1. GC, 08/2015 ULT Grenoble group Probing mesoscopic lengthscales in (super)fluid 3 He Funding: E. Collin H. Godfrin, A. Fefferman, O. Maillet, M. Defoort, A. Sultan, K.J. Lulla, T. Moutonet, J.-S. Heron Néel, Grenoble 1 µm E.C., Grenoble Y. Lee, Florida J. Saunders, RHUL J.P. Davis, Alberta

2. 3 He: unique model system for physics Context: Why 3 He? From: condensed matter – particle physics – cosmology 2 3 He is the paradigm for Fermions. Many-body physics of interacting Fermions. 1 µm E.C., Grenoble Y. Lee, Florida J. Saunders, RHUL J.P. Davis, Alberta Why mesoscopic? Why (nano)mechanics? What can we do? What do we learn?

3. Why 3 He? http://spindry.phys.northwestern.edu/he3.htmhttp://spindry.phys.northwestern.edu/he3.htm (W. Halperin) 3 http://www.physik.uni-augsburg.de/theo3/helium3/http://www.physik.uni-augsburg.de/theo3/helium3/ (D. Vollhardt) 3 He is the simplest Fermi liquid. No lattice. Properties very well known; tabulated Unique experimental realization of Landau Fermi Liquid Benchmark to test theories; i.e. zero sound 3 He, Fermi surface k-space Copper, Fermi surface k-space (valence 1) L.D. Landau, Soviet Phys. JETP 5, 101 (1957) 3 He is the purest material. Only impurity is 4 He, with exp. decreasing solubility Impurities adsorbed in experimental cells (e.g. on sinters) Reach intrinsic properties F. Pierre et al., Phys. Rev. B 68, 085413 (2003) 6N Silver nanowire 5N 1 ppm Mn 0.3 ppm Mn ! J. Wilks, Introduction to liquid Helium, 1987

4. Why 3 He? 4 Very simple, but still very complex. Superfluid p-wave BCS below T c ~ 1 mK Broken symmetries SO3 L x SO3 s x U(1) From weak coupling (s.v.p.) to strong coupling (melt. curve) Again, well known properties Phase diagram G. Volovik, The Universe in a Helium droplet, 2003 http://spindry.phys.northwestern.edu/he3.htmhttp://spindry.phys.northwestern.edu/he3.htm (W. Halperin) W.P. Halperin & L.P. Pitaevskii (Eds), Helium Three, 1990 D. Vollhardt & P. Völfle, The Superfluid Phases of Helium Three, 1990 (2013) Unique Benchmark to test theories; many complex phenomena R. Blaauwgeers et al., Nature 404, 471 (2000) Topological defects: vortices Y.M. Bunkov & G. Volovik, J. Phys.: Condens. Matter 22, 164210 (2010) HPD/BEC of magnons

5. Why 3 He? 5 Impact in many fields of physics. Paradigm for heavy fermion unconventional superconductor, e.g. UPt 3 Robert Joynt & Louis Taillefer, Rev. Mod. Phys. 74, 235 (2002) Particle physics With elementary excitations/collective modes of superfluid 3 He “Little Higgs” mechanism V.V. Zavjalov et al., ArXiv: 1411.3983v3 (2015) Cosmology in the laboratory Kibble-Zurek machanism: creation of topological defects at a fast cool-down through 2 d order phase transition V.M.H. Ruutu et al., Nature 382, 334 (1995) G. Volovik, The Universe in a Helium droplet, 2003 (COSLAB E.S.F. grant 2001-2006) C. Bäuerle et al., Nature 382, 332 (1995)

6. Why 3 He? 6 Experimentalist’s tools. NMR, Specific heat, transport (acoustic, thermal, spin diffusion), Mechanical probes (quartz forks, vibrating wires, grids) All for bulk… Today’s trend? Same as in electronic solid-sate devices Lamp Integrated processor Transistor Mesoscopic (e-) physics, Quantum electronics!

