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Exploring transport in a Tonks Girardeau gas

Exploring transport in a Tonks Girardeau gas. Carlo Sias. www.quantumoptics.eu. £££: EPSRC, University of Cambridge, Herchel -Smith Fund, ERC. Transport – a very general subject!. I. Open system: energy is continuously transferred into the system. U.

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Exploring transport in a Tonks Girardeau gas

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  1. Exploring transport in a TonksGirardeau gas Carlo Sias www.quantumoptics.eu £££: EPSRC, University of Cambridge, Herchel-Smith Fund, ERC

  2. Transport – a very general subject! I Open system: energy is continuously transferred into the system U potential difference U continuously accelerates electrons

  3. Transport experiments in cold atoms Ketterle group 2000 A simple transport experiment Three dimensions k -k One dimension -2ħk 0 +2ħk Scattered atoms with spherical (s-wave) symmetry Weiss group 2006 Other transport experiments: ETH, LENS, NIST, Orsay, Pisa, Stanford,, ...

  4. Transport in solid state: 1-dimension Transistors for transparent and flexible electronics Solar cell design Spin-charge separation

  5. What is a one-dimensional gas?

  6. What is a one-dimensional gas? • transverse degrees of freedom are frozen out Conditions for 1D kBT <hw┴ Bosons: m < hw┴ Fermions: EF =Nhwz < hw┴

  7. 1-dimensional Bose gas • Exactly solvable many-body problem! (Lieb-Liniger) • The many-body quantum state is characterized by a single parameter weakly interacting Bose gas crossover Tonks-Girardeau gas (“Fermionized Bosons”)

  8. Excitations in a weakly interacting Bose gas Bogoliubov spectrum g«1

  9. Excitations in a Tonks gas g→∞ Two branches of excitations: “particle” excitations and “hole” excitations q q k k -kF kF kF -kF

  10. Generating tight confining potentials Induced electric dipole potential: ac polarizability of the atom electric field of the laser Two options: „red detuned“ „blue detuned“ Optical lattice Energy scale: l/2

  11. Hybrid optical/magnetic trap Vertical confinement: purely magnetic Other experiments in 1D: ENS, ETH, LENS, Mainz, MIT, NIST, Orsay, Penn State, Rice, Vienna, Innsbruck …

  12. Hybrid optical/magnetic trap Experimental parameters: Atoms: 87Rb (bosons) Wavelength of lattice: 764 nm wx= wy ≤ 2p65 kHz (optical lattice) wz= 2p39 Hz (magnetic trap) N<50 per tube 0.5 < g < 10 Vertical confinement: purely magnetic Other experiments in 1D: ENS, ETH, LENS, Mainz, MIT, NIST, Orsay, Penn State, Rice, Vienna, Innsbruck …

  13. Generation of spin impurities F=2 ΔE(z) F=1 mF: -2 -1 0 1 2

  14. Generation of spin impurities F=2 F=1 quick transfer (RF p/2-pulse, 200 ms) mF: -2 -1 0 1 2

  15. Generation of spin impurities F=2 F=1 mF: -2 -1 0 1 2

  16. Generation of spin impurities • width of impurity wave packet: 2.5 mm (≈ 3 atoms) • same transverse confinement:propagation of impurities is purely one-dimensional • same scattering lengths: a-1,-1 ≈ a-1,0 ≈ a0,0 • accelerated impurity breaks integrability of the 1D Bose gas → interesting dynamics

  17. In situ detection of the spin wave packet F=2 imaging only F=2 F=1

  18. In situ detection of the spin wave packet F=2 imaging only F=2 F=1 Distance z [mm]

  19. Time evolution g • strong interaction-induced dynamics • significant back action of the impurity onto the majority component • open quantum system: impurity atoms can transfer continuously energy into trapped component by collisions S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  20. Center-of-mass motion of the impurities Distance z [mm] S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  21. Center-of-mass motion of the impurities Tonks gas Distance z [mm] weakly interacting Bose gas ballistic S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  22. Center-of-mass motion of the impurities Tonks gas weakly interacting Bose gas ballistic part of the impurities have already left the gas S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  23. Release measurement tdelay S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  24. Release measurement tdelay S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  25. Release measurement tdelay S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  26. Release measurement tdelay Simple model Every collision resets the impurity’s velocity to 0, then gravity accelerates again Mean time between collision events: Time delay accumulated: total number of collisions x time delay per collision S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  27. “Far field” distribution of the impurities

