Laboratoire Charles Fabry de l'institut d'optique Palaiseau Chris Westbrook Noise and correlation measurements using atom counting Quantum noise in correlated systems, 7 jan 2008
Outline 1. Quantum atom optics atom counting with metastable He 4 wave mixing and correlated atom pairs Hanbury Brown Twiss effect 2. 1D gases on atom chips density fluctuations
The team Orsay/Palaiseau Martijn Schellekens Aurélien Perrin Jose Gomes Valentina Krachmalnicoff Jean-Christophe Jaskula Jean-Baptiste Trebbia Thorsten Schumm Hong Chang Vanessa Leung Jérôme Estève Denis Boiron Isabelle Bouchoule Alain Aspect CW Discussions with K. Kheruntsyan K. Moelmer M. Trippenbach F. Masnou, J. Mur- Petit PhD student postoc permanent
A quantum optics milestone: photon pairs photo NIST param. downconversion (classical) + photon counters, Burnham and Weinberg PRL 25, 84 (1970) and many many more
Non linear atom optics (4 wave mixing) p 4 p 1 p 3 p 2 Proposals for pairs: Cirac/Zoller, Meystre, Drummond/ Kheruntsyan... NIST Nature 398, 218 (1999) MIT PRL 89, 020401 (2002)
Correlated pairs from molecules JILA PRL 94, 110401 (2005) Breakup of 40 K 2 molecule near Feshbach resonance gives back to back m=9/2, m=5/2 pairs. Very analogous to parametric fluorescence
Spontaneous atomic 4WM (aka collision) two colliding condensates produced by Raman laser pulses after expansion: collision sphere + pancake shaped condensates detection of shell in 3D in momentum space, no projection Other experiments studying collision sphere: Yale, Weizmann, Amsterdam, Otago...
Lasers Apparatus Detector 2 3 S 1 state (20 ev). Raman transition m = 1 to m = 0 mag. trap stays on
Single atom detector Detection of metastable atoms by μ-channel plate. (He* has ~ 20 ev) Excellent time (vertical) resolution (1 ns). ~ 10% quantum efficiency Delay-line anode gives in plane resolution (500 µm). 5 10 4 detectors in //. Max. data rate ~ 10 000 atoms/10 ms 20 Bytes/atom - 20 MB/s Long time of flight: position at detector is momentum in source
Animation of detected atom cloud available at http://atomoptic.iota.u-psud.fr/research/helium/helium.html
Data in 2 D ~ 3 ms slices 4 condensates I and II were intended. III is due to imperfect polarization IV is 4 wave mixing
Back to back correlations g (2) BB (v) ~ N pairs (V, V+v) / (N singles )2 units are v recoil (radians) width not resolved along x Anisotropy due to Heisenberg σ v ~ h/mr TF ~ 0.1 v rec R TF is (initial?) TF radius
Collinear correlations g (2) CL (v) ~ N pairs (V, +V+v) / (N singles )2 Hanbury Brown Twiss effect ~ same widths
Interlude: optical HBT and speckle laser L g (2) (Δx) = I(x) I(x+Δx) / I 2 I(x) 2 > I(x g (2) l C I(x) Δx x l C = Lλ/s g (2) (Δx) = 1 for large Δx = 2 for Δx 0
Interlude: atomic HBT bosons fermions Collaboration Amsterdam Jeltes et al. Nature 2007 Poster by W. Vassen Results from an interference between two 2 particle amplitudes: S 1 D 1 S 2 D 2 ± S 1 D 2 S 2 D 1 measures source (or mode) size
Other HBT experiments Yasuda and Shimizu for Ne* (1996) Hellwig et al. (Hannover) analysis of interference patterns from quasi condensate (2003) Fölling et al. (Mainz): g (2) (x) peaks at x = (hk/m)t for a Mott insulator in an optical lattice after expansion (2005). Rom et al. same for fermions (2006) Öttl et al. (Zürich), temporal correlation in atom laser (2005) Spielman et al (NIST) 2D optical lattice (2006) Fort et al. (LENS) in disordered lattice (2007) Burt et al. (JILA) g (3) T>TC(0) = 6 g (3) BEC (1997) and other collision experiments which are sensitive to the correlation function at short distances. (+ many others) On an atom chip (Orsay, 2006) iner et al. (JILA) g (2) (x) > 1 et after dissociation of molecules (2005). With electrons (1999, 2002) neutrons (2006)(anti-bunching) In accelerators with π, K
End of interlude, correlations at θ = π and θ = 0 θ = π back to back Perrin et al., PRL 99, 150405 θ = 0 collinear
Interpretation The match in widths increases our confidence that the back to back pairs indeed occupy back to back modes. (We could have gotten size wrong.) Good for recombining atoms. The back to back signal is "particle like". It would happen with marbles. The HBT (collinear) peak is "wave like". Interference of QM identical "particles". Involves 4 particles (2 pairs). Problem: the heights are both a factor of ~3 lower than expected.
