Ultrafast Pulse Shaping Approaches to Coherent Control

1. Ultrafast Pulse Shaping Approaches to Coherent Control Debabrata Goswami Tata Institute of Fundamental Research Mumbai, India Funding: TIFR & Min. Info. Tech.

2. An Ultrafast Laser Pulse • Coherent superposition of many monochromatic light waves within a range of frequencies that is inversely proportional to the duration of the pulse Short temporal duration of the ultrafast pulses results in a very broad spectrum quite unlike the notion of monochromatic wavelength property of CW lasers. e.g. Commercially available Ti:Sapphire Laser at 800nm 10 fs (FWHM) 94 nm wavelength time CW Laser Delta function ~0.1 nm wavelength time

3. Pulse Shaping • Control over the amplitude, phase, frequency and/or inter-pulse separation • Complex pulse shaping aims to control one or more of the above-mentioned parameters in a programmable manner, according to user specification. Can be represented by Linear Filtering Scheme: Time Domain: • Eout(t) = Ein(t)g (t)  => convolution • Hard Job—Timescales not quite accessible with conventional electronics (typically ns)! Frequency Domain • Eout() = Ein ()G ()

4. Possibilities… Typical Lasers Our Work • Terabit/sec data transmission capabilities for optical communication. • Coherent Control of atoms and molecules. • Exploring capabilities of experimentally realizing quantum computation. • Control of biomolecules in both center-of-mass and internal degrees of freedom motion. • Bring about analogs of pulsed NMR…

5. Time Pulse Shaping WDM: Why it’s better • Switching Window T (Switch Speed), DTR=1/ T • Pulse Width T0 (Bandwidth Available), DTR~1/ T0 Time

6. Ultrahigh Ratio Data Compression 4 ms 20 ps • Ultra-high Ratio (~105) Data Compression • High fidelity, good SNR • All-one Case Return to Zero format Amplitude Shift Keying

8. Transform limited laser pulse Frequency sweep generated by an optical fiber ~15 ps 20 ps Frequency sweep generated by an grating or prism pair

9. Effect of Simple Shaped Pulses: Frequency Chirped Pulses (a) Theoretical (b) Experimental (a) Comparison of the probability of excitation as a function of applied Rabi frequency, for 2 ps transform-limited (Gaussian) pulses. indicated by crosses (+), and bandwidth equivalent 20 ps frequency-swept (Gaussian) pulses, indicated by circles (0). (b)Fluorescence excitation curves for the pentacene/p-terphenyl mixed crystal system excited by 3 ps near transform-limited laser pulses, indicated by circles (0), and by bandwidth equivalent 20 ps laser pulses chirped by the diffraction grating method, indicated by crosses (+). Each point is the average of ten laser shots. JCP, 101,6439 (1994)

10. z y   x  =(2+2)1/2 Two Level Feynmann’s pseudo-Polarization Vector D = w~w0 E=e.ei(wt+f) hw0 m. e W= h

12. Interferometer Pulse Shaping Femtosecond Reaction Dynamics, p. 291 (D.A. Wiersma, editor, North-Holland, Amsterdam, 1994); Ultrafast Phenomena, IX.

13. Acousto-Optic Modulated Pulse Shaping Technology Acousto-optic laser pulse shaping Femtosecond Reaction Dynamics, p. 291 (D.A. Wiersma, editor, North-Holland, Amsterdam, 1994); Opt. Lett., 19, 737 (1994).

15. Ultrashort Pulse Version Grating 1 Concave Mirror 1 Mask Concave Mirror 2 Grating 2

16. Deformable Mirror Pulse Shaper Deformable Mirror

18. 1 experiment theory 0.8 0.6 Intensity (arb) 0.4 0.2 0 -5 -4 -3 -2 -1 0 1 2 Time (ps) The Pulse-Shaper Examples of Phase & Amplitude Modulation Intensity (arb) wavelength (nm)

20. Calibration Application:

21. Schematic of the Feedback Loop Initialize the system RF Pulse Shaper Computer Take spectrum from OSA; normalize it. Update the RF waveform Compare with normalized target; Within set limit? Optical Spectrum Analyzer (OSA) Ultrafast Laser Pulse Shaper END

22. Feedback Control of AOM Pulse Shaping

23. Examples: Amplitude Modulation • Real time programmable • Well confined temporal shape for TDM switching

24. Future Technology: Terabit per second communications system Acousto-optic laser pulse shaping

25. Phase Modulation: Tunable Delay Line • M(tRF)=ewRF*tRF • M(wlaser)=ewRF* a /vac (wlaser-w0,laser) • Eout(wlaser)=Ein(wlaser)* ewRF* a/vac (wlaser-w0,laser) • Eout(tlaser)=FT {Ein(wlaser)* ewRF* a/vac (wlaser-w0,laser)} =Ein(t+t) • t=a/vac DwRF

