Molecular alignment, wavepacket interference and Isotope separation

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1 Molecular alignment, wavepacket interference and Isotope separation Sharly Fleischer, Ilya Averbukh and Yehiam Prior Chemical Physics, Weizmann Institute Frisno-8, Ein Bokek, February 24, 2005

2 Kerr (1875) Rotation of the plane of polarization in passing through an optical medium subject to an applied electric field. first observed for glass; later for liquids. Can be done with gaseous sample!

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4 Motivation for seeking alignment Many physical and optical parameters are affected by the angular distribution and alignment of molecules. Refractive index Ionization or dissociation with polarized light Most spectroscopic methods in the bulk gas phase are averaged over orientations Will be useful if can be applied to macroscopic objects (nanotubes, nanowires ) Control of molecular degrees of freedom might be useful for laser pulse manipulation Interesting

5 Why femtosecond? Time scales for processes in atoms and molecules Faster than just about anything that moves Atomic and molecular processes: Spontaneous emission Vibrations Rotations Collisions in the gas phase 10 Collisions in liquids Thermal Motion 10 4 micron angstrom (per torr)

6 Why do the molecules without a permanent dipole moment align in an AC electric field? Molecules subject to an ultrashort pulse (kick) Interact with the field through the induced dipol moment: µ = α i E α α α α The potential energy gained by a molecule at angle : 1 V θ t = E t α α θ + α (, ) ( )[( )cos ( ) ] Can be approximated as: 2 V cos θ ω = αt α τ / I τ dθ dv ω ( θ) sin(2 θ) The angular velocity gained dθ θ dv

7 Short time Isotropic distribution Aligned state (Cigar) Aligned state appears short time after the pulse is applied! Perfect alignment cannot be reached with one pulse!

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9 The angular distribution affects the refractive index (n) n ε Dielectric coefficient ε = 1+ 4πχe P = i E µ χ = e P E parallel High n µ = α E Birefringence!!! α α Perpendicular Low n µ = α E

10 First observation of alignment CS 2 detector Time delay Induced birefringence n n Transmission intensity Hansen and Duguay (1969) Time delay (psec)

11 N 2 gas 200torr Time delay (fsec) Signal Intensity (a.u)

12 N 2 gas 200torr Periodic signal T= 8.3 ps Was seen also by Dantus, corkum

13 QUANTUM REVIVAL A diatomic molecule has one fundamental rotation described by a single Quantum number J. Rotational state energy : E = J( J + 1) Bc J The rotational wavefunction can be written as a superposition of spherical harmonics. () t c m Y m e + Ψ = lm, l l i l ( l 1) hbc * t

14 t=0: ψ (0) i l ( l + 1) hbc *0 m m m m cy l l e cy l l lm, lm, = = Now we seek for a time (T) such that: ψ ( T ) = ψ (0) The quantum revival time 1 ll ( + 1) hbct= 2π k 1 T = = T rev 2 Bc ( l) The wavefunction is periodic ψ () t = ψ ( t + T ) rev

15 Why a double peak???? Signal intensity 0 Time (T rev units) 1

16 How does the distribution change between cigar to disc? Once again we consider the 2D case A kick (first pulse) is applied at the molecular ensemble τ pulse 100 fs V cos 2 θ Molecules gain angular velocity And start rotating Low velocity Medium velocity High velocity polarization dv v( θ ) sin(2 θ ) dθ v max θ = π 4 Going back from T rev is the Same as rotating the molecules In the opposite direction until they align horizontally!

17 n T rev - τ n T rev + τ n T rev (Integer)

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20 0 Time (T rev units) 1 Signal intensity

21 Additional peaks between revivals ¼ ½ T rev units ¾ 1

22 1 T rev ½T rev ¼T rev 2 rotations per T rev rotation per T rev = = = alignment

23 Additional peaks between revivals ¼ ½ T rev units ¾ 1

24 Half T rev : Cigar Disc Full T rev : Disc Cigar

25 Experimental ~70 fsec pulse short compared to rotational times 1 KHz amplified system, ~1 mj per pulse total available energy Degenerate time delayed four wave mixing (insensitive to sign of polarization)

26 Degenerate Four Wave Mixing k = ( k k ) + k s a b c 1 (, ) e 2 = (3) i s ijkl a b c ik ( k+ k) ir i t P ω r χ E E E a b c e ω s Signal direction Sample alignment Input fields Signal frequency

27 DFWM TG measurements 2 beams interfere intensity grating Ea molecules at high intensity sites are kicked. Eb Ea E b Ec Es Ec Ea Time delay Ea = Eb = Ec = 800 nm Eb The alignment results in an index grating which scatters the probe pulse Ec z

28 N 2 gas 200torr full scan T rev (N 2 )= 8.30 ps

29 N 2 N 2 N 2 O 2 O 2 N 2 O 2 N O 2 2 N 2 T rev (N 2 )= 8.30 ps T rev (O 2 )= ps Was also shown by Dantus et al.

30 Isotope spectroscopic separation Cl 35-75% Cl 37-25% Cl 35 Cl 35 9/16 Cl 35 Cl 37 6/16 Cl 37 Cl 37 1/16 T rev (Cl 2 )~ 70 ps Time (ps)

