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Quantized conductance for neutral matter J.P. Brantut, S. Krinner, D. Stadler, D. Husmann, M. Lebrat and T. Esslinger Institute for Quantum Electronics ETH Zürich Sunday, June 29, 14 Mesoscopic Devices which size are comparable to the de Broglie wavelength of particles Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Mesoscopic Devices which size are comparable to the de Broglie wavelength of particles B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, C. T. Foxon, Phys. Rev. LeD. 60, 848 (1988) Cold atoms and beyond Sunday, June 29, 14 D A Wharam, T J Thornton, R Newbury, M Pepper, H Ahmed, J E F Frost, D G Hasko, D C Peacock, D A Ritchie and G A C Jones, J. Phys. C: Solid State Phys. 21 L209 J-P Brantut Conductance Quantization : Landauer theory Left reservoir Cold atoms and beyond Sunday, June 29, 14 Right reservoir J-P Brantut Conductance Quantization : Landauer theory Left reservoir Right reservoir Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Conductance Quantization : Landauer theory Left reservoir Right reservoir Group velocity Density of states Cold atoms and beyond Sunday, June 29, 14 p vg (✏) = 2✏/m 1 g1D (✏) = 2⇡~vg (✏) J-P Brantut Conductance Quantization : Landauer theory Left reservoir Right reservoir p vg (✏) = 2✏/m 1 g1D (✏) = 2⇡~vg (✏) Group velocity Density of states Current Cold atoms and beyond Sunday, June 29, 14 I= Z EF + µ EF µ g1D (✏)vg (✏)d✏ = h J-P Brantut Universal conductance quantum 1/h E E n n Left Reservoir Cold atoms and beyond Sunday, June 29, 14 Right Reservoir J-P Brantut Universal conductance quantum 1/h Net current carriers E E n n Left Reservoir Cold atoms and beyond Sunday, June 29, 14 Right Reservoir J-P Brantut Universal conductance quantum 1/h µ time Heisenberg relation Cold atoms and beyond Sunday, June 29, 14 h µ J-P Brantut Universal conductance quantum 1/h µ time Heisenberg relation h µ 1 1 1 1 time Pauli principle Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Universal conductance quantum 1/h µ time Heisenberg relation h µ 1 1 1 1 time Pauli principle Cold atoms and beyond Sunday, June 29, 14 µ I= h J-P Brantut Universal conductance quantum 1/h No reference whatsoever to electric charges, fields etc Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Universal conductance quantum 1/h No reference whatsoever to electric charges, fields etc VOLUME 83, NUMBER 19 Journal of Low Temperature Physics, Vol. 141, Nos. 3/4, November 2005 (© 2005) DOI: 10.1007/s10909-005-8223-3 PHYSICAL REVIEW LETTERS 8 NOVEMBER 1999 Quantum Point Contacts for Neutral Atoms J. H. Thywissen,* R. M. Westervelt,† and M. Prentiss On the Feasibility of Detecting Quantized Conductance in Neutral Matter Yuki Sato, Byeong-Ho Eom, and Richard Packard Department of Physics, University of California, Berkeley, CA 94720-7300, USA E-mail: [email protected] (Received May 18, 2005; revised July 18, 2005) Department of Physics, Harvard University, Cambridge, Massachusetts 02138 (Received 19 July 1999) We show that the conductance of atoms through a tightly confining waveguide constriction is quantized in units of l2dB !p, where ldB is the de Broglie wavelength of the incident atoms. Such a constriction forms the atom analog of an electron quantum point contact and is an example of quantum transport of neutral atoms in an aperiodic system. We present a practical constriction geometry that can be realized using a microfabricated magnetic waveguide, and discuss how a pair of such constrictions can be used to study the quantum statistics of weakly interacting gases in small traps. PACS numbers: 03.75. – b, 05.60.Gg, 32.80.Pj, 73.40.Cg LOW TEMPERATURE PHYSICS VOLUME 34, NUMBERS 4–5 APRIL-MAY 2008 to-width ratio of "105 . This new regime is interesting Quantum transport, in which the center-of-mass motion of particles is dominated by quantum mechanical effects, because deleterious effects such as reflection and interHELIUM When an electrochemical potential difference (i.e., a voltage) is appliedLIQUID has been observed