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Superfluids Under Rotation(SUR2007)

Superfluids Under Rotation(SUR2007). This is a follow-up meeting to “Superfluidity under Rotation” Held at Chuzenji Lake (Japan) in May 2003 Trento (Italy) in July 2004 and Manchester (UK) in April 2005. SuR 2003 Chuzenji Lake, May 2003.

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Superfluids Under Rotation(SUR2007)

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  1. Superfluids Under Rotation(SUR2007) This is a follow-up meeting to “Superfluidity under Rotation” Held at Chuzenji Lake (Japan) in May 2003 Trento (Italy) in July 2004 and Manchester (UK) in April 2005

  2. SuR 2003 Chuzenji Lake, May 2003

  3. Torsional Oscillator Experiments of Supersolid State of He Under AC and DC Rotation and Characteristic Length Scales Andrey Penzev, Yoshinori Yasuta, and Minoru Kubota Institute for Solid State Physics, Univ. of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan

  4. What to be discussed 1]. Existence of a Vortex State in the Supersolid State of He 2]. Characteristic length scales: 3D Josephson’s Length Single quantized circulation loop length L 3]. Mechanism of Supersolid State and TO responses in the normal state

  5. What is superfluid?What is Supersolid? Can one make a superfluid? Can one find a new supersolid? What are the esssence of supersolid? What are the critical linear velocities? What is the first critical angular velocity Ωc1? : What is the first critical angular velocity Ωc2? What are the essencial scales for the vortex state existance?

  6. What is supersolid state of He? Summary of so far reported experimental results: Fact 1. NCRIF = ~ 0.0001- 0.25 at T=0 K; Inperfection or disorder of crystal is essencial for NCRIF! Dislocations and/or grain boundaries or glassy state? Fact 2. Seemingly Independence of the characteristic temperatureson NCRIF Tonset ~ 0.2K? and Tpeak = ~80 mK+-40 mK? We will comment on this point: Fact 3. What is “AC critical velocity;VACC”? Summary of Critical velocities and experimental observations

  7. 3D Superfluid out of Low D Superfluid Our Back grounds: Fundamental study of quantized vortices, New superfluids search and 3D superfluid made of KT films.(Nobody has discussed seriously finite Tc 1D superfluidity yet) He sub-monolayer Superfluid film formed on the 3D connected pore surfaces of Porous Glass substrates with well controlled pore sizes: One can controll 3D vortex core by Pore diameter and we can have the following situation a30 >> a20 And detection of vortex lines became possible.

  8. Two kinds of 3D superfluidity made of sub-monolayer He film condensed on 3D connected pore surface Thermal Wave Length, ~μm in comparison with pore Size, determines the situation. Pore Size Thin film model Shirahama,Kubota,..: Thin Film model J. Reppy: Dilute gas BEC ~Å Lattice gas model Ref.: Stoof, PRA 45, 8398 (1992), Bijlsma et.al., PRA

  9. 3D superfluid made of monolayer He films Critical velocities: 1]. Landau critical velocity Δ/P0 ?? 2]. vortex ring nucleation critical velocity ~ ρs(T) 3]. single vortex line nucleation critical velocity ?? 4]. the thermodynamic, first critical angular velocity Ωc1= 5]. overlapp of vortex cores, the second critical angular velocity Ωc2= Ω 2R h: Plank const., m4: 4He atomic mass, a: vortex core diameter

  10. Helicity Modulusγ andJosephson’s Coherence Lengthξ in a 3D superfluid:(length scale of phase fluctuation）M.E.Fisher, M.N.Barber and D. Jasnow,Phys.Rev.A8,1111 Helicity Modulus: ΔF ≡(1/2)γ(T) <∇θ>2 V(Ω) whereas ΔF=(1/2)ρs(T)vs2 V(Ω) and Vs = (h/(2πm) ∇θ Therefore ΔF= (1/2)ρs(T){(h/(2πm)∇θ}2V(Ω) γ(T) = lim (ΔF/ <∇θ>2)(L/A) [γ(T)]= [energy/length] Volume V(Ω) ∇θ L(Ω) A(Ω) Phase change A length scale Λ represents a length scale of fluctuation: Λ(T)・γ(T) = kB T =>Λ(T) = ξ(T) = (kB T)/ γ(T) = m2kB T/{(h/2π)2ρs(T)} Replacing T with Tc does not change as long as 1-T/Tc<0.2

