A la frontière entre physique atomique et nanotechnologies : l'atome comme sonde haute-résolution des surfaces et interfaces

Transcription

1 A la frontière entre physique atomique et nanotechnologies : l'atome comme sonde haute-résolution des surfaces et interfaces Martial Ducloy Laboratoire de Physique des Lasers/CNRS Institut Galilée Université Paris Nord VILLETANEUSE (F) Funding : CNRS; Univ. PXIII; EU FASTNet network JPOM6

2 ATOM - MICRO/ NANOBODY INTERACTIONS: Implications in many domains of Science and Technology: Cavity QED (entanglement, decoherence) Quantum optics in semiconductors Photonic bandgap materials Spontaneous emission control, thresholdless microlasers STM/SNOM tunnelling microscopies Atom optical devices, integrated atom optics (atom chips, coherent atomic transport, low-d atom trap, nanoscale trap..) Atom lithography, nanotechnologies

3 ATOM-SURFACE INTERACTION The model of electrostatic images (perturbative regime, non resonant coupling) reflector ( ε) vacuum vdw potential (interaction between dipole and dipole-image) D im D 2 ε 1 D + D = ε z z H vdw 3 2 non-retarded and near-field interaction: z -3 D, atomic dipole operator 2 For a neutral atom, ede =, but ed e (atomic dipole fluctuations)

4 OUTLINE 1. Optical spectroscopy approach 2. Beam (momentum) spectroscopy approach 3. Conclusion-Outlook

5 OPTICAL SPECTROSCOPY APPROACHES to ATOM - DIELECTRIC STRUCTURE INTERACTION Reflection spectroscopy Wood 199 Cojan 1954 Woerdman et al dielectric gas Evanescent wave spectroscopy Boissel et al Simoneau et al gas SNOM fluorescence spectroscopy Betzig et al Girard et al etc. substrate fibre tip molecule WGM reflection spectroscopy (Whispering Gallery Mode) Vernooy et al microsphere gas Submicrometric gas cell spectroscopy D. Sarkisyan et al. 22 G. Dutier et al. 23

6 1. Laser spectroscopy of ultra thin cells 2. Reflection spectroscopy G. Dutier, I. Hamdi, P. Todorov, I. Maurin, M.-P. Gorza, M. Fichet, D. Bloch, M.D. (UPN, Villetaneuse, F) S. Saltiel (Sofia University, Bulgaria), A. Lezama (Montevideo, Uruguay) T. Varzhapetyan, D. Sarkisyan (Institute for Physical Research, Armenia)

7 ULTRA THIN GAS CELL Windows (YAG or Sapphire) separated by ring-shaped sapphire spacer low density cell : external pressure changes internal thickness locally Caesium vapour inside the cell D. Sarkisyan et al., Opt. Comm. 2, 21 (21)

8 THICKNESS MEASUREMENTS Ultra Thin Cell = Fabry-Pérot cavity Measurement of reflection coefficient for 3 different lasers : 633nm 852nm 13nm YAG Reflection interface / Reflection first window 2,8 2,4 2 1,6 1,2,8,4 633 nm 852 nm 13 nm Thickness (nm) Thickness between windows : 3nm to 13nm Accuracy < 5nm

9 THICKNESS MEASUREMENTS Thickness is measured by monitoring the reflection coefficient measurement at the point of the experiment using three laser sources (633nm; 894nm; 13nm) thickness (nm) thickness (nm) vertical position, h (mm) horizontal position, x (mm)

10 ω L 1µ m v r p(z) φ =1..1 mm L << φ, atom mean free path (low density) p()= z = z = L Atom dynamics dominated by wall adsorption/desorption: ultra short time-of-flight (TOF) transient behaviour is dominant in atom-light interaction atom motion + boundary effect non-local atom response p(z), i.e. spatial dispersion Strongly anisotropic time-of-flight: very long TOF for atoms moving quasi-parallel to the windows (v z =) absorption singularity, which is Doppler-free for normal incident light

