Coherence and Ultrashort Pulse Laser Emission Part 4 docx

18 Laser Pulses the A 1g mode does not participate to the phase transition. These results have also allowed the evaluation of the electrons phonon coupling constant (Mansart, 2010 , b), as well as to invalidate the Bardeen-Cooper-Schrieffer theory as origin of the superconductivity in this material. We point out here that the coherent phonon spectroscopy is the key approach to determine the electron phonon coupling constant of a given phonon mode. The extension of coherent phonon studies to many other processes can be reached also by the development of tunable sources in a large spectral range. Especially, the advance in both femtosecond X-ray sources and in THz sources will allows a deeper insight in the correlations between the phonons and the physical properties in many materials. 8. Conclusions In conclusions, in this chapter we have suggested how to approach the study of coherent optical phonon, focussing our attention on the pedagogical case of bismuth. We have shown that it is possible to control selectively the atomic displacement corresponding to one phonon mode. The study of the A 1g mode in bismuth has revealed some general properties of the coherent optical phonon as function of the pump pulse excitation as well as of the initial crystal temperature. As the changes in reflectivity gives only partial information on the electrons and phonon dynamics, we have shown the use of double probe pulse to recover the transient behavior of the real and imaginary part of the dielectric function. This study has demonstrated that the excess energy brought by the pump pulse is transported away from the skin depth by fast electrons diffusion, preventing any formation of liquid phase. We have discussed some examples of coherent phonon studies in strongly correlated electrons materials and shown that investigating coherent phonon dynamics will allow to gain fundamental knowledges on the physical properties of many materials. 9. 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Birth and decay of coherent optical phonons in femtosecond-laser-excited bismuth, Physical Review B, Vol. 78, October 2008, 134302. Hase, M. et al. (2002). Dynamics of Coherent Anharmonic Phonons in Bismuth Using High Density Photoexcitation. Physical Review Letters, Vol. 88, No. 6, January 2002, 067401. Ishioka, K. et al. (2006). Temperature dependence of coherent A 1g and E g phonons of bismuth. Journal of Applied Physics, Vol. 100, November 2006, 093501. Ishioka, K. et al. (2008). Ultrafast electron-phonon decoupling in graphite. Physical Review B, Vol. 77, March 2008, 121402. Kudryashov, S. I. et al. (2007). Intraband and interband optical deformation potentials in femtosecond-laser-excited alpha-Te. Physical Review B, Vol. 75, February 2007, 085207. Landolt-B ¨ ornstein (2006). Numerical Data and Functional Relationships in Science and Technology. Edited by O. Madelung, U. R¨ossler, and M. Schulz, Landolt-B¨ornstein, New Series, Group III, Vol. 41C (Springer-Verlag, Berlin, 2006). Lannin, J. S. et al. (1975). Second order Raman scattering in the group V b semimetal Bi Sb and As. Physical Review B, Vol. 12, No. 2, July 1975, 585-593. Mansart, B. el al. (2009). Observation of a coherent optical phonon in the iron pnictide superconductor Ba (Fe 1−x Co x ) 2 As 2 (x = 0.06 and 0.08). Physical Review B, Vol. 80, (November 2009), 172504. Mansart, B. el al. (2010). Ultrafast dynamical response of strongly correlated oxides: role of coherent optical and acoustic oscillations. Journal of Modern Optics, Vol. 57, June 2010, 959-966. Mansart, B. et al. (2010). Ultrafast transient response and electron-phonon coupling in the iron-pnictide superconductor Ba (Fe 1−x Co x ) 2 As 2 . Physical Review B, Vol. 82, July 2010, 