The Early Universe as a Complex System Driven Far from Equilibrium: Non-Equilibrium Superfluid 4 He as an Analogous System R.V. Duncan, University of New Mexico, and Caltech (University of Missouri, Columbia, effective 8/18/08) Quantum to Cosmos III Airlie Center, Warrenton, VA July 9, 2008 Sponsored by NASA through the Fundamental Physics Discipline within the Microgravity Project Office of NASA, and supported through a no-cost equipment loan from Sandia National Labs. R.V.D. thanks Gordon and Betty Moore for sabbatical support. Jet Propulsion Laboratory California Institute of Technology

CQ (Caltech) and DYNAMX (UNM) At UNM: Robert Duncan S.T.P. Boyd Dmitri Sergatskov Alex Babkin Mary Jayne Adriaans Beverly Klemme Bill Moeur Steve McCready Ray Nelson Colin Green Qunzhang Li Jinyang Liu T.D. McCarson Alexander Churilov At Caltech: David Goodstein Richard Lee Andrew Chatto At JPL: Peter Day David Elliott Feng Chuan Liu Talso Chui Ulf Israelsson

Non-equilibrium Quantum Systems Dense Sparse  TcTc TT Q T = h / p rms p rms = (3mkT) ½ T = h / (3mkT) ½ BEC when T ≈ d kT c ≈ h 2 /(3md 2 ) This system may form an SOC state where  T =  T c and quantized topological defects are continuously produced.   e i 

Properties of Liquid 4 He Near its Superfluid Transition 4 He never freezes under its vapor pressure, due to quantum zero-point motion, and due to weak He – He attractions –Zero-point kinetic energy E o ~ (m d 2 ) -1 –E o /k B in 4 He ~ 10 K and it never ‘freezes out’ –van der Waals attraction is about 5 K Superfluid transition at T under SVP (0.05 bar) Reduced Temperature:  = (T–T ) /T –Zero viscosity –Perfect thermal conductivity –‘superfluid’ component is effectively at T = 0

‘Two Fluid’ model of the superfluid transition  =  n +  s, j = j n + j s (  v =  n v n +  s v s ) When j = 0, either equilibrium or counterflow

Long-Range Quantum Order Below T :    e i  V s = (ħ/m)  s  m    Hence,  x V s ~  x  You can not rotate a perfect superfluid, but … You can rotate a ‘Type II’ superfluid provided that you create topological defects (quantized vortices)

Quantized Vorticity (QV) Source: Tilley and Tilley, Figure 6.10 Erkki Thuneberg,

QV / LRQO in many superfluids Superconductors (  o = h/2e) Superfluid 3 He (Cooper pairs) Bose-Einstein Condensates (2005) Neutron Stars Cosmology –Topological defects –Symmetry breaking –Event horizon model Source: Pines, LT12 (1971) p. 7

New Sub-Topic: Superfluids Near Criticality Correlation length measures range of fluctuations  o  , where  = |T - T |/T with  o = 2x10 -8 cm and = We routinely stabilize  ~ 10 -9, where the divergence of  is limited by gravity Thermal conductivity Diverges due to fluctuations:  =  o  -x with x ≈ ½ Field Theory: ‘Model F’ of Halperin, Hohenberg, Siggia See Hohenberg and Halperin, Rev. Mod. Phys. 49, 435 (1977). Renormalization: Haussmann & Dohm, PRL 67, 3404 (1991).

Pressure dependence of T breaks ‘up-down’ symmetry and stabilizes an interface 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 (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. T c (Q) = T [1 – (Q/Q o ) y ], but  c =  Theory: Q o = 7 kW/cm 2, y = 1/2 = Onuki, JLTP 55, and Haussman & Dohm, PRL 67, 3404 (1991) Experiment: Q o = 568 W/cm 2, y = 0.81± 0.01 Duncan, Ahlers, and Steinberg, PRL 60, 1522 (1988) Thermal conductivity     x, but now define  Q,z  = [T(z) – T c (Q,z)] / T

Experimental Concept 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/cm 2

Jet Propulsion Laboratory California Institute of Technology National Aeronautics and Space Administration

‘T5’Critical Thermal Path

Experimental ‘T5’ Apparatus

Open System: ‘Heat from Below’ He-II He-I  Q The ‘simple’ critical point (‘lambda’ point) transforms into a complex nonlinear region where the onset of long-range quantum order is limited by the heat flux Q, and by gravity

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)].

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.

HfB: T c (Q), T NL (Q), T T c (Q) and T NL (Q) are expected to extrapolate to T as Q goes to zero in microgravity, but not on Earth, as explained by Haussmann.