11 Excitation of Cs D 1 resonance line (894 nm) 6P 1/2 R extremely thin cell (ETC) FM laser (λ = 894 nm) P = 1 nw f = 1 cm f = 1 cm T 6S 1/2

12 Transmission: Dicke narrowing and revival Rb nanocell ; λ = 78nm ; I =.4 mw/cm2 ; transitions F=2 F=1, 2, 3 Sarkisyan et al., Phys Rev A 69, 6582 (24)

13 Transmission in an ETC : the Dicke narrowing Linear interaction + Transient regime σ 1 Λ ( ) ( Λt t z/v 1 e ) = with Λ = γeg i( δ kv) ABSORPTION over z (z [,L]) α = I I Re ( v ) dv σ ( t z/v ) + L W eg = dz + ( ) ΛL L v + v α Re W v ( 1 e ) dv 2 Λ Λ Linear absorption A log singularity Interferometric effect Dicke effect: At δ =, and for L = λ/2, all velocities contribute constructively to the signal, like 1/v

14 The Bloch vector model for Dicke narrowing Sarkisyan et al, Phys Rev A 69, 6582 (24) r Ω ds dt a) r r = S B Z Ω =δ-kv B S, B r = δ kv Y X L=λ/2 Y L=λ For δ=: S rotates around B at angular velocity ~ kv (if Ω ) up to a duration τ = L/v X X b) c) dsy (Coherent) Transmission S y dz (Incoherent) Fluorescence dz S z Y

15 Collapse and revival of Dicke narrowing : λ/2, 3λ/2, etc... Direct Cs(D 1 ) Transmission J. Opt. Soc. Am. B, 2, 793 (23) 22 nm 335 nm 447 nm (x7.6) (x1.8) (x.9) λ/2 Europhysics Letters, 63, 35 (23) FM Transmission 45 nm 67 nm (x1.8) 78 nm (x1.4) 89 nm (x1) λ 89 nm 15 nm (x1) 111 nm 1235 nm 1 MHz (x1.7) (x.8) <3λ/2 1 MHz 115 nm

16 Dicke narrowing in two-photon transition k 1 +k 2 3> k 1 i B ω 2 ω 1 2> 1> k 2 r r k 1 + k L=Λ/2 with Λ =2π/ 2 Dutier et al, Phys. Rev. A72, 451R (25)

17 Cavity Quantum Electrodynamics in Dielectric Nanocells

18 Cs (D 1) FM transmission for very small thickness (5-2nm) and YAG windows F=3 225 (5)nm 9 (5)nm 53 (3)nm F=4 1 GHz CELL THICKNESS (nm) vdw SHIFT (MHz)

19 Transmission, FM mode, D1-Cs line, YAG windows F = 3 F = 4 THEORY YAG D1 L = 225;9;55 nm γ = 24;4;23 MHz ku = 25 MHz C 3 = 3 KHz.µm 3 EXPERIMENT 225 nm 117 MHz 13 o 9 nm 15 o red shift 55 nm 2 o detuning (MHz) detuning (MHz)

20 COMPARISON THEORY vs EXPERIMENT vdw SHIFT (MHz) EXPERIMENT THEORY 1/L 3 slope 1 CELL THICKNESS (nm) 2

21 Thin cell transmission at L = λ/2 (46nm)/sapphire window 6 D 5/2 6 D 3/2 921nm 917nm 6 P 3/2 852nm 6 S 1/2 Cesium

22 Transmission en Cellule Ultra Mince à d = 32 nm Objectif : Résolution Spatiale du van der Waals à moins de 5nm,8 T = 38/33 d = 32 nm P 852 = 2.6 mw abs pompe (852) = 5% - 11 GHz Bruit ~ 2.1-6,6 Signal ~ Absorption,4,2, 917, 917,5 918, nm

