activité University of Toulouse-CNRS Bertrand Girard

Wavepacket dynamics and interferences in atoms and molecules Laboratoire Collisions Agrégats gats RéactivitR activité University of Toulouse-CNRS Bertrand Girard Thanks to: Damien Bigourd (post-doc) Antoine Monmayrant (ph D) Sébastien Weber (ph D) Béatrice Chatel (CNRS) Région Midi-Pyrénées Fondation Del Duca Ministère de la Recherche ANR, IUF Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 1

Wave packets and interferences A wave packet is a Coherent superposition of several states: - Vibrational wave packet (many levels) - Rydberg electron wave packet (many levels) - Free electron wave packet (continuum of levels) - Spin-orbit wave packet ( levels) Single level Interferences: - between wave packets created by different laser pulses - within the excitation process Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008)

Principle of experiments single ultrashort pulse or sequence of ultrashort pulses or complex shaped pulse τ Ι(τ) Ι(shape) Observation of the temporal evolution with a probe pulse of the final state without time resolution Quantum system (atom, molecule) Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 3

Invited talks Wave Packets Dynamics (Magpie A) 1:00 Helen Fielding, University College, London (UK) Setting the quantum clock: Localisation of Rydberg wave packets in H 1:0 Kenji Ohmori, Institute for Molecular Sciences, Okazaki (Japan) Tailoring Picometric Quantum Carpets by Controlling Ultrafast Wave-Packet Interference 1:40 Terry Mullins, Albert-Ludwigs-Universität Freiburg (Germany) Coherent transients in the photoassociation of ultracold atoms by femtosecond pulses Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 4

Invited talks Wave Packets Dynamics (Magpie A) 1:00 Helen Fielding, University College, London (UK) Setting the quantum clock: Localisation of Rydberg wave packets in H 1:0 Kenji Ohmori, Institute for Molecular Sciences, Okazaki (Japan) Tailoring Picometric Quantum Carpets by Controlling Ultrafast Wave-Packet Interference 1:40 Terry Mullins, Albert-Ludwigs-Universität Freiburg (Germany) Coherent transients in the photoassociation of ultracold atoms by femtosecond pulses Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 5

Outline I. Wave packet Interferences in atoms 6d, 8s Rb τ 6p II. III. IV. Quantum state holography Control of wave packet dynamics 5p P 1/ Interferences within the excitation of a multiphoton transition 5s Fluorescence (40 nm) Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 6

E(t) Interferences between identical time-delayed quantum paths : Ramsey fringes - Theory τ L π / ω L τ L π / ω L t 0 t 0 + τ t weak field regime : ( ) Ψ t = i + a e e + ( ) i ω t iω t T t i a e e a e e Period = π/ω a << 1 ω 0 Φ CC t0 t0 + T e i interference phase oscillates rapidly with Τ φ cc = ωτ φ cc = 0 [π] constructive interferences φ cc = π [π] destructive interferences Excited state population Time delay Τ Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 7

Ramsey interferences with a pulse shaper (1) 6d, 8s Rb f f f f 5p P 1/ 5s τ 6p Fluorescence (40 nm) High Res. Pulse Shaper: Phase - Amplitude control with 640 pixels. shaping window of 35 ps. high complexity. 75 % power transmission. Angular dispersion γ G1 i 1 + e θ E ( t) E ( t) L1 X M( X) L G E () E t ES () t E S ( ω) = H( ω) E ( ω) Weiner, A.M., RSI, 71, (5), 000 E H ( ω) = M ( f γω. ) γ A. Monmayrant, B. Chatel. "A new phase and amplitude High Resolution Pulse Shaper." Rev. Sci. Inst. 75, 668 (004) Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 8

Ramsey interferences with a pulse shaper () A sequence of FT limited pulses with a relative phase θ { θ ω ω } p H ( ω ) = 1 + exp i + it ( ) / Cross-correlatoin a e (t) (arb. u) 4 3 1 0 T θ=0 θ=π θ=0 θ=π -1 0 1 3 4 5 Pump-probe delay (ps) a e (t) (u. arb.) 4 0 0π 1π π 3π 4π Phase θ (rad) 1+1 = 0 to 4 Ramsey fringes Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 9

Outline I. Wave packet Interferences in atoms II. Application of wave packet interferences to Quantum state holography Measuring the time evolution of the quantum state and not only the population 6d, 8s Rb III. IV. Control of wave packet dynamics Interferences within the excitation 5p Pof 1/ a multiphoton transition τ 6p Fluorescence (40 nm) 5s Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 10

Coherent transients produced by a chirped pulse: Interferences within a single pulse Excited state evolution through chirped pulse excitation Im(a (t)) e 6d, 8s 0.05 5p P 1/ 0.00-0.05 5s -0.10-0.15-0.0 τ 6p Rb Fluorescence (40 nm) -0.1 0.0 0.1 0. Cornu spiral Re(a e (t)) T. Mullins talk (parallel session) t 1 t φ " 6p-5s Fluorescence t τ c t ln t i τ φ c ae () t e e dt Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 11 0ps at resonance 5 φ = 8 10 fs - 0 4 6 8 10 Delay (ps) Zamith, et al, PRL 87, 033001 (001) Degert et al, PRL 89, 03003(00)