The Direction of Q is Important : He-II He-SOC  He-II He-I  Q Q SOC! HfA HfB

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 below C: Cell is completely self-organized D: As heat is added the normalfluid invades the SOC from above (Suggested by A. Onuki and independently by R. Ferrell in Oregon, 1989) q 

Approach to the SOC State Simply integrate  [  (z,Q)] dT/dz = - Q (numerically) Moeur et al., Phys. Rev. Lett. 78, 2421 (1997) z (10 -3 cm) T  = T - T c (z,Q)

T c (Q) - T T soc (Q) What is T soc (Q)?  T = Q, so  soc = Q /   soc    soc -x = Q /   soc = [Q/(    )] -1/x T  soc = T soc (Q,z) – T c (Q,z) T soc - T c = T [Q/(    )] -1/x   ≈ W/(cm K), x ≈ 0.48  ≈ 1.27  K / cm T soc - T c = T [Q / (12.7 pW/cm 2 )] = 2,000 nK (Q = 10 nW/cm 2 ) = 0.14 nK (Q = 1,000 nW/cm 2 ) Moeur et al., Phys. Rev. Lett. 78, 2421 (1997)

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Q

New SOC Anisotropic Wave Propagation T-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), and Chatto, Lee, Day, Duncan, and Goodstein, J. Low Temp. Phys. (2007) The basic physics is simple: So : u =  D, where D =  /C

New Anisotropic Wave Speed Chatto, Lee, Duncan, and Goodstein, JLTP, More generally: u = - ∂Q SOC /∂T (Chatto et al.)

Similarity in Temperature and Mass SOC ∂T/∂t = (  /C p )  2 T + u  T where u = C p -1  Likewise, for concentration c(z,t) of some agent, ∂c/∂t = D c  2 c + u  c where u =  D c If D c is singular along a critical line, then similar SOC waves should be observed. Will spinoidal decompositions create singular mass diffusivities? Intermittency in ion channels? Iodine waves near the basement membrane of the thyroid gland?

What is going on microscopically? How does helium develop the huge thermal conductance (> 10 W/(cmK)) necessary to self-organize at high Q? –Weichman and Miller, JLTP 119, 155 (2000): Q-induced vortex sheet shedding Vortex production rate increases as Q decreases –New experiments to measure vorticity creation –Experiments that sense second sound noise

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):

Recent Results (Chatto et al.) C soc has been measured and agrees with microgravity C P for 250 nK ≤ T – T ≤ 650 nK –C soc agrees with static heat capacity from Lambda Point Experiment on Earth orbit –NO OBSERVED GRAVITATIONAL ROUNDING! Reason suggested for why C soc diverges at T and  soc diverges at T c (Q)

Recent results on the Self-Organized Critical State Chatto, Lee, Duncan, and Goodstein, JLTP (2007) Predicted by Haussmann ‘Unrounded Earth- based data in 3 cm tall cell! High-Q data R. Haussmann, Phys. Rev. B 60, (1999).

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

Next Point: This ‘CMP’ measurement technology has opened the door to a new class of experimental possibilities that may be useful in observational cosmology …

Fundamental Noise Sources Heat fluctuations in the link one independent measurement per time constant  = RC (noise) 2   / C  (  T Q ) 2  = 4Rk B T 2 so  T Q  √R and  T Q  T See: Day, Hahn, & Chui, JLTP 107, 359 (1997) Thermally induced electrical current fluctuations mutual inductance creates flux noise  (  ) 2   T N 2  r 4 / L  M =  / s, s ≈ 1    so  M    √T SQUID noise  (  SQ ) 2  1/2 ≈ 4    √Hz with shorted input external circuit creates about three times this noise level so  ≈ 12    √Hz and  SQ ≈ 12 pK/√Hz T, C T bath R r N  L

Heat Fluctuation Noise Across the Link R = 40 K/W  (  T Q ) 2  = 4Rk B T 2 so  T Q = 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 cm 2 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 ~ 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  T Q ≈ 7 pK/√Hz Minimize  T M with a gap to reduce mutual inductance to the SQUID loop  is PdMn thickness = 0.76 mm r 4  4 r  3 r 3 /(4  3 ) ≈ 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 V n = n (h/2e) f h/2e =  o = 2.07  V/GHz f = GHz R el = 1,015  P n = V n 2 / R el = 37.3 n 2 pW

Standoff vs. Josephson Quantum Number n R el = 1,015  R so = 4,456 K/W T cool T R so

n = 7 n = 10 n = 0 A New ‘Fixed-Point’ Standard T = T – 125  K

Future Work: Radiometric Comparisons Three 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 and eventually to the CMB with 0.05 nK resolution New control theory has been developed (suggested in part by Phil Lubin, UCSB)