024513. Merlin, R. (1997). Generating coherent THz phonons with light pulses. Solid State Communications, Vol. 102, No. 2-3,1997, 207-220. Murray, E. D. et al. (2005). Effect of lattice anharmonicity on high-amplitude phonon dynamics in photoexcited bismuth. Physical Review B, Vol. 72, August 2005, 060301. Papalazarou, E. et al. (2008). Probing coherently excited optical phonons by extreme ultraviolet radiation with femtosecond time resolution, Applied Physics Letters, Vol. 93, July 2008, 041114. Pippard, A. B., et al. (1952). The Mean Free Path of Conduction Electrons in Bismuth. Proceedings of Royal Society A, Vol. 65, August 1952, 955-956. Rini, M. et al. (2007). Control of the electronic phase of a manganite by mode-selective vibrational excitation. Nature, Vol. 449, September 2007, 72-74. Rousse, A., et al. (2001). Non-thermal melting in semiconductors measured at femtosecond resolution. Nature, Vol. 410, March 2001, 65-68. Sciaini, G. et al. (2009). Electronic acceleration of atomic motions and disordering in bismuth. Nature, Vol. 458, March 2009, 56-59. Sokolowski-Tinten, K. et al. (2003). Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature, Vol. 422, March 2003, 287-289. 113 Coherent Optical Phonons in Bismuth Crystal 20 Laser Pulses Stevens, T. E. et al. (2002). Coherent phonon generation and the two stimulated Raman tensors. Physical Review B, Vol. 65, March 2002, 144304. Uteza, O. P. et al. (2004). Gallium transformation under femtosecond laser excitation: Phase coexistenceand incomplete melting. Physical Review B, Vol. 70, August 2004, 054108. Yan, Y X. et al. (1985). Impulsive stimulated Raman scattering: General importance in femtosecond laser pulse interaction with matter, and spectroscopy applications. Journal of Chemical Physics, Vol. 83, 1985, 5391-5399. Wu, A. Q. et al. (2007). Coupling of ultrafast laser energy to coherent phonons in bismuth. Applied Physics Letters, Vol. 90, June 2007, 251111. Zeiger, H.J. et al. (1992). Theory for displacive excitation of coherent phonons. Physical Review B, Vol. 45, January 1992, 768-778. Ziman, J. M. (2004). Electrons and Phonons, ISBN 0-19-850779-8, Oxford University Press, New York, United States of America. 114 Coherence and Ultrashort Pulse Laser Emission 6 Quantum Interference Signal from an Inhomogeneously Broadened System Excited by an Optically Phase-Controlled Laser-Pulse Pair Shin-ichiro Sato and Takayuki Kiba Division of Biotechnology and Macromolecular Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628 Japan 1. Introduction Control of quantum interference (QI) of molecular wavefunctions excited by a pair of femtosecond laser pulses that have a definite optical phase is one of the basic schemes for the control of versatile quantum systems including chemical reactions. The QI technique with the pulse pair, or the double pulse, has been applied to several atomic, molecular systems in gas phase (Scherer et al., 1991; Scherer et al., 1991; Ohmori et al., 2006) and condensed phases (Bonadeo et al., 1998; Mitsumori et al., 1998; Htoon et al., 2002; Sato et al., 2003; Fushitani et al., 2005). A basic theory of the double-pulse QI experiment for a two-level molecular system in gas phase has been given in the original paper by Scherer et al.