26. Rapid Tunable Delay Line 110 MHz 115 MHz 120 MHz 125 MHz 130 MHz 7 135 MHz 140 MHz 145 MHz 6 150 MHz (Start) 150 MHz (End) 155 MHz 160 MHz 5 165 MHz 170 MHz 175 MHz Crosscorrelation sig. (arb. units) 4 180 MHz 185 MHz 190 MHz 3 195 MHz 2 1 0 10 12 14 16 18 20 22 24 26 28 2 4 0 6 8 Time (ps)

27. Detection Scheme: Spectrally and Temporally Resolved Upconversion Technique (STRUT)

28. 2500 Retrieved Phase 40 Linear Sweep 2000 Retrieved Spectrum 20 E() = ei2 1500 Measured Spectrum Intensity (arb) 0 Delay (ps) 1000 -20 500 -40 0 780 790 800 810 820 830 392 396 400 404 408 1 experiment theory 6 0.8 Cubic Phase 4 E() = ei3 0.6 2 Delay (ps) Intensity (arb) 0 0.4 -2 0.2 -4 -6 0 -5 -4 -3 -2 -1 0 1 2 397 398 399 400 402 403 401 Time (ps) STRUT-Wavelength (nm) Examples of STRUT-trace Direct measurement of phase and amplitude-profile of shaped pulses 1 Phase (rad) 0.5 0 Wavelength (nm) STRUT-Wavelength (nm)

29. 6 4 2 Delay (ps) 0 -2 -4 -6 397 398 399 400 402 403 401 Wavelength (nm) Linear Sweep: eiw2t Cubic Phase: eiw3t Cubic Phase: e-iw3t

30. 5 4 3 2 1 0 ' (ps), intensity (arb) -1 -2 -3 Intensity -4 ’ -5 788 793 798 803 wavelength (nm) 1.0 Population 0.5 0 15 15 10 5 10 0 -5 5 Detuning (cm-1) Rabi Frequency (cm-1) -10 -15 0 Hyperbolic Secant Pulse Time-Domain Spectrum 1.0 Real Imaginary 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 Time (ps) • Population inversion through adiabatic rapid passage. • Robust because of rectangular inversion-profile. • Little Reshaping when propagating through dense media Inversion Profile

31. A: Femtosecond Gaussian pulse (plotted as a function of time in the box below A) B: Grating that spectrally spreads the pulse. C: Acousto-optic modulatoris in the center of the system D: The RF-wave propagates through the AOM, creates a spatial mask inside the crystal and shapes the optical pulse. E: The undiffracted beam passes out of the system F: Grating that recombines the spectrum G: Pulse picker picks the shaped output pulse In this schematic, the input optical pulse is modeled as consisting of four different wavelengths, blue, yellow, orange, and red, which would represent a 4-bit system. In principle, the AOM is capable of shaping 1000 bits. The white parts of the diffracted spectrum are left undiffracted by the AOM. The output (G and the box below the G) shows the shaped output pulse as a function of wavelength. As the rf wave propagates, different shapes are created. The pulse picker G picks the pulse at the correct time out of the pulse train. Here the pulse picker is shown separately selecting a particular pulse H, but in the experiment, the pulse picker is located inside the regenerative amplifier I.

32. Complex Shaped Pulse Generation: Secant Hyperbolic Pulse

33. Advantage of STRUT: Analysis of Complex Pulse Shape

34. Quantum Example: Effect of Ultrashort Pulses on Rubidium Atoms -6 -4 -2 0 2 4 Rubidium atoms when excited with femtosecond pulses show hitherto unknown strong stimulated emission that lasts only a few picoseconds as seen from the STRUTs’ below. We believe pulse propagating effects are manifested in terms of chirp generation of the pump pulse that is showing adiabatic sweeping effects. Rubidium atoms in particular spin-polarized state are used for Magnetic Imaging Studies and are useful in medical diagnostic applications. Delay (ps) -8 405 -4 385 400 405 380 395 Time (ps) 400 Wavelength (nm) 4 Wavelength 385 8 380

35. Transform-Limited Pulse vs. Sech Pulse -8 -4 405 4 Time (ps) 400 8 385 380 Wavelength (nm) -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Delay (ps) 396 397 398 399 400 396 397 398 399 400 396 397 398 399 400 STRUT Wavelength (nm) Rubidium atoms when excited with femtosecond pulses show hitherto unknown strong stimulated emission that lasts only a few picoseconds as seen from the STRUTs’ below. Pulse propagating effects are manifested in terms of chirp generation of the pump pulse that is showing adiabatic sweeping effects. Rubidium atoms in particular spin-polarized state are used for Magnetic Imaging Studies and are useful in medical diagnostic applications.