in both electron and neutral-atom mode nonadiabatic transitions are minimized [12], allowacross a metal wire whose transverse dimensions are on the order of the systems. Pioneering experiments demonstrated quantum ing for accuracy of conductance quantization limited only 3 electron’s Fermi wavelength, the conductance G ≡ I /!V becomes quantizedQuantum-limited transport in periodic structures. example, mass flow ofFor liquid HeBloch by finite-temperature effects. Furthermore, the observa2 in units of 2e / h. We present calculations that show that when a chemical oscillations and Wannier-Stark ladders were observed in tion of conductance quantization at new energy and length G. Lambertofand G. Gervais potential difference !µ3 is applied across an array of small apertures whose the conduction electrons through superlattices [1] with scales is of inherent interest. sizes are comparable to the !Fermi wavelength of 3He in a 3He:4 He mixture, an applied electric field,McGill as well as in the transport of If a QPC for neutral atoms were realized, it would " Department of Physics, University, 3600 rue Université, Montréal, Qc, Canada 2 accelerating optical lattices [2,3]. provide excellent opportunities for exploring the physics the mass conductance G ≡ !µI3/m∗ will be quantized in units of 2m∗3 / h neutral atoms through a! 3 W. J.work Mullin 3 Further with neutral atoms in optical lattices has of small ensembles of weakly interacting gases. For where m∗3 is the 3He effective mass. We show that the mass conductance will utilized their slower time scales (kHz instead of THz) and instance, the01003, transmission through a series of two QPC’s Department of Physics, University of Massachusetts, Amherst, Massachusetts USA be quantized for a 0.1% mixture passing through 10 nm diameter pores at longer coherence lengths29,to2007" observe a clear signature of would depend on the energetics of atoms confined in the !Submitted October temperatures below 25 mK. The phenomenon should be observable in a filter dynamical Bloch band suppression [4], an effect originally trap between the two constrictions. The physics of such a Fiz. Nizk. Temp. 34, 321–325 !April–May 2008" material made by nuclear track etching. predicted for but not yet observed in electron transport [5]. “quantum dot” for atoms is fundamentally different from Quantum transport also occurs in aperiodic systems.unusual that quantum of electrons, since theinCoulombic charging energy We consider theoretically the possibility of observing fluid behavior liquid 3 3 4 KEY WORDS: conductance; Fermi wavelength; quasiparticle; ballistic For example, a quantum (QPC)confined is a single that dominates the energetics of an electron quantum He and solutions of point He in contact He systems to nanochannels. In the case of pure ballistic transport. constriction through the conductance is always anquantized dot [13] is absent The quantum / h. neutral We showparticles. that flow at very low which temperature the conductance will be in units of 2m2for Cold atoms and beyond J-P Brantut integer of some base conductance. quanstatistics atoms energetically thesemultiple steps should be sensitive to increases The in temperature. We also of useneutral a random scattering ma- restricted to sub2 tization of electrontoconductance in multiples of 2escattering. three-dimensional spacesfluctuations has already aroused theoretical !h, trix simulation study flow with diffusive wall Universal conductance Sunday, June 29, 141. INTRODUCTION in novel effects such as the fermionization [14] and where e is the charge of the electron and h is Planck’s analogous to those seen in electron systems should then beinterest observable. Finally we consider Experimental setup 7.5 104 6Li atoms T ~ 0.11 TF TF = 352 nK Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Experimental setup : cloud shaping Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Experimental setup : cloud shaping Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Experimental setup : cloud shaping Binary mask Gaussian