23 MODELS FOR SURFACE INTERACTIONS IN ETC s n n d L=2d z 1. Two-window model: sum of the potentials of the two windows; the contribution of multiple reflections between thin cell windows is neglected. 1 ε vdwshift( δ d ) Re d ε + 1 ( 1 δ d ) ( 1+ δ d ) where δ = z d 2. Exact solution : account for multiple reflections between the two windows; solution in form of trilogarithm functions (Li 3 or Lerch function) [Nha - Jhe, 1996; Barton, 1997] 3. (Polynomial fit to the exact solution)

24 Role of the cell thickness on transmission spectra two level theoretical model with vw λ = 917 nm (x1.1) (x4.97) L=5nm L=65nm ku=25 MHz γ = 3 MHz C 3 =7.55 khz.µm (ω ω ) MHz L=8nm (x2.96) L=13nm

25 YAG/Cs thin cell transmission and reflection strong red shift L=5 nm λ=917 nm T=22 C, change of transmission 5 GHz free space resonance 6 D 5/2 6 P 3/2 917 nm tunable probe 852 nm pump reflection signal Fit obtained with C 3 = 7.55 khz.µm 3 6 S 1/2 Cesium frequency detuning

26 ATOM-SURFACE INTERACTION : dielectric interface The model of Electrostatic images vw potential : an interaction between dipole and dipole-image reflector (ε) vacuum H vw = - ε -1 ε + 1 D² +D z ² 16 z 3 A summing over virtual transitions ω ij D im D z <i D² i> = Σj r(ω ij )<i D j> <j D i> For ε(ω ij ) complex (i.e. absorption) How the image coefficient r behaves?

27 DIELECTRIC SURFACE Dielectric permittivity ε(ω) : complex, dispersive (ω) Ground State : quantum fluctuations : level shift δe g g h = δeq = 3 4π z atomic polarisability du α g ( iu) ε ε ( iu) ( iu) dielectric ( 1) (surface response) Excited state : - resonant shift induced by VIRTUAL EMISSION COUPLINGS. i δe δe i i δe δe i r = Q + R 1 2 ε ( ωij ) 1 D 3 ij Re z j< i ε ωij + 1 = 16 ( ) Surface resonance determined by the poles of [(ε(ω i-j ) -1) / (ε(ω i-j ) +1)] i.e. a virtual atomic de-excitation coupled to a "virtual" polariton of the dielectric surface - AND ALSO : i j via real emission in a polariton mode: 1/z 3 Im [(ε(ω i-j ) -1) / (ε(ω i-j ) +1)]

28 Dispersive dielectric ε 2 =ε(ω) k z ε k x Λ=1/Κ x e -Kz vacuum ε 1 =1 z Surface guided mode : for ε(ω)+1< Wave vector : k x 2 = k 2. ε/(ε+1) ; k z 2 (vacuum) = -K 2 = k 2 /(ε+1) (k = ω/c) Surface polaritons : poles of 1/(ε(ω)+1) ε -1 : - phase velocity - evanescent wave depth, Λ=1/K mode volume decreases vacuum field, E v, increases (diverges if no dissipation) maximum coupling strength between photon and material excitation (e.g. phonons for dielectric media) The near-field of the excited atom dipole (scaling like 1/z 3 at the interface) couples to surface polariton two coupled oscillators

29 THE DIELECTRIC IMAGE COEFFICIENT The case of SAPPHIRE 1 r (ω> ) Virtual, r(ω< ) -2,,1,2,3,4,5 ω (1 14 Hz ) ABSORPTION of the atom (always non resonant) Virtual EMISSION of the atom : possibility of a resonant COUPLING to a ABSORPTION in a SURFACE POLARITON MODE

30 Re[( ε -1)/( ε -1)] extraord. ordinary wavelength (µm) Surface response for an isotropic medium whose permittivity ε is either ε ord or ε extr of sapphire 1 Re[( ε -1)/( ε -1)] 5-5 θ= wavelength (µm) Sapphire window with different directions of the birefringence axis: normal to the interface (i.e. ε eff = (ε ord ε extr) 1/2 ) off- normal to the interface parallel to the interface