Entanglement? Violation of Bell's inequalities (e.g. Orsay 1982) Bell's inequalities in momentum : p, p + q, q q p p q Is there an easier way via entanglement witnesses?
2 photon interference, Bell's inequalities Rarity and Tapster PRL 1990. An inequality is formed using coincidence rates from different pairs of counters as a function of the position of the phase plates. Atom optical analog?
Auto correlations, cross correlations Cauchy-Schwartz inequality for a fluctuating variable: xy < 1/2 ( x 2 + y 2 ) "auto correlation is bigger than cross correlation" If it were light, the violation of a CS inequality would signal a non classical state and is related to squeezing. Is there (number) squeezing? Maybe.
Future Anisotropy of shell "atomic superradiance" simulation by Perrin, Kheruntsyan Boson antibunching by collision of B and F clouds other pair production mechanisms photoassociation (J. Petit, F. Masnou) correlated photons (P. Lett)...
Jean-Baptiste and the chip
Correlations in a 1D gas correlations imply changed fluctuations δn 2 = ( N N) 2 = N + N 2 /g Einstein 1925 g (2) (0) = N 2 / N 2 1 ideal Bose gas cloud on atom chip CCD If kt ~ hν, fluctuations in position space should be visible in an image.
One interpretation of N 2 : speckle l corr = 1/Δk large fluctuations δn 2 ~ N 2 not N (Hanbury Brown Twiss effect) What is g? g 1D = Δx/l corr g 3D =(ΔpΔx/h) 3 = (Δx/λ db ) 3 l corr Δx in a 1D geometry g = Δx/λ db (kt/hν) 2
Einstein (S. Ber. Preuss. Ak., 1925, p. 18) In addition to discovering Einstein condensation, he considered number fluctuations in a small volume: δn 2 = ( N N) 2 = N + N 2 /g particles waves " if the molecules were independent." (shot noise) " for radiation corresponds to interference fluctuations" (Interferenzschwankungen) " a mutual influence between molecules of an altogether puzzling nature." " eine gegenseitige Beeinflussung der Moleküle von vorläufig ganz rätselhafter Art." g = (ΔpΔx/h) 3 is the number of phase space cells in the volume
Density fluctuations on a chip T ~ 10 hν (1.2 μk): excess noise is negligible T ~ 2 hν (200 nk) low density: ideal gas behavior. number of atoms/6 μm pixel T ~ 1.4 hν high density: suppression of fluctuations by mutual repulsion. Crossover from a uncondensed gas to a quasicondensate. Estève et al. PRL 96, 130403 (2006) Theory: Petrov et al. PRL 85, 3745 (2000)
chip parameters ν = 3 khz et 7 Hz N total ~ 5000 T = 200 nk, l C = 160 nm, k B T/hν 2 typical image (10 3 photons/pixel) <n(x) 2 > <n(x)> 2 = (1/)<n(x)> 2 + <n(x)> shot noise (1/) ~ (hν/k B T) 2 (l c /Δ ) ~ 0.01 mainly resolution but if n per pixel ~ 100, excess noise = shot noise There must be no other noise, photon shot noise must be subtracted. Chips premit a stable apparatus.
future chip work Towards the Tonks-Girardeau regime g/s > h 2 /(ms 2 ) expect δn 2 sub shot noise Need high confinement g = 2h 2 a/(mσ 2 ) good resolution (3 µm) few atoms, high sensitivity s ~ 1 µm 1