beam (@ 532 nm) Microscope objective Demagnification x11 Images a “split gate” onto the atoms Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Experimental setup : cloud shaping Attractive “Gate” potential Gaussian envelope (@ 767 nm) Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Experimental setup : cloud shaping c d Z E2 µ E1 Cold atoms and beyond Sunday, June 29, 14 E0 1 J-P Brantut 0 Energy / kB (µK) 10 µm Experimental setup : cloud shaping c b Mask Lens e 10 µm E(ky) e d Z E2 x-frequency Cloud 0 Cold atoms and beyond Sunday, June 29, 14 ky -40 -20 30 µkHz E1 z-frequency 0 10 kHz E0 0 1 Energy / kB (µK) Dichroic mirror 20 40 Channel ground state Position y (µm) 1 µK Chemical potential 0.32 µK Temperature 42 nK Gate Potential 0 - 3 µK J-P Brantut Experimental setup : cloud shaping c b Mask Lens e 10 µm E(ky) e d Z E2 x-frequency Cloud 0 Cold atoms and beyond Sunday, June 29, 14 ky -40 -20 30 µkHz E1 z-frequency 0 10 kHz E0 0 Contact ground state Position y (µm) 1 Energy / kB (µK) Dichroic mirror 20 40 1 µK Chemical potential 0.352 µK Temperature 42 nK Gate Potential 0 - 3 µK J-P Brantut Measurement E(k)" !"! !#! k" Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Measurement E(k)" !"! !#! k" Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Measurement E(k)" !"! !#! k" Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Measurement E(k)" !"! !#! k" Landauer theory No free parameter Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Measurement E(k)" !"! !#! k" ⌫z = 10.4 kHz ⌫z = 8.2 kHz Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Measurement ⌫z = 10.4 kHz ⌫z = 8.2 kHz Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Varying the split gate strength Cold atoms and beyond Sunday, June 29, 14 J-P Brantut What do we learn ? Cold atoms and beyond Sunday, June 29, 14 J-P Brantut It works... ... with neutral particles: no forces are applied to the atoms Cold atoms and beyond Sunday, June 29, 14 J-P Brantut It works... ... with neutral particles: no forces are applied to the atoms ... with closed, microcanonical reservoirs: only elastic processes take place in the reservoirs, no dissipative dynamics Cold atoms and beyond Sunday, June 29, 14 J-P Brantut It works... ... with neutral particles: no forces are applied to the atoms ... with closed, microcanonical reservoirs: only elastic processes take place in the reservoirs, no dissipative dynamics ... with very little interparticle scattering in the reservoirs: mean free path much larger than the cloud size Wide control over the reservoirs dynamics Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Wide tunability of the geometry Using “optical lithography”, any geometry can be implemented Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Wide tunability of the geometry Using “optical lithography”, any geometry can be implemented Example: quantum wire with sharper edges In-situ picture of the potential shape Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Wide tunability of the geometry Using “optical lithography”, any geometry can be implemented Example: quantum wire with sharper edges In-situ picture of the potential shape Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Conclusions and perspectives Strongly interacting gases: BEC-BCS crossover Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Conclusions and perspectives Strongly interacting gases: BEC-BCS crossover Engineering reservoirs: non thermal, coherent, small size Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Conclusions and perspectives Strongly interacting gases: BEC-BCS crossover Engineering reservoirs: non thermal, coherent, small size Other transport coefficients: heat conductance, thermopower J.P. Brantut et al, Science 342, 713 (2013) Cold atoms and beyond Sunday, June 29, 14 J-P Brantut Charles Grenier JPB Sebastian Krinner Dominik Husmann Martin Lebrat Tilman Esslinger arXiv:1404.6400 Discussions: C. Chin, W. Zwerger, T. Ihn, K. Ensslin, Y. Imry, G. Blatter, A. Georges, T. Giamarchi Cold atoms and beyond Sunday, June 29, 14 J-P Brantut