(Scherer et al., 1991; Scherer et al., 1991). In their beautiful work, they derived the expression for the QI signal from a two-level system including a molecular vibration. However, the effect of inhomogeneous broadening, which is not very significant in the gas phase, has not been taken into account. Although the overwhelming majority of chemical reactions take place in solution, there have been very few experimental studies on the coherent reaction control of polyatomic molecules in condensed media, due to rapid decoherence of wavefunctions. Electronic dephasing times of polyatomic molecules in solution, which have been mainly measured by photon-echo measurements, are reported to be < 100 fs at room temperature(Fujiwara et al., 1985; Bardeen &Shank, 1993; Nagasawa et al., 2003). These fast quantum-phase relaxations are considered to be caused by solute-solvent interactions such as elastic collisions or inertial (librational) motions (Cho &Fleming, 1993). Thus, understanding the role for the solvent molecules in dephasing mechanism and dynamics is strongly required. Here, we (1) derive a compact and useful expression for the QI signal for an inhomogeneously broadened two-level system in condensed phases, when the system was excited by an optically phase-controlled laser-pulse pair (Sato, 2007), and (2) introduce our experimental results on the electronic decoherence moderation of perylene molecule in the γ–cyclodextrin (γ-CD) nanocavity (Kiba et al., 2008). Coherence and Ultrashort Pulse Laser Emission 116 2. Theory In general, the homogeneous broadening gives a Lorentz profile: () ()() 22 0 1 2 /2 l L l S γ ω π ωω γ = −+ . (1) On the other hand, the inhomogeneous broadening gives a Gauss profile: () () 2 2 0 / 1 g G g Se ω ωγ ω πγ −− = . (2) When both the homogeneous and inhomogeneous broadening exist, the spectral profiles are given by a convolution of ( ) L S ω with ( ) G S ω , namely, Voigt profile: () ( ) () 0VLG SdSS ω ωω ωωω ∞ −∞ ′ ′′ =+− ∫ . (3) As pointed out by Scherer et al., the QI signal is the free-induction decay and the Fourier transform of the optical spectral profile. According to the convolution theorem in the Fourier transform, the expression for the QI signal should have the form in principle: () () () () [] 22 0 cos exp exp 24 g d ld dV L G d t t QIt FTS FTS FTS t γ γ ωωωω ⎡ ⎤ ⎡⎤ ⎢ ⎥ =⎡ ⎤=⎡ ⎤⋅⎡ ⎤∝ − − ⎣⎦⎣⎦⎣⎦ ⎢⎥ ⎣ ⎦⎢ ⎥ ⎣ ⎦ , (4) where t d is a time delay between the laser-pulse pair. However, in the above discussion, the laser pulse is assumed to be impulsive, that is, the effects of a finite time width or a spectral width of the actual laser pulse is not taken into accounts. The purpose of this paper is to derive the expression for the QI signal that includes the effects of non-impulsive laser pulses. The procedure for derivation is two steps; first, we derive the expression for the homogeneously broadened two-level system, and then we obtain the expression for the inhomogeneously broadened system by integrating the result of the homogeneously broadened system weighted by the inhomogeneous spectral distribution function. 2.1 homogeneously broadened two-level system Let us consider a two-level electronic system interacting with a phase-controlled femtosecond-laser pulse pair (Figure 1). When the ground-state energy is assumed to be zero, that is the system is referenced to the molecular frame, the electronic Hamiltonian for the two-level system with the homogeneous broadening is given by ( ) ˆ /2 l Hi ee εγ =− , (5) where l γ is a homogeneous relaxation constant that stands for a radiative or a non-radiative decay constant. An electronic transition dipole operator is expressed as ( ) ˆ eg eg ge μμ =+. (6) The interaction Hamiltonian between the system and a photon field is given by Quantum Interference Signal from an Inhomogeneously Broadened System Excited by an Optically Phase-Controlled Laser-Pulse Pair 117 ( ) ˆ ˆ VEt μ =− , (7) where photoelectric field ( ) Et in the double-pulse QI experiments is given by the sum of E 1 and E 2 , each of which has a Gauss profile： ( ) 12 () ()Et E t E t=+, (8) () 22 10 () exp /2 cosEt E t t τ ⎡⎤ = −Ω ⎣⎦ , (9) () 22 20 () exp ( ) /2 cos dd Et E t t t t τ ⎡⎤ ⎡ ⎤ =−− Ω− ⎣ ⎦ ⎣⎦ , (10) where τ is a standard deviation of an each laser pulse in time domain, and related to a standard deviation Γ of the each