7. Why 3 He? 7 Experimentalist’s tools. NMR, Specific heat, transport (acoustic, thermal, spin diffusion), Mechanical probes (quartz forks, vibrating wires, grids) All for bulk… Today’s trend? Same as in electronic solid-sate devices Integrated processor Mesoscopic (e-) physics, Quantum electronics! Go meso in 3 He! Unravel old questions, Tackle radically new problems

8. Why mesoscopic? 8 Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions F ~ few A atomic ° l Zero sound ~ few µm ~ few µm @ mK & MHz (decay length of non-prop. transverse) Relevant lengthscales: A. Duh et al., J. of Low Temp. Phys. 168, 31 (2012) Direct observation of transverse zero sound? Micro-mechanical/nano-fluidic cavity Identified only through superfluid… J.P. Davis et al., Phys. Rev. Lett. 101, 085301 (2008)

9. Why mesoscopic? 9 Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions Relevant lengthscales: l Mean-free-path ~ few 10 µm @ mK Study Knudsen layer in quantum fluid? A. Casey et al., Phys. Rev. Lett. 92, 255301 (2004) (macro)torsional oscillator/slab cavity A growing literature on micro/nano (classical) fluidics. Technological implications, and fundamental questions: Slippage? Boundary layers? A. Siria et al., Nature 494, 455 (2013) e.g. gigantic flow of water in nanotubes F ~ few A atomic °

10. Why mesoscopic? 10 Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions Relevant lengthscales: l Mean-free-path ~ few 10 µm @ mK Study Knudsen layer in quantum fluid? A. Casey et al., Phys. Rev. Lett. 92, 255301 (2004) A growing literature on micro/nano (classical) fluidics. Technological implications, and fundamental questions: Slippage? Boundary layers? Local probe in 4 He gas with nano-mechanics M. Defoort et al., Phys. Rev. Lett. 113, 136101 (2014) (macro)torsional oscillator/slab cavity F ~ few A atomic °

11. Why mesoscopic? 11 Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions Relevant lengthscales:  de Broglie ~ 15 nm @ mK (“size” of quasi-particle)  de Broglie ~  0 @ T c /10 Double-slit doable today with F.I.B., QP flow from “black-body radiator”, detected with “bolometric camera” (mm resolution), performed in quantum vacuum (superfluid @ T=0) F ~ few A atomic °

12. Why mesoscopic? 12 Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions Relevant lengthscales:  de Broglie ~ 15 nm @ mK (“size” of quasi-particle)  de Broglie ~  0 @ T c /10 Young’s diffraction experiment with 3 He quasi-particles? 1 cm (calculated) Performed with photons Massive objects, from free electrons to e.g. ! Electrons in metal (Aharonov-Bohm effect, also a QP!) T. Young, Royal Society (1803) C. Jönsson, Zeitschrift für Physik,161, 454 (1961) R.A. Webb et al., Phys. Rev. Lett. 54, 2696 (1985) ; Stefan Gerlich et al., Nature Comm. 2, 263 (2011) C 60 F 48 F ~ few A atomic °

13. Why mesoscopic? 13 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: “Healing” lengths ~ about 1 - 100 µm Can couple to superfluid order parameter: create distortion, collective modes A.M. Guénault et al., Phys. Rev. Lett. 51, 589 (1983) e.g. with a vibrating wire… …. understanding? What about micro/nano-machined oscillators? May be a mess… E.C. et al., J. of Low Temp. Phys. 162, 653 (2011) M. Defoort et al., J. of Low Temp. Phys. 171, 731 (2013)

14. Why mesoscopic? 14 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Becomes meters at ULT! Ballistic motion of quasi-particles l Mean-free-path ~ mm @ Tc/4 How do we relate Knudsen problem in Classical gas – Fermi gas – superfluid? What about Knudsen layer/slippage Phenomenon in ULT 3 He? e.g. within a Lancaster ”black-body radiator” C. Bäuerle et al., Phys. Rev. B 57, 14381 (1998)

