BEC meets Cavity QED

Transcription

1 BEC meets Cavity QED Tilman Esslinger ETH ZürichZ Funding: ETH, EU (OLAQUI, Scala), QSIT, SNF

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3 Superconductivity BCS-Theory

4 Model Experiment

5 Fermi-Hubbard = J cˆ ˆ U nˆ ˆ i, σ j, σ + i, i,,, σ i H c n { i j} d-wave superconductor Scalapino, Phys. Rep. 250, 329 (1995) Hofstetter et al., Phys. Rev. Lett. 89, (2002)

6 + Quantum Gases Optical Lattices

7 Fermi Surfaces Increasing number of atoms in the lattice M. Köhl, H. Moritz, T. Stöferle, K. Günter and T. Esslinger, PRL 94, (2005). See also: Chin, J. K. et al., Nature, 443, (2006). Rom, T. et al., Nature, 444, (2006).

8 Repulsive Interactions

9 Tuning interactions: Feshbach Resonance energy closed channel open channel tuning by external magnetic field interatomic distance

10 Tuning interactions: Feshbach Resonance Weak interactions: 40 K: F=9/2, m F =-9/2> F=9/2, m F =-7/2> Strong repulsive interactions: 40 K: F=9/2, m F =-9/2> F=9/2, m F =-5/2>

11 Mott insulator of fermions Crossover from conductor to Mott-Insulator

12 What is a Mott insulator? Interaction-induced localization (U>>T) insulator incompressible energy gap reduced number fluctuations

13 Measure double occupancy

14 Energy spectrum μ

15 Energy spectrum μ

16 Energy spectrum μ

17 Measuring Double Occupancy 4. release 2. Feshbach and 1. Stern-Gerlach suppress 3. Rf induced transition tunneling energy separation shift

18 Measuring Double Occupancy m F =-9/2 m F =-7/2 m F =-5/2

19 Suppression of double occupancy U/(6J)=0 U/(6J)=4.8 R. Jördens, N. Strohmeier, K. Günter, H. Moritz, T. Esslinger, cond-mat , accepted for publication in Nature

20 Occupation of upper Hubbard band Fit: T=0.2 ± 0.1 T F

21 Compressibility with respect to D U/6J=4.8 Theory (solid line): Hubbard model in the atomic limit, finite T/T F

22 Temperature determine temperature in dipole trap: T/T F ~0.14, T rev /T F ~0.24 constant entropy 3 % vacancies in the center T/U=0.1

23 Mott-insulator direct measurement one atom per site Temperature + Hubbard model Recent theory: Leo, Kollath, Georges, Ferrero, Parcollet, cond-mat

24 Modulation spectroscopy U Modulation of the lattice amplitude with frequency U/h: Particle-hole excitation C. Kollath et.al, Phys.Rev.A., 74, (2006) T. Stöferle et.al., Phys.Rev.Lett., 92, (2004)

25 Gapped excitation mode U/(6J)=1.3 U/(6J)=4.2 U/(6J)=7.5 U/(6J)=14.9

26 Spectral weight

27 Quantum Simulation Lower temperature Mott-insulator Quantum degeneracy Neel temperature d-wave open questions Control create system determine phases quantitative understanding microscopic access

28 Cavity QED with a BEC

29 Cavity QED meets BEC Cavity QED BEC Single mode of light field Single mode of matter field

30 Individual atoms in a high-finesse cavity γ κ g Strong coupling regime: g > γ, κ Optical cavity-qed: Kimble, Rempe, Chapman Microwave cavity-qed: Haroche, Walther

31 Jaynes-Cummings model + e g 1 0 e,0, g,1 2g atom + field g,0 g,0

32 Jaynes-Cummings with detuning detuning of probe laser + _ empty cavity bare atom cavity detuning

33 Individual atoms in a high-finesse cavity γ κ g(r)

34 A BEC in a high-finesse cavity BEC N atoms in delocalized wavefunction of BEC coupling to the cavity Theory, see e.g. Meystre, Ritsch, Lewenstein

35 Cummings Models Jaynes-Cummings Tavis-Cummings 1 atom + field N atoms + field e,0, g,1 + 2g #g #e #ν (N-1), 1,0 N,0,1 + 2g N g,0 g,0 N,0,0 N,0,0

36 High-Finesse Optical Cavity γ κ g 0 Length: L=178 μm Mode waist: w=26 μm Finesse: F= g 0 = 2π 10.4 MHz γ = 2π 3.0 MHz κ = 2π 1.4 MHz Optical cavity-qed: Kimble, Rempe, Chapman,

37 Setup

38 Setup Related work: Stamper-Kurn (Berkeley), Reichel (ENS)

39 Spectroscopy of Cavity-BEC probe laser BEC Probe frequency scan over 2.5 GHz at fixed cavity detuning

40 Cavity-BEC Energy Spectrum F=1 F F=2 F F=1 F=2 collective cooperativity: Ng 2 /(2κγ)=1.6x10 6 F. Brennecke, T. Donner, S.Ritter, T. Bourdel, M. Köhl, T. Esslinger, Nature 450, 268 (2007)

41 Varying the number of atoms

42 Dispersive regime E ω c The bare cavity resonance frequency is refractively shifted by BEC

43 BEC Cavity Dynamics BEC 35 khz 25 khz

44 BEC Cavity Dynamics BEC wavefunction photons in cavity resonance condition mode overlap

45 E 4 ω r -2 ћk 2 ћk p

46 BEC as a mechanical oscillator

47 BEC as a mechanical oscillator ( ) ( ) ( ) Ψ x = c t p = 0 + c t p=± 2 k 0 2 ( x) 2 N c N ( kx) ( t) Ψ + 2 cos 2 cos 4ω r

48 Cavity opto-mechanics with a BEC

49 Cavity opto-mechanics with a BEC ( ) â â ( â ) H = ω cˆˆ c Δ â â+ g cˆ+ cˆ i â M

50 Cavity opto-mechanics with a BEC F. Brennecke, S. Ritter, T. Donner, T. Esslinger, arxiv: accepted for publication in Science See also: Stamper-Kurn (Berkeley), Nature Physics 2008

51 BEC as a mechanical oscillator adiabatic elimination of excited state ĉ 2 Consider two modes: BEC and diffracted mode ( ) Strong coupling: g 0.3 κ

52 Equations of Motion Mean field description non-local and non-linear coupling overlap integral α 2 5

53 Stationary Solutions

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55 Cavity field / count rate

56 Frequency Experiment with maximum α 2 3.6±0.9 Simulation with atom-atom interactions

57 Challenges Role of quantum fluctuations Prepare and detect single mechanical excitation Back-action free measurement Entanglement of several oscillators

58 Conclusions and Outlook Mott Insulator Cavity QED with a BEC Cavity opto-mechanics with a BEC

59 Thanks! Funding: ETH, SNF, QSIT, EU (OLAQUI, SCALA) Quantum Gases in Lithium: Optical Lattices Bruno Zimmermann Henning Moritz Torben Müller Niels Strohmaier Henning Moritz Robert Jördens Jakob Meineke Daniel Greiff Leticia Tarruell Kenneth Günter (ENS, Paris) Michael Köhl (now Cambridge, UK) Thilo Stöferle (now IBM) Yosuke Takasu (now U Kyoto) Administration: Veronica Bürgisser BEC and Cavity Stephan Ritter Tobias Donner Ferdinand Brennecke Christine Guerlin Kristian Baumann Michael Köhl (now Cambrigde) Thomas Bourdel (now Orsay) Anton Öttl (now Berkeley) Electronics: Alexander Frank