Micro-machined Probes for the Study of Quantum Fluids

Transcription

1 Micro-machined Probes for the Study of Quantum Fluids Yoonseok Lee University of Florida

2 UF Group Dr. Miguel Gonzalez (PhD, Saudi Aramco) Pan Zheng (Grad Stu) on 3He Colin Barquist (Grad Stu) on 4He Wenguang Jiang (Grad Stu) on 3He Dr. Byoung Hee Moon (PhD, SKKU, Korea) Joshua Bauer (UG, NI) Erik Garcell (UG, Rochester) Aleksander Levental (UG, Star-up Co.) HKUST Group Ho Bun Chan

3 Quantum Fluids

4 Species n (cm -3 ) T C (T o ) 3 He F 1.6 x mk (3 K) 4 He B 2.2 x K (3 K) e - (Nb) F 5.5 x K (10 4 K) n-star F 4.0 x K (10 12 K) They all go into superfluid or superconducting state at low enough temperature. Emerging Complex Phenomena from Simple Ingredients

5 3 He G. Volovik

6 Y A = D A p x +ip y ( )( + ) Chiral SF, Quantum Hall State in slab) G = SO L (3) x SO S (3) x P x T x U(1) x t From Helsinki Univ. of Technology picture archive { + p x -ip y Y B = D B ( p x +ip y ) (TRI 3D Topological SF) ( ) + p z ( + )}

7 Excitations of Superfluid 3 He Femionic Excitations 3 He quasi-particles 3 He-A: Weyl chiral fermion out of Dirac cone (two nodes) 3 He-B: Massive Dirac fermion (isotropic gap) Bosonic Excitations 18 Order parameter collective modes Finger Print of Underlying Symmetry Some are Goldstone modes (zero gap) Some are massive modes with a finite gap E 2 = c 2 q 2 + b 2 (D) Topological Excitations Vortices (regular, ½, q-vortex, vortex sheet) Particle-like topological excitations in superfluid films.

8 Suppression of Order Parameter near the Boundary Pair-breaking Scattering Specular Okuda and Nomura, J. Phys.: Condens. Matter (2012) Parallel Comp. Specular Diffusive Perpend. Comp. Andreev Surface Bound States Aoki et al., PRL (2005) Diffusive z/x

9 SDOS SDOS Surface Scattering in 3 He-B Specular limit Diffusive limit S = 1 S = 0 E p y S=1.0 E S=0.0 p x p // P p // P

10 N(,z = 0) / N(0) T = 0.2 T c s = 0.0 s = 0.2 s = 0.5 s = 1.0 D* D bulk

11 Vorontsov and Sauls, PRL 98, (2007). Superfluid + Spontaneously Broken Trans Symmetry Last symmetry survived in Superfluid 3 He is broken. Confinement effect (c.f. Zeeman splitting) Inhomogeneous superfluid Orbital version of FFLO

12 Interesting physics emerging from the localized surface excitations*** in superfluid 3 He: Inhomogeneous SF*, Topological excitations (Majorana)**, Lack of spatial/momentum resolved probes in quantum fluids - crucial in understanding the nature of excitations. e.g. ARPES, Neutron scattering, STM... Imbed detectors, quasi-particles generated internally in quantum fluids. * Vorontsov, Sauls, Phys. Rev. Lett. (2007). ** Chung and Zhang, Phys. Rev. Lett. (2009). ** Murakawa et al., Phys. Rev. Lett. (2008); J. Jpn. Phys. Soc. (2011). Tsutsumi, Ichioka, and Machida, Phys. Rev. B (2011). Sauls, Phys. Rev. B (2011). Mizushima, Phys. Rev. B (2012). Wu and Sauls, accepted in Phys. Rev. B (2013).

13 DEVICE

14 DEVICE CRITERIA Form a well-defined slab or film of variable d < 1 mm at any sample pressure High resolution surface sensitive probe Controllable surface quality or structure Scalable

15 D = 0.75,1.25, 2.00 mm L = 200 mm Fixed electrode L Bulk fluid Center plate Fixed electrode Fluid film Bottom plate Substrate D

16 PolyMUMPS

17 González et al. Rev. Sci. Instrum. 84, (2013)

18 Hz Hz Shear X-pivot Hz Hz Z motion Y-pivot

19 + DETECTION SCHEME Inductance ratio transformer Y 200kΩ X V LF < 1 2 Sum #1 s 220nF MEMS a + V DC Lock-in Lock-in MEMS Amp #1 #2 HF Ref LF Ref V HF t a d < 1 2 Sum #2 s 220nF 200kΩ Transduction Factor V DC Measured voltage

20 x, v = o x D Q RT» Q 4K» 10 5

21 LINEAR DAMPING

22 d = 2h rw z» A d h V < z» A d h d >> Slide Film Damping d» Slip boundary condition

23 RT Air Damping o Pressure dependent damping o Slide film damping model Bruschi et al., Sensors and Actuators (2004) = md Effective viscosity

24 Pressure Dependence at RT

25

26 Heat Exchanger Device Cell Device Socket Device Cell Electric Connectors Pt NMR Thermometer

27 Quasi-particle spectrum in fermion system E E v L =D/p F Fermi Energy p D p æ N qp (T << T C )µ N(E F )k B T expç- D è k B T ö æ» ç T ø èt F ö æ expç- D ø è k B T ö ø

28 Quasi-particle Thermal Damping in 3 He-B at Low T S.N. Fisher et al., PRL (1989) æ N(p F )k B T exp - D ö ç è k B T ø æ µ expç- D è k B T öì u 2 ía 1 u - A 2 øî k B T ü ý þ v Additional Damping from Pair-breaking F

29 æ exp - D ö ç è k B T ø D =1.57 k B T C D B =1.86k B T C

30

31 NON-LINEAR RESONANCES

32 Non-linear Behavior in Vacuum at 4 K (Duffing Oscillation)

33 Non-linear Behavior in 3 He-B Normal Liquid 3 He

34 Superfluid 3 He P = 21.2 bar and T = 0.57 mk

35 T F d = F damp (T)+ F a l p Fu k B T < 0.1

36

37 F ~ u 6

38 FUTURE

39 Silicon-on-Oxide (SOI)

40 Position-Momentum Resolved Detection

41

42 SUMMARY

43 Using a commercial MEMS process we have developed robust oscillators with high quality factors suitable for ULT applications. Device measures fluid properties: damping in hydrodynamic and ballistic limit. Sensitive to quasi-particle collision in 3He-B Observed nonlinear temperature independent damping New tool for quantum turbulence study Effective surface sensitive tool in superfluid 3He. Future work/improvements: Simpler process (SOI MEMS) and simpler structure Detector array position-momentum resolved detection in 3 He