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32 computer mixture of 14 N N 2 Separate measurements

33 15 N N2 real mixture Time (ps) Signal intensity (a.u)

34 Now we can analyze the mixing effect: Signal intensity (a.u) 15 N N 2 real mix 1:1 3¾F+3½S 14 N 2 - Fast 15 N 2 - Slow 7½F+7S 15F+14S 11¼F+10½S Time (ps)

35 7½F + 7S Signal intensity (a.u) Time (ps)

36 F + 14S Time (ps) Signal intensity (a.u)

37 Revival dynamics Molecular alignment during the revival cycle: n(t) / n gas (a.u) cigar disc ¼ ½ ¾ 1 1¼ 1½ 1¾ (T rev ) positive ratio Negative ratio half T rev : cigar disc disc full T rev : disc cigar cigar

38 Full revival time Disc Cigar Half revival time Cigar Disc Time

39 Separation Based on Field-free Alignment pulse isotopic mixture several revival periods Ilya Averbukh: Wavepacket Isotope Separation", (WIS) Phys. Rev. Lett. 77, 3518 (1996) (vibrational wave packets) Ionization, dissociation, deflection, Anything with linearly polarized light

40 Alignment detection techniques Alignment dependent ionization Coulomb explosion Corkum et al. Analyzed also by Time Of Flight detectors Stapelfeldt et. al.

41 Not only rotations. Vibrational Wave packet Isotope Separation (1) (2) (3) excitation pulse ionizing pulse

42 Theory Experiment: Averbukh, Stolow et al PRL 77, 3518 (1996)

43 (TD) 2 CARS at various evolution times, depicting the optimal delay T e =460fs T e =440fs T e =420fs Intensity V e =12,13 T e =400fs T e =360fs T e =340fs V g =3,4 T e =320fs T e =300fs Wavenumbers / cm -1

44 Intermediate Conclusions We have observed many tens of revivals over hundreds of psec Isotope mixtures (in Chlorine and nitrogen) separate and the different isotopes align at different times When two isotopes revive at the same time, destructive and constructive interferences are observed The best time for isotope separation is when the two isotopes are aligned perpendicular to each other. At these times, FWM destructive interference is observed Vibrational wave packets have been used previously the physics is the same

45 Advanced topics

46 Opposite rotational direction excitation

47 Selective excitation using a designed pulse series.

48 Multi pulse alignment 1 kick 1- cos 2 θ 2 kicks 3 kicks Width of the angular distribution for a model rigid rotor subject to orienting (a) and aligning (b) delta-pulses of different intensity.

49 Cl 2 Standard double peak. Multipeak signal due to centrifugal distortion. Cl E = BJ( J+ 1) + DJ ( J+ 1) +... J

50 Frequency domain approach and pulse shaping EJ = BJ( J + 1) Raman selection rule J =± 2 EJ + J 2 = B(6+ 4 J) Rotational levels of a rotor (energies are given in units of the rotational constant, B)

51 The pulse is centered at 800 nm ~ 400 THz Bandwidth ~ 20 THz Rotational resonances ~ 0.1THz Therefore Raman process! (both frequencies come from The same pulse) Ω E t e cc iω1t+ iϕ1 () = ρ ω ( +.) 1 1 ( ) iω2t+ iϕ2 E2 () t = ρ( ω2 )( e + cc EE i( ω1+ ω2) t+ i( ϕ1+ ϕ2) () = ρ ω ρ (. 1 ω ( ) ( ).) t e cc sum frequency i( ω1 ω2) t+ i( ϕ1 ϕ2) + e + difference frequency ρ c. c) ( ω ω0 ) 2 σ ( ω ) = Ne FWHM = σ 4ln(2) 2

52 All frequency pairs separated by Ω contribute to the Raman excitation at that frequency E = ω = ω ω Ω + J J+ 2 i f 1 2 ρ ( ω ω0 ) 2 σ ( ω ) = Ne iϕ( ω) iϕ( ω+ω) eff ( Ω ) = ρωρω ( ) ( +Ω ) e e dω+ cc. 2 ϕ( ω) - Phase as a function of the frequency component

53 Frequency ω0 Frequency 0 ω Transform limited pulse ϕ( ω ) = 0 Chirped pulse ϕ( ω) = K( ω ω ) 0 2

54 Chirp effect on rotational state population For a transform limited pulse, the population transfer efficiency is proportional to: σ e Ω 2 σ 2 2 For a chirped pulse, with chirp coefficient K the population transfer efficiency is proportional to: σ e 2 Ω ( + K σ ) 2 2 σ The transfer efficiency to each given state is reduced for increasing chirp. For a given chirp the transfer efficiency to higher states is reduced.

55 Cl 2 Standard double peak. Multipeak signal due to centrifugal distortion. Cl E = BJ( J+ 1) + DJ ( J+ 1) +... J

56 K F 2 1 Normalized efficiency of Raman population transfer from an initial state J for different chirped pulses. F is the FWHM of the chirped pulse relative to the transform limited pulse.

57 Professor Ilya Averbukh Sharly Fleischer, Alexander Milner, Yuri Paskover, Arik Bar haim, Kaiyin Zhang, Mark Vilensky, Valery GaArmider and Vladimir Batenkov Thank you!

58 Thank you The End