31 REPULSIVE vw INTERACTION µm 6 D 3/2 SAPPHIRE surface response µm 7 P 3/2 7 P 1/2 1 21µm 12 µm 6 P 1/2 876 nm 894 nm Re[( ε -1)/( ε -1)] 5-5 θ=9 45 sapphire surface polaritons 6 S 1/2 Cs wavelength (µm) birefringence axis: normal to the interface off- normal to the interfac parallel to the interface Observation by selective reflection (i.e. 1-wall, probing at ~λ/2π) H. Failache et al, Phys. Rev. Lett. 83, 5647 (1999) ; Eur. Phys. J D 23, 237 (23) M. P. Gorza et al, Eur. Phys. J D 15, 113 (21)

32 R=R + R(ω) z E NR +E res z E i Vapour v z > : transient dipole response (desorbing atoms) v z < : steady-state dipole response Spatial dispersion Non-local response of dipole polarisation, whose amplitude P depends on z sub-doppler singularity at normal incidence Singular contribution of v z = atoms [ Cojan, 1954 ; Woerdman Schuurmans, 1975 ] REFLECTION CHANGE : E res dz p(z) exp (2ikz) Doppler - free vapour dispersion explored on a layer z ~ 1/k ~ λ opt /2π ( typically 1-15 nm)

33 15.57 µm 6 D 5 3/ MHz 4 7 P 3/ MHz µm 3 7 P 1/ MHz 876 nm 4 6 P 1/ GHz nm 21µm 12 µm 4 6 S 1/ GHz 3 Sapphire surface polaritons Cs Sapphire YAG Pump (894 nm) FM probe (876 nm) SR cell SA cell

34 YAG Sapphire 8 MHz

35 γ 5 4 (MHz) F = 4 F = Pressure ( mtorr ) C 3 (khz.µm 3 )

36 vdw shift near the ω S resonance for µ vdw shift) (in 2 µ 2 /L 3 ) Position in the cell x/l ω / ω S

37 vdw shift for ω/ω S =.999 for µ vdw shift for position in the cell x/l ω/ω S =1.1 for µ ε 1 Re ε + 1 ω S

38 lλ (µm) mm waveguide modes (between sapphire walls) Waveguide modes Sapphire walls 2 λ T 18 Transverse mode (antisymmetric) λ L Surface mode λ λ S =12.2µm at =12.15 (Cs 6P-6D) Longitudinal mode (symmetric) KL L: surface distance ; K: wavevector along surface

39 SURFACE RESONANCES in ATOM - STRUCTURE INTERACTION 1/ Dielectric microstructure High-Q morphology dependent resonances (MDR): Ex.: Mie resonances, or Whispering Gallery Modes (WGM) of microspheres Braginsky et al 1987 Haroche et al Influence on atom-surface interaction : Vacuum Rabi splitting Klimov et al 1997 For nano-bodies, no propagation no resonances 2/ Dispersive dielectric / metal surface polariton Polariton frequency tuning via : Material birefringence (c-axis orientation) Form factor in surface response * plane : (ε-1)/(ε+1) * nanosphere : (ε-1)/(ε+2) * nano-ellipsoid.

40 DIPOLE DECAY RATE NEAR ANY BODY γ γ 3 de ( r, ω) R atom = 1+ Im dk E R - field reflected by nanobody d - dipole momentum γ - free space decay rate This result is valid within classic as well as quantum perturbation theory For nanobodies one can use pertubation theory quasistatic de ( r', ω ) ( R) 2 d solution = a1 + b1k + ck 1 + id1k + nonradiative lo sses radiative losses γ 3 a1 3 = I m Re ( d1 +...) γ 2 k 2... γ radiative 2 total = d 2 γ d d total - dipole momentum of atom + nanobody system a 1 =?, d total =?

