Observation and control of ultrafast quantum interferences in atoms Béatrice Chatel

Transcription

1 Observation and control of ultrafast quantum interferences in atoms Béatrice Chatel 1

2 Control using quantum paths interferences Following the wave function during the interaction.. Following and controlling the spin orbit precession : Towards non Franck-Condon transition Quantum interferences in a two-photon transition : Towards factorisation scheme

3 Control using quantum paths interferences τ Following the wave function during the interaction.. Following and controlling the spin orbit precession : Towards non Franck-Condon transition τ Quantum interferences in a two-photon transition : Towards factorisation scheme Our tools 3

4 Our tools: ultrashort pulses and pulse shaper i E() t = E() t e ϕ () t F F f f f f -1 i ( ) E ( ω) = E ( ω) e φ ω Linear passive Filter G1 L1 X M( X) L G E () E t ES () t γ E ( ω) = H( ω) E ( ω) S with i ( ) H( ω) = A( ω) e φ ω E E S ( ω) = M ( f γ ω) E E ( ω) Weiner, A.M., RSI, 71, (5),

5 Our high resolution pulse shaper Phase/Amplitude control over 640 pixels. shaping window of 35 ps. high complexity. high amplitude dynamic (30 db). 75 % power transmission. A. Monmayrant, B. Chatel. "A new phase and amplitude High Resolution Pulse Shaper." Rev. Sci. Inst. 75, 668 (004) 5

6 Observation and control of ultrafast quantum interferences in atoms Following the wave function during the interaction 6

7 Coherent transients : principle ω Fourier limited pulse t φ( ω ) = 0 ω Chirped pulse () φ τ 0 () φ φ( ω) = ( ω ωeg ) t P () t = a () t e e ( ) E ω eg P () t = a () t e e τ 0 Et () E() t τ c t (fs) eg a ( τ ) Et () e dt e τ iω t t (fs) N. V. Vitanov et al., PRA (59), 988 (1999). 7

8 Control of the CT t 1 t Perturbative solution of the Schrödinger equation 6p-5s Fluorescence (a.u.) φ " τ c 0ps on resonance Φ = fs Delay (ps) Observation of Coherent Transients in Rb vapor S. Zamith et al., PRL 87, (001). 8

9 CT Theory: Cornu Spiral P a e() t e (t) ² = ae() t Time Im(a (t)) e Before resonance : Slow variation Passage through resonance: (stationary phase) After resonance: Oscillations φ τ 0 t Re(a e (t)) t ln t i τ φ c ae () t e e dt Quadratic phase 9

10 Control of CT: π jump Time-frequency correspondence ω ω j φjump ( ω) ω eg t eg t j t 10

11 Control of CT: π jump This has been done experimentally in the rubidium a e (t) (a.u.) δt = φ π-jump 0.6 nm from resonance Experiment: Normal transients Shaped transients Theory: Normal transients Shaped transients time(fs) J. Degert et al., PRL 89, (00). W. Wohlleben et al., APB 4 (79), 004. In collaboration with Motzkus s group (Garching MPQ) 11

12 Reconstruction of the atomic wave function No signal before resonance : no information on the first part of the spiral ω ω eg t eg t Im(a (t)) e P e (t) Re(a e (t)) 0.3 1

13 Reconstruction of the atomic wave function Change the excitation scheme : Add a new Fourier Limited pulse! The two pulses have to be separated. CT behavior will depend on the relative phase at resonance A) E ( t) + E ( t) 1 CT () t a () t + a () t A e1 e Im(a (t)) e B) a e E ( t) + i E ( t) 1 CT () t a () t + i. a () t B e1 e deduced from CT A and CT B Re(a e (t)) The atom excited by the first pulse acts as a local oscillator

14 Prerequisite: A probe, the reference pulse f a f ( τ ) e τ E pr () t with iω fet Epr( t) e + τ t iω egt ae() t E( t ) e e a t dt ( ) dt Fluo g E () t 1 E () t If the probe is short enough, then it is like a delta function. a ( τ ) a ( τ ) e f 14

15 Experimental Set-up 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 E5 µjω Delay line () (1) φ H( ω) = 1+ exp iθ + iφ ( ω ωp) + i ( ω ωp) / τ EI ( ω) O ( ) 15

16 Experimental Results 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) CT A CT B τ (ps) By combination of the two CT 16

17 Experimental Temporal Evolution of a e (t) By combination of the two CT the evolution of the atomic wave function A. Monmayrant et al PRL 96, (006). A. Monmayrant, et al Opt. Commun. 64, (006). 17