36. Self-Induced Transparency at Resonance

37. Shaped Pulse A B AB “Inverting” Pulse 1 1 0 1 0 1 “Dark” Pulse 0 1 1 0 0 0 Ensemble CNOT Gate A quantum mechanical ensemble B that can either be in the ground (state 0) or excited (state 1) interacts with the control pulse A, which provides robust chirped pulse inversion (condition 1) and the self-induced transparency or dark pulse (condition 0)

38. What is Coherent Control? • Study of possible control on the future of any coherent light-matter interaction is Coherent Control. • Since the original inception of control over quantum phenomenon as a goal, the potential applications have broadened out beyond chemical reactivity • Coherent control could lead to logic gates for Quantum Computer

39. Laser Selective Chemistry: the "Holy Grail" Example: excite a high overtone of the C-H stretch in toluene H H H H H H Chemical Laser H OH H OH OH Reaction H H H H H H In practice, this almost never works. The overtones of the normal modes carry the oscillator strength, but they are not eigenstates. Usually many different modes end up excited; this is called "intramolecular vibrational redistribution" (IVR).

40. Bond Selective Chemistry: Choice of Molecules H D O O Laser Laser D H HOD + H  H2 + OD HOD + H  HD + OH Chemical reactions break bonds between atoms in a molecule. Before the bond breaks, it must be elongated first. If the molecule begins to vibrate along the "reaction coordinate" before the reaction starts, the bond will be weakened and hence facilitate the reaction. In 1995, Prof. F. Fleming Crim took the partially deuterated water molecule, HOD, as an example to show the first ever example of bond-selected chemistry. HOD can react with H atoms in two ways. They demonstrated that it is possible to control the path the reaction takes by judiciously choosing the initial vibrational state of the HOD with laser excitation. States that are predominantly OH-stretching produce H2 + OD, while OD-stretching states react to produce HD + OH. In essence, the initially excited bond is the one that breaks in the reaction.

41. Fe+ FeCO+ Fe(CO)2+ Fe(CO)3+ Fe(CO)4+ Fe(CO)6+ (b) (a) (a) Schematic experimental setup. Femtosecond laser pulses are modified in a computer controlled pulse shaper. Ionic fragments from molecular photodissociation are recorded with a reflecton TOF mass spectrometer. This signal is used directly as feedback in the controlling evolutionary computer algorithm to optimize the branching ratios of photochemical reactions. (b) Relative Fe(CO)5 photodissociation product yields. The yields are derived from the relative peak heights of the mass spectra. The ratio of Fe(CO)5+/Fe+ is maximized (solid blocks) as well as minimized (open blocks) by the optimization algorithm, yielding significantly different abundances of Fe+ and Fe(CO)5+ in the two cases. The peak heights of all other masses [Fe(CO)+ up to Fe(CO)4+] have not been included in the optimization procedure. Gerber et.al. SCIENCE 282, 1919 OCTOBER 1998

42. Molecular Decoherence: IVR Ever since the early days of quantum mechanics, there has been an implicit dream of controlling atomic and molecular dynamics. It was pursued with even greater vigor with the discovery of the first laser. However, such quantum mechanical "control" has remained as an evading issuea dream. The major reason for its elusive nature is the energy and coherence randomization due to the typically strong coupling amongst the molecular degrees of freedom, such as intramolecular vibrational relaxation (IVR). Normal Mode Picture Eigenstate Picture Couplings • • • Normal Mode Doorway Overtone: states "Bright State" Other rovibrational Oscillator strength levels: "Dark States" from normal mode is distributed among many eigenstates Ground state Ground state

43. |5> |2> |4> |3> 1420cm-1 excitation |1> Manifestation of IVR in Anthracene Effect of Gaussian Pulse Experimental Results: Felkar & Zewail, 82, 2961-3010 (1985)

44. Model Calculations with Shaped Pulses Anthracene |5> |2> |4> |3> 1420cm-1 excitation |1> Adiabatic Passage With Intense Pulses Adiabatic Half Passage Resonance QC Theory: Goswami, (PRL, 88, 177901-1,2002) Goswami & Warren, JCP(92), PRA(94))

45. Generating complex waveforms: Applications Amplification Applications (e.g. Quantum Control)

46. Conclusions • Programmable Ultrafast Pulse Shaping approaches involve linear filtering either in the time-domain or Fourier domain modulation techniques. • Choosing a combination of two specific shaped pulses: one that always generates inversion and the other that always generates self-induced transparency allows us to construct a scalable CNOT gate. • Single or multi-photon intramolecular dephasing can be kept to a minimum for the duration of “locking” period under adiabatic conditions. The effect occurs under adiabatic condition & is insensitive to inhomogeneities in Rabi frequency.