41 SPONTANEOUS EMISSION OF AN ATOM PLACED NEAR PROLATE NANOSPHEROID GENERAL EXPRESSION γ γ 2 = d total 2 d d total - dipole momentum of atom + nanospheroid system d - dipole momentum of atom RESULTS ξη, = 1 ( ξ ) 2 γ dq1 = 1+ G1 γ dξ γ dq1 ( ξ ) ξ 1 = 1+ G11 γ dξ ξ ξη, = G 1 G 1 и G 11 - reflection coefficients = G 11 ( ε 1) ξ ( Q1 ( ξ) ) ξ εq1 ( ξ) = ( ε 1) ξ 1 ( Q ( )) ξ ξ 1 εξq1( ξ) Q - Legendre functions,

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44 Conclusion Interest of nm-thin gas cells for investigating: QED in dielectric FP nano-cavity Nanophysics with free atoms; atom-surface interaction in 2-2nm range Novel regime of atom dynamics and atom-light interactions (Dicke regime) PROSPECTS Modification of atomic fluorescence, branching ratios ; non-radiative decays Repulsive walls [e. g., Cs (6D) with sapphire windows], or prism windows (evanescent-wave atom mirrors): Atom confinement, atom bound states, new type of atom traps, atom optics in nm-confined space Nano-structured walls for higher-d confinement Nano-cavity QED in the non-zero temperature limit Atom-atom interaction in confined space

45 HR Beam Spectroscopy: Off-Diagonal van der Waals interaction and Atom interferometry J.-C. Karam, J. Grucker, F. Perales, G. Vassilev, J. Baudon, J. Robert, M. Boustimi, V. Bocvarski (1), J. Reinhardt, M.D. Laboratoire de Physique des Lasers Université Paris Nord (1) Institute of Physics, Pregrevica, Beograd, Yugoslavia

46 "BEAM SPECTROSCOPY" APPROACHES TO ATOM-STRUCTURES INTERACTION - Beam deflection by metal surfaces Raskin et al. 1969, Shih et al Beam transmission in microslits Haroche et al. 1988, Hinds et al Energy thresholds in atomic mirrors (evanescent wave mirror) Aspect et al Coherent atomic diffraction by material gratings (small angle) Toennies et al Inelastic beam diffraction by micro/nano-gratings (large angle) Boutsimi et al Quantum reflection of ultra-cold atom Shimizu et al. 21

47 Non scalar van der Waals Potential Induced dipole induced dipole image interaction non retarded regime ( z < 1 nm ) D D D V = 1 4πε 4 3 D 2 + D 16z D + D z = D + 3 D z 2 z 3 -z z Scalar ( ) T Quadrupolar ( 2) T The quadrupolar term is not rotating-invariant (anisotropic) Coupling between internal state and external motion

48 Metastables levels of Ar spin-orbit coupling of 3p hole, spin of the 4s electron

49 Coupling between the two metastable levels of Ar, Kr 2,m,;2, P T P P D P z 3 ( 2) = D if m=, P P m = = D = = = i m, 2 3 z z 3 m, z 3 P D i i D P P D P 174meV E *: Ar = 65meV E *: Kr =

50 Kinematics of inelastic transitions Conservation of total Energy of the atom Conservation of the momentum in the plan // to the surface v v = f = v 2 cosθ vf cosθf + 2 E m 1/2 θ E > θ cosθ cosθf = 1+ E E < E θ f θ f Threshold for E < v 2 2 E m

51 Experimental Device Exo-energetic process Time of flight detection 3slits disc X*( 3 P 2 ) Pulsed source T 3-4 µs v Grating ( or slit ) θf v f Z X*( 3 P ) X Distances are 121 mm and 164 mm

52 Source and detection. Thermal Effusive Beam ( v = 55m/s for Ar) Pulsed electronic Bombardment ( T=3-4 µs, T 1,5 ms) δv v 8% Velocity selection Angular width after collimation : θ = 1.4 Maximum flux of 2 atoms/s Angular resolution of the detection :.43 Detection Noise <1-3 Hz Good detection efficiency (plate + channeltron) 2 % Acquisition time : 1 3 s s for each point!