18 Quantum state holography Principle (Leichtle, Schleich, Averbukh, Shapiro PRL 80 (1998)): Interference between a reference and an object quantum state. Several measurements at different delays provide reconstruction of the object state by numerically inverting the matrix of the cross term. Two experiments : - Vibrationnal wave packet measurement (Walmsley, Waxer J. Phys. B 31 (1998)) - Rydberg state wave packet measurement (Weinacht, Ahn, Bucksbaum, PRL 80, 5 (1998). Weinacht, Bucksbaum, Nature 397, 33 (1999). ) 18

19 Measuring the Quantum state Parameters : - number of levels -Timedelay - phase between the two states In the quantum holography method, the time resolution is used to obtain a nonsingular matrix. Walmsley, J. Phys. B 31 (1998) Atomic wave function during free evolution In our experiment we have just one levelsowekeepthetimeevolution. Weinacht, PRL 80, 5 (1998) Atomic quantum state during DRIVEN evolution 19

20 Quantum control using pathways interferences Following and controlling the spin orbit precession : Towards non Franck-Condon transition τ 0

21 Spin orbit precession and control 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> g> g> 1

22 Spin-orbit precession in Rb Rb M 0, M = 1 M L 1, M = 1 L = S = S S 61 nm L = 1, S = 1 J L S L J 5p P 3/ P 1/ 790 nm FLUO ω 5s S 1/ L= 0, S = 1 S M L 0, M = 1 = S First observed in Potassium then in Rubidium S. Zamith et al, EPJD 1, 55 (000) E. Sokell, et al, JPB 33, 005 (000)

23 Spin-orbit precession in Rb Rb M 0, M = 1 M L 1, M = 1 L = S = S S 61 nm L = 1, S = 1 J L S L J 5p 790 nm P 3/ P 1/ FLUO PM (u.a) ω 5s S 1/ L= 0, S = S M L 0, M = 1 Delay (fs) = S 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? 3

24 Spin orbit precession and control Changing the phase to have a pi-step between both levels. 3 3 Without pi-step Coupled Uncoupled fluorescence pop(a.u.) time(fs) With pi-step Coupled Uncoupled time(fs) pop (a.u.) The uncoupled state is first populated after the pulse time(fs) 4

25 Control using quantum paths interferences Quantum interferences in a two-photon transition : Towards factorisation scheme 5

26 Na ladder climbing : Excitation scheme φ < 0 5S 3, s hν 4P 3P3 / 3P 1/ 3P 3/ 3P1/ Ti:Sa Oscillator CPA 60 nm 3S 800 nm 1 khz 1mJ 130 fs PMT 605 nm, 30 fs width 5nm 10 µj NcOPA Fluorescence 330 nm SF58 rod Fixed chirp Dressed states Stretcher Variable chirp 5 S, hν hν Fluorescence observed as a function of chirp 6

27 Na (3s 3p 5s) at 605 nm Chatel et al, Phys. Rev. A 68, (003) Phys. Rev. A 70, (004) δ θ = 1 φδ Strong enhancement with small chirp 7

28 From two to multiple intermediate states W. Merkel, W. P. Schleich, I. Averbukh, B. Girard, et al, Int. J. Mod. Phys. B 0, (006). W. Merkel, I. S. Averbukh, B. Girard, G. G. Paulus and W. P. Schleich, Fortschr Phys. 54, (006). 8

29 Optical scheme in progress Several schemes in preparation. the simplest way : Sequence of equally spaced short pulses prepared with a pulse shaper Preliminary experiments to test the feasibility Other nice results obtain in NMR based also on pulses sequence NMR experiment factors numbers with Gauss sums M. Mehring, K. Muller, I. Sh. Averbukh, W. Merkel, and W. P. Schleich arxiv:quant-ph/ v1 Sep 006 Each term of the sum is realised by a RF pulse with the appropriate phase 9

30 Summary Observation of the atomic wave function during the light interaction 0.5 fluorescence Control of the spin orbit precession time(fs) Quantum paths interferences.factorisation using Gauss sums in optical schemes spectrum (a.u.) N=105 4 pulses l 30

31 Thank you for your attention The FEMTO group: Bertrand Girard (group leader, prof.) Valérie Blanchet (associate researcher) Béatrice Chatel (associate researcher) Elsa Baynard (Laser Engineer) Jean-Benoit Hamard (Post doc) Damien Bigourd (Postdoc) Antoine Monmayrant (PhD stud now post doc.) website: Funds : CNRS Univ. P. Sabatier, Région Midi-Pyrénées Fondation Del Duca, Ministère de la Recherche 31

32 THE LAB : a key point!!!! 3