Superfluid 4He Critical Phenomena in Space, and in the SOC State on Earth

R.V. Duncan, University of Missouri

NASA ISS Workshop on Fundamental PhysicsDana Point, CA, October 14, 2010

Sponsored by NASA through the Fundamental Physics Discipline within the Microgravity Project Office of NASA. R.V.D. thanks Gordon and Betty Moore for sabbatical support.

Jet Propulsion LaboratoryCalifornia Institute of Technology

CQ (Caltech) and DYNAMX (UNM)

At UNM:Robert Duncan S.T.P. Boyd Dmitri Sergatskov Alex Babkin Mary Jayne AdriaansBeverly KlemmeBill Moeur Steve McCready Ray Nelson Colin Green Qunzhang LiJinyang LiuT.D. McCarsonAlexander Churilov

At Caltech:David Goodstein Richard Lee Andrew Chatto

At JPL:Peter Day David ElliottFeng Chuan Liu Talso Chui Ulf Israelsson

Pressure dependence of T breaks ‘up-down’ symmetry and stabilizes an interface on Earth

He-II

He-I

| = 1.3 K/cm

h

T

(h)He-I

He-II

Non-equilibrium interface stabilizes without gravity! See Weichman et al., Phys. Rev. Lett. 80 4923 (1998)

Now apply a heat flux Q:

Electrical currents in superconductors lower the ‘quench temperature’ in much the same way that a heat flux lowers the temperature where superfluidity abruptly fails in helium.

Tc(Q) = T [1 – (Q/Qo)y], but c =

Theory: Qo = 7 kW/cm2, y = 1/2 = 0.744Onuki, JLTP 55, and Haussman & Dohm, PRL 67, 3404 (1991) Experiment: Qo = 568 W/cm2, y = 0.81± 0.01Duncan, Ahlers, and Steinberg, PRL 60, 1522 (1988) Thermal conductivityx, but now Q,z = [T(z) – Tc(Q,z)] / T

Experimental Concept

He-SOC

Q + Q

Q

Sidewall Thermometry Probes: Thickness: 50 75 125

Interface

He-II

Science objectives are obtained from the thermal profile data (noise level of < 100 pK/√Hz), while the heat flux is extremely well controlled to Q ~ 1 pW/cm2

The Direction of Q is Important :

He-II

He-SOC

He-II

He-I

Q

Q

SOC

HfA

HfB

HfB: ‘Heat from Below’

He-II

He-I

Q

- Correlation length divergence is cut-off on Earth - Nonlinear thermal resistivity near T

HfB: The Nonlinear Region

Theoretical prediction of the nonlinear region [Haussmann and Dohm, PRL 67, 3404 (1991); Z. Phys. B 87, 229 (1992)] with our data [Day et al., PRL 81, 2474 (1998)].

HfB: Tc(Q), TNL(Q), T

Tc(Q) and TNL(Q) are expected to extrapolate to T as Q goes tozero in microgravity, but not on Earth, as explained by Haussmann.

0 50 100 150 200

-50

-40

-30

-20

-10

0

10

20

TC(Q)

TNL(Q)

15 nK = dT/dh * g, but what is T?

[ nK

, arb

. orig

.]

Q (nW/cm2)

Gravitational Effect: g

As the superfluid transition is approached from above, the diverging correlation length eventually reaches its maximum value g = 0.1 mm, at a distance of 14 nK from T.

HfA: Heat from Above

A: Cell is superfluid (hence isothermal), and slowly warming at about 0.1 nK/s B: SOC state has formed at the bottom and is passing T3 as it advances up

the cell, invading the superfluid phase from belowC: Cell is completely self-organizedD: As heat is added the normalfluid invades the SOC from above

(Suggested by A. Onuki and independently by R. Ferrell in Oregon, 1989)

q

Tc(Q) - T

Tsoc(Q)

What is Tsoc(Q)?