53 Transition 3 P 3 P 2 of Kr* Results with a single slit Efficiency I / I = (1.46 ±.26 ) µm,8 Kr* 436 m/s 73 6 Kr* m/s 1 µm Counts,6,4 DCS 8, TOF channel (1 channel = 3.33µs) θ (deg.)

54 Results for the 3 P 3 P 2 transition of Ar* 4 Velocity dependence of the peak angular position Section efficace différentielle (arb. unit) Ar* 356 m/s 535 m/s θ (deg.)

55 Experimental Device (bis) 3 slits disc Endo-energetic process Ar*( 3 P ) Time of flight Detection Grating Pulsed source T : 3-4 µs v θr θ f v f Z X Ar*( 3 P 2 )

56 Results for the 3 P 2 3 P transition of Ar* Grating angle to the atomic beam axis o θ r = 6 TOF Analysis Integration time : 16 s! 1 v = 13m.s ± 15% v f,expected = 51m. s 1 Wide Peak : Velocity selection less efficient at high velocities Channel At long TOF : Metastability exchange with residual gas?

57 Influence of initial velocity Counts in the expected TOF domain as a function of the selected velocity v threshold Velocity Resolution limited by the velocity selection width : δv v 15%

58 Coherence and initial velocity. * Slow Atoms : λ 3 nm for Ar* (.2 nm in a thermal beam) Large transverse coherence length accessible by collimation. - Coherent irradiation of several grating slits - Reduced roughness effects at scales < λ («atomic speckle») Necessity of a E of a few µev Zeeman Transitions

59 Coupling between Zeeman sublevels 3 X* P2 x : J B = 2 [ ] 1 [ ( )] 2 3 V C + Q J J /3 x α, j = 3 3, α α Z m i Z V m j x m =, ± 2 D D Transitions are possible! -z z ± ; 2 x x x ; x x ; x x x x m = ±2

60 Kinematics of Zeeman transitions Ar* 3 P2 E = m g µ m = ±2 B B Grazing incidence : tanθ f E = E 1/2 v 3.3m/ s = B of a few 1 2 Gauss E E 4 = 6.1 B( G)

61 METASTABILITY-EXCHANGE SOURCE Supersonic beam ~ 3 K nozzle v few K Shock wave 1 bar 1-4 bar skimmer Intense pressure difference narrow beam narrow velocity distribution δv/v ~ 1% + Metastability exchange Supersonic beam Ar e - Electron bombardement Ar* Ar* Exchange Ar* +Ar Ar + Ar* Low momentum transfer during the exchange process Metastable atoms with the supersonic beam properties = δθ.35 mrad

62 Application: He *, Ar* diffraction Double collimation θ =.3 mrad Silicon nitride grating Λ= 1 nm counts counts angle (mrad), -,5-1, -1,5-2, -2,5-3, angle (mrad) He* λ ~ 162 nm (Linear plot) Ar* λ ~ 51 nm (Log plot) calculations experiment

63 Ne* B γ : Inelastic scattering angle Position Detector γ G 289G 145G G-test counts γ - angle (mrad)

64 γ E g µ = B B m E E B 1 m γ (B (G)) 1/ X X 2 X X X 3 X X? angle γ (mrad) Experimental evidence for surface-induced vdw Zeeman transitions

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66 Next step : cooling of Ar* ( 3 P 2) Zeeman slower Ar* 3 P 2 B detector V =3.6 m/s laser λ = 811 nm mirror M laser Grating increase of l C λ db P m,m (θ,ρ) deviation γ atom interferometer?

67 Conclusion New metastable atom source for atom optics and atom surface interaction studies Study of atom-surface interaction effects on magnetic sublevels (e.g. scattering with ) m