15. Why mesoscopic? 15 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Coherence length  0 : “Size” of topological defect, e.g. vortex Quantum turbulence imaging: down to smallest scale Kolmogorov/Richardson cascade measurement D. I. Bradley et al., PRL 96, 035301 (2006) S. L. Ahlstrom et al., J. Low Temp. Phys. 175, 725 (2014) “Bolometric camera” with nano-mechanics? Typical: 100 nm x 100 nm x 100 µm

16. Why mesoscopic? 16 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Coherence length  0 : “Size” of Cooper pair, smallest relevant scale of superfluid (below superfluidity suppressed/modified) J.V. Porto, J.M. Parpia, Phys. Rev. Lett. 74, 4667 (1995) D. T. Sprague et al., Phys. Rev. Lett. 75, 661 (1995) Macroscopic scale: “Dirty” superfluidity T c is suppressed by disorder induced from aerogel New superfluid states: e.g. superfluid “glass” (LIM state) V.V. Dmitriev, JETP Lett. 91, 599 (2010) J.I.A. Li et al., Nature Physics 9, 775 (2013)

17. Why mesoscopic? 17 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Coherence length  0 : “Size” of Cooper pair, smallest relevant scale of superfluid (below superfluidity suppressed/modified) Confined superfluid: NMR and mechanical slabs L. Levitin et al., Science 340, 841 (2013) X. Rojas and J.P. Davis, Phys. Rev. B 91, 024503 (2015) M. Gonzalez et al., J. Low Temp. Phys. 162, 661 (2011) Dimensions comparable to  0 New superfluid states: e.g. “crystalline” superfluid (striped), polar phase A. B. Vorontsov and J. A. Sauls, Phys. Rev. Lett. 98, 045301 (2007)

18. Why mesoscopic? 18 Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Coherence length  0 : “Size” of Cooper pair, smallest relevant scale of superfluid (below superfluidity suppressed/modified) Surface states: Andreev bound states in 3 He-B are Majoranas! Y. Tsutsumi et al., PRB 83, 094510 (2011) e.g. Viewpoint in physics, Shou-cheng Zhang, Physics 1, 6 (2008) Xiao-Liang Qi, Rev. of Mod. Phys. 83, 1057 (2011) G. Volovik, Pis'ma v ZhETF 90, 440 (2009) New type of order for quantum matter: Topological states, elementary excitations are Majoranas Macroscopic measurements: specific heat & acoustics S. Murakawa et al., Phys. Rev. Lett. 103, 155301 (2009) H. Choi et al., Phys. Rev. Lett. 96, 125301 (2006)

19. Why nano-mechanics? 19 Go meso in 3 He! Unravel old questions, Tackle radically new problems V. Mourik et al., Science 336, 1003 (2012) Stevan Nadj-Perge et al., Science 346, 602 (2014) e.g. solid-state: topological superconductor, quest of Majorana particles efficient local probes, but dirty, order parameter structure not well known Complementary system to solid-state physics In superfluid 3 He: ultra-clean, well-known order-parameter, But not yet efficient local probes!

20. Why nano-mechanics? 20 Go meso in 3 He! Unravel old questions, Tackle radically new problems Complementary system to solid-state physics In superfluid 3 He: ultra-clean, well-known order-parameter, But not yet efficient local probes! Nano-mechanical objects could be the solution: inserted in slabs, well-suspended far from wall, or confined within the walls (within  0 ) Perform transport measurement within Majorana states? Can we learn from their statistics & dispersion relation? Hao Wu and J. A. Sauls, Phys. Rev. B 88, 184506 (2013)

21. Open discussions 21 Go meso in 3 He! Unique playground for physics Complementary system to solid-state physics 1 µm E.C., Grenoble Y. Lee, Florida J. Saunders, RHUL J.P. Davis, Alberta Need for local probes: Nano-mechanics