T = Q, so soc = Q / soc soc

-x = Q /

soc = [Q/( )]-1/x

T soc = Tsoc(Q,z) – Tc(Q,z)

Tsoc - Tc = T [Q/( )]-1/x

≈ 10-5 W/(cm K), x ≈ 0.48 ≈ 1.27 K / cm

Tsoc - Tc = T [Q / (12.7 pW/cm2)]-2.083

= 2,000 nK (Q = 10 nW/cm2) = 0.14 nK (Q = 1,000 nW/cm2)

Moeur et al., Phys. Rev. Lett. 78, 2421 (1997)

How does He-II do this?Synchronous phase slips – each slip creates a sheet of quantized vortices See: Weichman and Miller, JLTP 119, 155 (2000):

Wave travels only against Q, so ‘Half Sound’Sergatskov et al., JLTP 134, 517 (2004)Weichman and Miller, JLTP 119, 155 (2000)And now Chatto et al., JLTP (2007)

A New Wave on the SOC State

Q

New SOC Anisotropic Wave PropagationT-wave travels only against Q (bottom to top). See:“New Propagating Mode Near the Superfluid Transition in 4He”, Sergatskov et. al., Physica B 329 – 333, 208 (2003), and“Experiments in 4He Heated From Above, Very Near the Lambda Point”, Sergatskov et. al., J. Low Temp. Phys. 134, 517 (2004), andChatto, Lee, Day, Duncan, and Goodstein, J. Low Temp. Phys. (2007)

The basic physics is simple:

2

dTC Qdt

Q TdTC T Tdt

So : u = /CIf C ~ constantThen u = DD = /C

Wave Speed v(Q)Following Chatto et al., 2007

= (T – T)/T

New Anisotropic Wave SpeedChatto, Lee, Duncan, and Goodstein, JLTP, 2007.

u = - C-1 ∂QSOC/∂T

Sergatskov et al., (2003)

STP Boyd et al., unpublished

How do we measure Csoc?

Q1 Q2

Total cell heat capacitymeasurements as the SOC interface advanceshave been made by R.A.M. Lee et al., JLTP134, 495 (2004).

Q1 > Q2

Heat Capacity on the SOC StateChatto, Lee, Duncan and Goodstein, JLTP (2007)

Predicted by

Haussm

ann

‘Unrounded Earth-based data in 2.5 cm tall cell!High-Q data

13>Q> 6W/cm2

R. Haussmann, Phys. Rev. B 60, 12349 (1999).

Lambda Point Experiment Data (Microgravity)

Recent Results (Chatto et al.)

• Csoc has been measured and agrees with microgravity CP for 250 ≤ T – T ≤ 650 nK – Csoc agrees with static heat capacity from Lambda

Point Experiment on Earth orbit– Notice that T is still the true critical point even

when driven away from equilibrium – NO OBSERVED GRAVITATIONAL ROUNDING!

• Reason suggested for why Csoc diverges at T and soc diverges at Tc(Q)

Space flight is the only way to avoid g

See Barmatz, Hahn, Lipa, and Duncan, “Critical Phenomena Measurements In Microgravity: Past, Present, and Future”, Reviews of Modern Physics 79, 1 (2007)

Past CDR in 2003

Cancelled in 2004

All 117 ‘ClassB’approved hardware drawingsare in place.

Need:- new PI team- flight dewar- platform- ride

Also… Interested in theFundamental Measurement Limits of Thermometry? [‘Cruise Control’: f =1,000+, so M > 2]Statistically, δT/T ~ 1/√N Other limits:Electronic Johnson noise / shot noise… if resistive, but our thermometers are too good to resist!Thermal energy fluctuation limits

Paramagnetic Susceptibility Thermometry

Magnetic flux is trapped in aniobium tube

A paramagnetic substance with T > Tc is thermally anchored to the platform

M = H (T)

[(T – Tc)/Tc]- so small changes in T create large changes in M, and hence in the flux coupled to the SQUID

Gifford, Web, Wheatley (1971)Lipa and Chui (1981)

H

Fundamental Noise Sources

Heat fluctuations in the linkone independent measurement per time constant = RC(noise)2 / C(TQ)2 = 4RkBT2

so TQ √R and TQ TSee: Day, Hahn, & Chui, JLTP 107, 359 (1997)

