macroscopic length scales

Single valued wave function

∫ =mnhdv rr).(

Normal viscous processescannot occur → zero viscosity at T=0

Ψ(r,s)

in solid

Can still be connected over macro lengthscales 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.

RotatingAu Foil

Beam Direction

OCylinder of solid He4 inDilution fridge

92 Back scatteringdetectors

VESUVIO Measurement

he can

can

He4

Binned data

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

liquid

O

single crystal high purity He4X

polycrystal

high purity He4□

10ppm He3 polycrystal

solid

J. Mayers, F. Albergamo, D. Timms Physica

B

276

(2000) 811

σ

MKE

223 22σh

=

T (K) (101) (002) (100)

0.070 2.758 (7) 3.1055

(300)

0.115 2.759 (7) 3.1055

(300)

0.150 2.758 (7) 3.1056 (300)

0.400 2.759 (7) 3.1055 (300)

Measured hcp

lattice spacings

SingleCrystalPure He4

PowderPure He4 0.075 2.758 (2) 2.934 (4) 3.131 (2)

PowderHe4+10ppm He3

0.075 2.757 (3) 2.940(3) 3.128 (2)

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.

S. O. Diallo,J.V. Pearce, R. T. Azuah, O. Kirichek, J.W. Taylor, and H. R. GlydePRL 98, 205301 May 2007n0

= 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?

Recent Experiments

Proposed experiment (POLARIS)

Perform in situ NCRIF experiment

Measure diffraction with and without supersolidity