laser pulse in frequency domain by / τ = 1Γ, and Ω is a common carrier frequency of the laser pulses. The phase shift of the photon field is defined as delay-time (Xu et al., 1996): the delay-time t d between double pulses is finely controlled with attoseconds order in the optical phase-controlled experiments. This definition is natural in the optical phase-shift experiments (Albrecht et al., 1999). To derive the expression for the QI signal, we divide the time region into the free-evolution regions and the interaction regions. (Fig. 2) Then, the time evolution of the system from the initial electronic state ( ) 0tg ψ == is given by the equation: ( ) ( ) 21 ˆˆ ˆˆ () 2 dd tUtt WUt Wg ψδδ =−− − , (11) where the time evolution operator in the absence of the photon field is defined by () ( ) ˆˆ ,exp / Utt iHt t ⎡ ⎤ ′′ =−− ⎣ ⎦ = , (12a) or by replacing as ttt ′ Δ =− () ˆˆ exp / Ut iHt ⎡ ⎤ Δ= − Δ ⎣ ⎦ = . (12b) Within the framework of the first order perturbation theory, (Louisell, 1973) the time evolution operator ( ) ˆ 1,2 j Wj= in the presence of the photon field is given by () () () () () () 1 ˆ ˆˆˆ ˆ (,)1 () 1 ˆˆˆ ˆ 21 () 1 ˆˆ 2(1 ). j j j j t jjj j j j t t jj j t j WUt t dtUtt EtUtt i UdtUttEtUtt i UF i δ δ δ δ δδ μ δμ δ + − + − ⎧ ⎫ ′′′′ =+− − − − ∫ ⎨ ⎬ ⎩⎭ ⎧⎫ ′′′′ =− − − ∫ ⎨⎬ ⎩⎭ ≡− = = = (13) The substitution of Eq. (9) into Eq. (8) yields () () () ()() 12 ˆˆ ˆˆˆ ˆˆ () dd ii tU Ut UtF UttFUt g ψδ ⎛⎞ =++− ⎜⎟ ⎝⎠ == , (14) Coherence and Ultrashort Pulse Laser Emission 118 where ˆ F is defined as an electronic transition operator, and ( ) ˆ U δ a global phase factor, which will be neglected hereafter, because it does not affects final results in the state density matrix. The projection of Eq. (10) onto the excited state e gives () () () ()() () ()() () () () () () 12 12 010 2 ˆˆˆˆˆˆ ˆˆˆ ˆˆ ˆˆ exp /2 exp /2 dd dd lld ii et eUt UtF UttFUt g i e UtF Ut t FUt g i iteF g itteF g ψ ωγ ωγ ⎛⎞ =++− ⎜⎟ ⎝⎠ =+− ⎡⎤⎡ ⎤ =−− +−−− ⎣⎦⎣ ⎦ == = = , (15) where 0 / ωε = = . The matrix element of an electronic transition operator ˆ j F is calculated as ( ) ( ) () () () () () () () () () 0 (/2) ˆˆˆ ˆ ˆˆ . j j j j j j lj j j t jjj t t eg j j j t t eg j j j t itt t eg j t eF g e dtU t t U t t g e dtUtt ge egUttgEt dt e U t t e g U t t g E t dt e E t δ δ δ δ δ δ ωγ δ δ μ μ μ μ + − + − + − ′ −− − + − ′′′ =−− ∫ ′ ′′′ =−+− ∫ ′′′ ′ =−− ∫ ′′ = ∫ (16) Using a rotating-wave approximation, the matrix element is further calculated as () ( ) () () 22 0 /2 / 2 0 22 22 00 0 1 ˆ 2 exp exp . 22 2 l xx ix jeg eg e F g E dxe e EF γτ ω μ ωτ ωτ π μτ −− −−Ω +∞ −∞ = ∫ ⎡ ⎤⎡ ⎤ −Ω −Ω ⎢ ⎥⎢ ⎥ =−≡− ⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦ (17) The substitution of Eq. (13) into Eq. (11) yields () ()() {} () ( ) 2 2 0 /2 00 , exp /2 1 exp /2 dl ld iF ett i t i t e ω ψωγωγ − −Ω Γ ⎡⎤⎡ ⎤ =−− + + ⎣⎦⎣ ⎦ = . (18) The absolute square of Eq. (14) gives the density matrix element ( ) 0 ,, , ee d tt ρω Ω for the excited state ( ) ( ) ( ) () () [] {} 22 0 0 2 /2 ()/ /2 0 2 ,, , , , 2 cos . ld ld ll ee d d d tt tt tt d tt e tt tt e F eeeee t γγ ωγ γ ρω ψ ψ ω −− −− −−ΩΓ − − Ω= =++ = (19) The first and second term give population decays of the excited state created by the first and second pulses, respectively. The third term is the interference term that is the product of coherence decays and an oscillating term. 2.2 inhomogeneously broadened system In the previous section, the inhomogeneous broadening was not taken into consideration. The effects of inhomogeneous decay can be taken into account by summing up ee ρ that Quantum Interference Signal from an Inhomogeneously Broadened System Excited by an Optically Phase-Controlled Laser-Pulse Pair 119 originates from inhomogeneously broadened spectral components (Allen &Eberly, 1975). When the inhomogeneous spectrum function is given by a Gauss