  28. “Far field” distribution of the impurities

  29. “Far field” distribution of the impurities

  30. “Far field” distribution of the impurities unscattered scattered g =3 g =5 g =7 c) b) a) S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  31. “Far field” distribution of the impurities unscattered scattered g =3 g =5 g =7 c) b) a) • Fermionization? • Enhancement of multiple collision events due to strong interactions? • ? S. Palzer, C. Zipkes, C. S., Michael Köhl, PRL 103, 150601 (2009)

  32. How to control the impurities in the gas? • Problem: once created, the impurity dynamics cannot be controlled

  33. How to control the impurities in the gas? • Problem: once created, the impurity dynamics cannot be controlled • FORGET ABOUT SPIN IMPURITIES, • WE NEED A NEW STRATEGY!

  34. Impurities in a Bose gas: a new approach • Quantum degenerate atoms • Macroscopic quantum systemat nano Kelvin temperature • Collective quantum states of 106 particles • Very long coherence times • Ultracold trapped ions • Single particle detection and manipulation • Pristine source for quantum information processing & precision spectroscopy Hybrid quantum system • A new approach to • Ultracold collisions & quantum chemistry • Quantum information processing and decoherence • Quantum many-body physics with impurities related work with trapped ions @ MIT, Innsbruck/Ulm, Uconn, Weizmann,UCLA,..[free ions: Rice, Michigan, Durham, Maryland, ... ]

  35. Atom-ion hybrid trap

  36. Ultracold atom-ion collisions Ion trap (level spacing  5 mK) Bose-Einstein condensateT  100 nK, trap depth  3 mK

  37. Ultracold atom-ion collisions Ion trap (level spacing  5 mK) Bose-Einstein condensateT  100 nK, trap depth  3 mK Measured atom loss cross section: sloss= (2.2±0.2)·10-13 m2 C. Zipkes, S. Palzer, CS, Michael Köhl, Nature, 464 388(2010) Determine ion temperature from sloss = sel(kBT) + p (2 kBT/mw2) T  2 mK (almost Doppler temperature)

  38. Sympathetic cooling of an ion in a BEC • Rapid cooling • First demonstration of cooling an object different from other neutral species using ultracold atoms • Ultimate cooling limits need to be explored with a different technique (eg. Raman spectroscopy) C. Zipkes, S. Palzer, CS, Michael Köhl, Nature, 464 388(2010)

  39. Atom-ion reaction processes • Elastic collisions ion changes vibrational quantum state, atom heats up • Charge-exchange collisions Yb+ + Rb→ Yb + Rb+ Yb+ + Rb→ (YbRb)+ C. Zipkes, S. Palzer, L. Ratschbacher, CS, Michael Köhl, ArXiv:1005.3846

  40. A single impurity as a local probe C. Zipkes, S. Palzer, L. Ratschbacher, CS, Michael Köhl, ArXiv:1005.3846

  41. Summary • Quantum transport in a strongly interacting Bose gas with an accelerated impurity • High resolution tomography • Strong dynamics and back action of the impurity • Far field distribution: effects of fermionization? • New approach to study impurities: single trapped ion in a BEC

  42. Thanks! PI M. Köhl Ion & BEC: S. Palzer, C. Zipkes, L. Ratschbacher, H. Meyer, M. Steiner. C.S. Fermi gas: M. Feld, B. Fröhlich, E. Vogt, K. Beck (first Fermi gas in the UK since Nov 2009) Funding: EPSRC, ERC, Univ. of Cambridge, Herchel-Smith Fund

  43. Dynamic structure factor Scattering rate of an impurity (Fermi’s golden rule): S(q,w): dynamic structure factor ki, kf : initial and final momentum of the impurity w(q): excitation spectrum of the gas

  44. Collision rate and energy dissipation For equal masses: impurities move collisionless through a superfluidand a Tonks-Girardeau gases for v<c. Collision rate (v>c) Energy dissipation (v>c) constant force  50% of gravity for heavy impurities: Astrakharchik & Pitaevskii, Davis et al., ...

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