  11. TO Experiments : 1 μm pore system: Period shift ΔP/P --> absolute superfluid density. Critical behavior of 3D superfluid

  12. Submonolayer Sfl He Films in Porous Glass with 10 μm pores: see: Mikhin, Syvokon, Obata, and Kubota, PhysicaB 329-333 (2003) 272-273. ΔP/P We can measure the absolute superfluid density, ρs(T) in g/cm3. From which we can evaluate Josephson’s phase coherence lengthξ(T): See next page.

  13. 3D coherence (Josephson’s) length ξ3 of Films on 10 μm pore An interesting observation is ξ(t) approaches a constant size as T --> 0K,(t ->1). And ξ is always larger than pore size even for 10 μm pore size porous glass!! Absolute superfluid density: ρs(T)-->ξ(T), by Josephson’s relation: ξ(T) = {kBT mHe2(2π/h)2} 1/ρs(T)

  14. Vortex State of a 3D superfluid 1]. Turbulence/ laminar flow 2]. Vortex lattice formation under rotation

  15. Vortex lines are introduced with nv ~ Ω,but the superfluid density σs is not much affected untill Ω approaches Ωc2, where vortex core starts to overlap.

  16. Torsional oscillator(TO) Experiments:Energy dissipation measurements ΔQ-1 FIG. 3: Energy dissipation curves in static condition for nonlinearregime. AC drive velocity for each curve correspondsto VAC =0.095(No.1), 0.19, 0.36, 0.52, 0.66, 0.94(No.6) cm/sec respectively.

  17. TO response to DC and AC rotation TO under DC rotation: There is no change in TO freq. AC velocity dependence of TO: M. Fukuda, et al., in preparation M.Fukuda, et al.PRB(2005)

  18. TO experiments of Solid 4He Blocked capilary method Small sample volume

  19. Experimental details High Speed Rotating Dilution Refrigerator Q=1.5∗106 Pempty=0.998374 msec

  20. Solidification process and calibrations

  21. ΔQ-1s and a characteristic temperature T*~ 0.443K for a single stable sample T (K) Q=π⋅τ⋅f Q=ΚA/Vex s

  22. Vac dependence changes its sign atT = ~ 0.4~0.5K

  23. M. Fukuda, et al.,Czechoslovak J Phys.Vol.46 S1 143 (1996), “He monolayer films on 1μm pore”

  24. ・NCRI ・10-20[μm/sec]:Vc (NCRIF starts to decrease) NCRI has 2 different part? ・ One decreasing toward 700[μm/sec] ・The other toward 4[mm/sec] Two superfluid components？ 4000[μm/sec] 10-20[μm/sec] 700[μm/sec] Sample A Estimate of a single quantum circulation Path length L: Length of L corresponding to Vs m: starting with using mass of 4He h: Planck’s constant n=1 Vs: Vac

  25. Persistence of NCRI under DC Rotation up to 1 Revolution per second (6.28cm/s) NCRI remainsUnchanged under DC Velocity at least 15 times the VAC which is necessary to depress Completely NCRI to zero. Which can be explained By either existance of vortices like in Superfluid liquids or by Absence of Centrifugal Force acting on dislocations. The latter can not be the case. Therefore we do have Quantized Vortex state.

  26. What to be discussed 1]. Existence of a Vortex State in the Supersolid State of He Confirmed!? 2]. Characteristic length scales: 3D Josephson’s Length Single quantized circulation loop length L 3]. Mechanism of Supersolid State and TO responses in the normal state: Vibrating dislocation model: Frequiency dependence ---> X

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