Probing mesoscopic lengthscales in superfluid 3 He ULT

Probing mesoscopic lengthscales in (super)fluid 3 He ULT Grenoble group 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 J. Saunders, RHUL J. P. Davis, Alberta Y. Lee, Florida Funding: GC, 08/2015

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

Why 3 He? 3 He is the simplest Fermi liquid. No lattice. Properties very well known; tabulated 3 He, Fermi surface k-space J. Wilks, Introduction to liquid Helium, 1987 http: //www. physik. uni-augsburg. de/theo 3/helium 3/ (D. Vollhardt) http: //spindry. phys. northwestern. edu/he 3. htm (W. Halperin) Unique experimental realization of Landau Fermi Liquid Benchmark to test theories; i. e. zero sound L. D. Landau, Soviet Phys. JETP 5, 101 (1957) 3 He is the purest Copper, Fermi surface k-space (valence 1) material. Only impurity is 4 He, with exp. decreasing solubility Impurities adsorbed in experimental cells (e. g. on sinters) Reach intrinsic properties 6 N Silver nanowire 5 N 0. 3 ppm Mn ! 1 ppm Mn F. Pierre et al. , Phys. Rev. B 68, 085413 (2003) 3

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

Why 3 He? 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) Cosmology in the laboratory (COSLAB E. S. F. grant 2001 -2006) G. Volovik, The Universe in a Helium droplet, 2003 Kibble-Zurek machanism: creation of topological defects at a fast cool-down through 2 d order phase transition C. Bäuerle et al. , Nature 382, 332 (1995) V. M. H. Ruutu et al. , Nature 382, 334 (1995) Particle physics With elementary excitations/collective modes of superfluid 3 He “Little Higgs” mechanism V. V. Zavjalov et al. , Ar. Xiv: 1411. 3983 v 3 (2015) 5

Why 3 He? 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 Transistor Integrated processor Mesoscopic (e-) physics, Quantum electronics! 6

Why 3 He? 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 Go meso in 3 He! Unravel old questions, Tackle radically new problems Integrated processor Mesoscopic (e-) physics, Quantum electronics! 7

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

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

Why mesoscopic? Go meso in 3 He! Even in the normal state Unravel old questions, Tackle radically new problems Some interesting questions Relevant lengthscales: ° l few A atomic F Study Knudsen layer in quantum fluid? ~ l. Mean-free-path ~ few 10 µm @ m. K A growing literature on micro/nano (classical) fluidics. Technological implications, and fundamental questions: Slippage? Boundary layers? (macro)torsional oscillator/slab cavity Local probe in 4 He gas with nano-mechanics M. Defoort et al. , Phys. Rev. Lett. 113, 136101 (2014) A. Casey et al. , Phys. Rev. Lett. 92, 255301 (2004) 2 µm 10

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems Relevant lengthscales: ° l few A atomic F Even in the normal state Some interesting questions Young’s diffraction experiment with 3 He quasi-particles? ~ Lde Broglie ~ 15 nm @ m. K (“size” of quasi-particle) (calculated) 10 nm 6 cm Lde Broglie ~ x 0 @ Tc/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) 2 cm 100 nm 1 cm 11

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems Even in the normal state Some interesting questions Young’s diffraction experiment with 3 He quasi-particles? Relevant lengthscales: ° l few A atomic F ~ Lde Broglie ~ 15 nm @ m. K (“size” of quasi-particle) (calculated) 10 nm 6 cm Lde Broglie ~ x 0 @ Tc/10 Performed with photons T. Young, Royal Society (1803) C 60 F 48 Massive objects, from free electrons to e. g. ! C. Jönsson, Zeitschrift für Physik, 161, 454 (1961) ; Stefan Gerlich et al. , Nature Comm. 2, 263 (2011) Electrons in metal (Aharonov-Bohm effect, also a QP!) R. A. Webb et al. , Phys. Rev. Lett. 54, 2696 (1985) 2 cm 100 nm 1 cm 12

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems Relevant lengthscales: In the superfluid state New problems in physics e. g. with a vibrating wire… “Healing” lengths ~ about 1 - 100 µm Can couple to superfluid order parameter: create distortion, collective modes 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) A. M. Guénault et al. , Phys. Rev. Lett. 51, 589 (1983) …. understanding? 13

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

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

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems Relevant lengthscales: In the superfluid state New problems in physics Macroscopic scale: “Dirty” superfluidity Coherence length x 0: “Size” of Cooper pair, smallest relevant scale of superfluid (below superfluidity suppressed/modified) 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) J. V. Porto, J. M. Parpia, Phys. Rev. Lett. 74, 4667 (1995) D. T. Sprague et al. , Phys. Rev. Lett. 75, 661 (1995) Tc is suppressed by disorder induced from aerogel 16

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Coherence length x 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) Dimensions comparable to x 0 New superfluid states: e. g. “crystalline” superfluid (striped), polar phase A. B. Vorontsov and J. A. Sauls , Phys. Rev. Lett. 98, 045301 (2007) M. Gonzalez et al. , J. Low Temp. Phys. 162, 661 (2011) 17

Why mesoscopic? Go meso in 3 He! Unravel old questions, Tackle radically new problems In the superfluid state New problems in physics Relevant lengthscales: Surface states: Andreev bound states in 3 He-B are Majoranas! Coherence length x 0: “Size” of Cooper pair, smallest relevant scale of superfluid (below superfluidity suppressed/modified) New type of order for quantum matter: Topological states, elementary excitations are Majoranas Macroscopic measurements: specific heat & acoustics H. Choi et al. , Phys. Rev. Lett. 96, 125301 (2006) S. Murakawa et al. , Phys. Rev. Lett. 103, 155301 (2009) 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 Zh. ETF 90, 440 (2009) 18

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

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

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