Thermally induced electrical current fluctuationsmutual inductance creates flux noise()2 T N2 r4 / L M = / s, s ≈ 1 so M √T

SQUID noise(SQ)21/2 ≈ 4 √Hz with shorted inputexternal circuit creates about three times this noise levelso ≈ 12 √Hz and SQ ≈ 12 pK/√Hz

T, C Tbath

R

r

N

L

Heat Fluctuation Noise Across the Link

R = 40 K/W

(TQ)2 = 4RkBT2

so TQ = 0.10 nK/√Hz

3 dB point at 10 Hz,suggesting ≈ 50 ms

(collaboration with Peter Day)

HRT Time Constant

Method:

• Controlled cell temperature with T1

• Pulsed a heater located on T2

• Cell in superfluid state

• Contact area of only 0.05 cm2

• Rise time ~ 20 ms

• Decay time = 48 ms

Collaboration with Peter Day

New Ultra-Stable Platform

The helium sample is contained within the PdMn thermometric element. Power dissipation is precisely controlled with the rf-biased Josephson junction array (JJA). Stabilized to T ~ 10-11 K.

1

2

Green, Sergatskov, and Duncan, J. Low Temp. Phys. 138, 871 (2005)

Reduce the Heat Fluctuation Noise

Reduce R from 40 to 0.25 K/W

Now TQ ≈ 7 pK/√Hz

Minimize TM with a gap toreduce mutual inductance to the SQUID loop

is PdMn thickness = 0.76 mm

r4 4 r 3 r3/(43) ≈ 18

Noise: Thermally Driven Current Fluctuations

Thermal current fluctuations: = 38 /(Hz K)1/2 √SQUID circuit noise: SQ = 12.5 /√Hz

RF-biased Josephson Junctions for Heater Control

Vn = n (h/2e) fh/2e = o = 2.07 V/GHzf = 94.100000000 GHzRel = 1,015 Pn = Vn

2 / Rel = 37.3 n2 pW

Standoff vs. Josephson Quantum Number n

Rel = 1,015

Rso = 4,456 K/W

Tcool

T

Rso

n = 7

n = 10

n = 0

A New ‘Fixed-Point’ Standard

T = T – 125 K

Future Work: Radiometric ComparisonsThree independent BB references

Inner shield maintained at T± 50 pK

Each reference counted up from T

to 2.7 K using Josephson heater control

Compare to each other with 0.1 nK resolution in a well controlled cryostat

New control theory has been developed

(Discussions with Phil Lubin, UCSB and with George Seidel at Brown)

Conclusions• Fundamental noise sources in PST

identified and reduced• Lowest noise 25 pK/√Hz at 1.6 K• New rf-biased Josephson junction heater

controller developed• Technology in place now to develop a

reference standard more stable than the CMB temperature (< 200 pK/year drift) in a weightless lab, provided that T does not vary with the cosmic expansion

0

5

10

15

20

25

30

35

40

1.5 2 2.5 3 3.5 4

Temp (K)

Sens

itivi

ty (f

lux

quan

ta/m

K)

6 G

35 G

150 G

250 G

0

5

10

15

20

25

30

35

40

1.5 2 2.5 3 3.5 4Temp (K)

Sens

itivi

ty (f

lux

quan

ta/m

K)

Decreasing T - 6gauss

Increasing T - 6 gauss

Decreasing T - 35gauss

Increasing T - 35gauss

PdMn0.9% 12 m Film Magnetic Susceptibility ThermometrySee R.C. Nelson et al., JLTP (2002) For thermometry, See Duncan et al., 2nd Pan Pacific Basin Workshop, 2001.

Thin film sensitivity vs. T and H No hysteresis was observed

New Data, PdMn0.4%, 6.67 m thick films

Tc=1.17 ± 0.01 K

= 1.41 ± 0.01

Data by… Ray NelsonColin GreenDmitri SergatskovR. V. Duncan