Quantum state holography (1) 6d, 8s Rb Principle: 5p P 1/ τ 6p Fluorescence (40 nm) Use a first pulse to create a local oscillator in the atom The population in 5p (probed in real time) reflects the beating between this local oscillator and the wave function excited by the chirped pulse 5s Two level system: 5s- 5p²P1/ in Rb Red pump: resonant and chirped Yellow probe: shorter than pump and CT dynamic Fluorescence is monitored as function of the pumpprobe delay Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 1

Quantum state holography () 6d, 8s 5p P 1/ 5s τ 6p Rb Fluorescence (40 nm) Two level system: 5s- 5p²P1/ in Rb Red pump: resonant and chirped Yellow probe: shorter than pump and CT dynamic Fluorescence is monitored as function of the pumpprobe delay Ti:Sa Oscillator O CPA 795 nm 1kHz 1 mj 130 fs ( ω) = ( ω) ( ω) E H E I Rb Rb PM NOPA 607 nm 1kHz 5 µj 0 fs 795 nm 1kHz 5 µj Delay line () (1) φ H( ω) = 1+ exp iθ + iφ ( ω ωp) + i ( ω ωp) / Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 13 τ EI ( ω) EO ( ω)

Quantum state holography (3) A) B) From CT to E ( t) + E ( t) 1 CT () t a () t + a () t A e1 e E ( t) + i E ( t) 1 CT () t a () t + i. a () t B e1 e Fluorescence (arb. units) 0.6 0.5 0.4 0.3 0. 0.1 CT A CT B 0.0-1 0 1 3 4 5 6 7 8 9 10 11 τ (ps) By combination of the two CT Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 14

Quantum state holography (4) the evolution of the atomic quantum state By combination of the two CT A. Monmayrant, B. Chatel, B. Girard, PRL, 96 10300 (006) ; Opt. Lett. 31, 410 (006) ;, Opt. Comm. 64, 56 (006) Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 15

Outline I. Wave packet Interferences in atoms II. Quantum state holography III. Control of wave packet dynamics IV. Interferences within the excitation of a multiphoton transition Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 16

Condition to observe interferences: The coupled and uncoupled states should have different probe probabilities Δ φ> φ1> Coupled Uncoupled state Δ Ψc>=Ω1 φ1> + Ω φ> Ψuc>=Ω φ1> Ω1 φ> Interference phase g> g> The wave packet evolves freely back and forth between the coupled and uncoupled Femto group states. - LCAR - Toulouse Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 17

Spin-orbit precession in Rb M 0, M = 1 M L 1, M = 1 L = S = S 61 nm Rb L = 1, S = 1 J L S L J S 5p P 3/ P 1/ ω 790 nm FLUO 5s S 1/ L= 0, S = 1 S M L 0, M = 1 = S Fine structure : The coupled and uncoupled states belong to the uncoupled basis set. The free evolution corresponds to the spin precession around the total angular momentum. The spin of the electron is spectator during the pump step. Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 18

Spin-orbit precession in Rb Rb -0,6 61 nm -0,5 5p P 3/ P 1/ Pump- probe signal -0,4-0,3-0, FT pulse 790 nm FLUO -0,1 0,0 0 00 400 600 800 1000 Time delay (arb. origin) 5s S 1/ First observed in Potassium then in Rubidium S. Zamith et al, EPJD 1, 55 (000) E. Sokell, et al, JPB 33, 005 (000) Is it possible to populate the uncoupled state first? Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 19

Can we populate directly the uncoupled state? Δ φ> φ1> Coupled Uncoupled state Δ Ψc>=Ω1 φ1> + Ω φ> Ψuc>=Ω φ1> Ω1 φ> Interference phase g> g> Use a shaped pulse with a phase shift of π between the two resonances. Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 0

Spin orbit precession and control o apply a π phase step between the two excitation frequencies 3 Without π-step Coupled Uncoupled With π-step Coupled Uncoupled pop(a.u.) 3 1 1 pop (a.u.) 35 30 5 0 15 10 5 0 0 0 100 00 300 400 time(fs) -5 0 100 00 300 400 time(fs) The uncoupled state is first populated after the pulse. Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 1

Experimental results The oscillations produced by the shaped pulse are phase shifted by π with respect to the reference case -0,6-0,5 Pump- probe signal -0,4-0,3-0, -0,1 FT pulse π-shifted pulse 0,0 0 00 400 600 800 1000 Time delay (arb. origin) No violation of first principles: The shaped pulse is longer than the spin-orbit precession! Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008)

Application to molecules This demonstration on the fine structure could be extended to molecular vibrational levels. Can we make a non- Franck-Condon transition? av v v v ( ) 1 v v a v? Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 3

Ramsey fringes with several excited states: wave packet interferences Excitation of a superposition of the two states Period = π/ω Excited state population Time delay τ Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 4

Interferences between identical time-delayed quantum paths : Ramsey fringes - Experiment Cs + V. Blanchet et al, Phys. Rev. Lett. 78, 716 (1997). M. A. Bouchene et al, Eur. Phys. J. D, 131 (1998). 10 T opt =.56 fs T quant =1.8 fs 7d D 3/,5/ τ=1.6 ps 8 769 nm 769 nm Cs + / a.u 6 6s S 1/ τ (1) Cs () Pulse sequence produced by a Michelson interferometer τ 4-10 0 10 35040 35060 1.6 ps Similar studies by 0 G. Fleming et al, JCP 93, 856 (1990); 95, 1487 (1991); 96, 4180-3 (199) 0 3 6 9 1 15 W. J. van der Zande et al, PRL 7, 3783 (1994) delay / ps R. Jones, P. Bucksbaum et al, PRL 71, 575 (1993); 75, 1491 (1995) T. Hänsch et al, Opt Lett, 540 (1997) K. Ohmori et al, PRL 91, 43003 (003), 96, 09300 (006) Beats due to spin-orbit precession Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 5

In Molecules: Wave packet interferences K. Ohmori s talk (parallel session) In bound states nd wave packet Interferences in the total cross-section (Ramsey fringes) V. Blanchet et al, JCP 108, 486 (1998) K. Ohmori et al, PRL 96, 09300 (006) Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 6

Outline I. Wave packet Interferences in atoms II. III. IV. Quantum state holography Control of wave packet dynamics Interferences within the excitation of a multiphoton transition Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 7

Interferences in Ladder climbing e Quantum ladders : Vibration in molecules Rotation (within Raman process) Rydberg levels e i ω eg / g Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 8

Interferences within the excitation process e i ω eg / Takes advantage of the broad spectrum of ultrashort pulses: Interferences between several quantum paths associated to different frequency components in multiphoton transitions Control of interferences by changing the pulse shape (spectral phase) direct excitation g sequential excitation Many examples Chirped pulses Noordam et al, Chatel-Girard et al, Shaped pulses Silberberg et al, Dantus et al, Faucher et al 1 pulse Two-photon transition Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 9

Na ladder climbing with chirped pulses 5S φ < 0 3, shν 3P 3/ 3P 1/ 4P 3P3 / 3P1/ Ti:Sa Oscillator CPA 800 nm 1 khz 1mJ 130 fs 60 nm 3S Na cell PMT 605 nm, 30 fs width 5nm 10 µj NcOPA SF58 rod Fluorescence 330 nm Fixed chirp Stretcher Variable chirp 5 S, hν hν Dressed states Fluorescence observed as a function of chirp rate Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 30

Na (3s 3p 5s) at 605 nm J S L δ k i e φ δ k Contrast of 97% L S FT limit B. Chatel, et al, PRA 68, 04140 (003) PRA, 70, 053414 (004). J Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 31

From to many levels : numbers factorization with Gauss sums W. Merkel, W. P. Schleich, I. Averbukh, B. Girard, et al, Int. J. Mod. Phys. B 0, 1893 (006). W. Merkel, I. S. Averbukh, B. Girard, G. G. Paulus and W. P. Schleich, Fortschr Phys. 54, 856 (006). Number to factorize If l is not a factor of N then the phase oscillates rapidly and the sum is small If l is a factor of N then the phase is a multiple of π and the sum is equal to 1 Goal : Implement the Gauss sum in a physics experiment to factorize numbers Trial number Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 3

From to many levels : numbers factorization with Gauss sums W. Merkel, W. P. Schleich, I. Averbukh, B. Girard, et al, Int. J. Mod. Phys. B 0, 1893 (006). W. Merkel, I. S. Averbukh, B. Girard, G. G. Paulus and W. P. Schleich, Fortschr Phys. 54, 856 (006). Number to factorize If l is not a factor of N then the phase oscillates rapidly and the sum is small If l is a factor of N then the phase is a multiple of π and the sum is equal to 1 Goal : Implement the Gauss sum in a physics experiment to factorize numbers Trial number Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 33

First successful attempts Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 34

Conclusion: Interferences!!! Observation of the atomic quantum state during the light interaction Measurement with a reference, but no spectral condition for the reference (unlike conventional interferometric methods) Extension to multiple states (molecular nuclear wave packets) Pulse shape measurements (from da e /dt): Feasibility of reconstructing the phase and the amplitude using coherent transients No intrinsic limitation to measure complex shapes The only temporal limit is the linewidth of the atomic transition! Requires a resonant bound state as a local oscillator!! Interferences in ladder climbing Towards «non Franck-Condon» transitions More interferences to come! Physics of Quantum Electronics 38, Snowbird, Utah (7-11 Jan 008) 35

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