function in Eq. (2), the expectation value of the excited-state density function can be written as: ( ) ( ) ( ) () () () () () {} 2 2 00 2 /2 / /2 0 2 ,, , ,, ,cos ld ld ll ee d G ee d tt tt tt G d tdSt F dS e e e e e t γγ ω γγ ρω ωωωρω ωωω ω + ∞ −∞ −− −− −−Ω Γ +∞ −− −∞ Ω= Ω ∫ =++ ∫ = (20) In the above equation, the two-center Gaussian functions can be rewritten as a one-center Gaussian function; () () () () () 2 22 2 22 0 / // 0 2 2 22 2 2 0 0 22 22 22 1 , 1 exp exp . g G g gg gg g g Se e e ωω γ ωω ωω πγ γωγ ω ω πγ γ γ γ −− −−ΩΓ −−ΩΓ = ⎡ ⎤ ⎡⎤ ⎛⎞ +Γ Γ + Ω −Ω ⎢ ⎥ ⎜⎟ ⎢⎥ =− −− ⎢ ⎥ ⎜⎟ +Γ Γ +Γ ⎢⎥ ⎝⎠ ⎣⎦ ⎢ ⎥ ⎣ ⎦ (21) By defining a reduced decay constant γ a and a reduced frequency ω a ; 22 222 1 g ag γ γγ + Γ ≡ Γ ， 22 0 22 g a g ωγ ω γ Γ +Ω ≡ +Γ (22) Eq. (21) becomes a simple form: () () () () 2 2 22 / 0 0 22 2 1 ,expexp a G gg a Se ω ωωω ωω πγ γ γ −−Ω Γ ⎡⎤⎡⎤ −Ω − ⎢⎥⎢⎥ =− − +Γ ⎢⎥⎢⎥ ⎣⎦⎣⎦ (23) By carrying out the Gauss integral and the Fourier integral of the Gaussian function, the final form of Eq. (20) becomes: () () () [] () 22 2 2 /2 0 /2 4 0 222 ,, , exp 2cos ad ld ld ll t tt tt tt a ee d ad g g F tt e e t e e e γ γγ γγ ω γ ρω ω γ γ − −− −− −− ⎧ ⎫ ⎡⎤ −Ω ⎪ ⎪ ⎢⎥ Ω= − + + ⎨ ⎬ +Γ ⎢⎥ ⎪ ⎪ ⎣⎦ ⎩⎭ = (24) In the conventional QI experiments, the QI signal is obtained as total fluorescence integrated over time. Thus, the QI signal is calculated from Eq. (24) as following: () () () [] 22 0 0 2 2 0 24 222 (, , , ,, , exp 1 2cos d ld ad ld ee d deedd t t t t a ad g g dtt QI t dt dt t t t dt F etee γ γ γ ρ ω ρω ω γ ω γ γ ∞ − − − Ω =− = = Ω ∫ ⎧ ⎫ ⎡⎤ −Ω ⎪ ⎪ ⎢⎥ =− ++ ⎨ ⎬ +Γ ⎢⎥ ⎪ ⎪ ⎣⎦ ⎩⎭ = (25) In the above derivation, the pure dephasing was not taken into account and a transverse relaxation time constant T 2 and a longitudinal relaxation constant T 1 is related by 21 11 22. l TT γ == (26) Coherence and Ultrashort Pulse Laser Emission 120 However, in general, there also exists a pure dephasing γ* that is brought about from elastic solute-solvent collisions. (Louisell, 1973) Thus, the transverse relaxation time constant should be rewritten as: * 21 2 111 * 22 l TT T γ γ =+= + The final expression for the QI signal is given by () () [] 22 12 2 2 0 4 222 exp 1 2 cos . dd ad tt t TT a dad g g F QI t e t e e γ ω γ ω γ γ −− − ⎧ ⎫ ⎡⎤ −Ω ⎪ ⎪ ⎢⎥ =− ++ ⎨ ⎬ +Γ ⎢⎥ ⎪ ⎪ ⎣⎦ ⎩⎭ = (27) By comparing the third term in Eq. (27) with Eq. (4), we obtain [] 22 2 () cos exp exp 4 dad dad tt QI t t T γ ω ⎛⎞ ⎛⎞ ∝−− ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ . (28) We notice that ω 0 and γ g in the impulsive excitation are replaced by ω a and γ a , respectively, in the non-impulsive excitation. These reduced constants, of course, approaches ω 0 and γ g in the limiting case of impulsive laser pulses; that is, when g γ Γ >> , the following relations can be deduced. 0a ω ω ≅ , a g γ γ ≅ . In the reverse limiting case of g γ >> Γ , that is, in the case of quasi continuum wave (CW) laser, we notice that a ω ≅ Ω , a γ ≅ Γ . Under this condition, if we further assume that 2 1 T >> Γ , the QI signal can be approximately written as () () [] 12 2 2 0 22 exp 1 2cos . dd tt TT dd g g F QI t e t e ω γ γ −− ⎧ ⎫ ⎡⎤ −Ω Γ ⎪ ⎪ ⎢⎥ =− ++Ω ⎨ ⎬ ⎢⎥ ⎪ ⎪ ⎣⎦ ⎩⎭ = (28) This result may be the time-domain expression for the hole-burning experiments. These two extreme situations are schematically drawn in Fig. 3. Figure 3 infers that the overlap of the laser-pulse spectrum with the absorption spectrum plays a role of the effective spectral width for the system excited by the non-impulsive laser pulse. Figure 4 shows the interference term of QI signals calculated for intermediate cases. The red sinusoidal curve of the QI signal was calculated for 1 100 g cm γ − = and 1 200 cm − Γ= , while the blue one was calculated for 1 200 g cm γ − = and 1 100 cm − Γ= . All the other parameters were common for the two calculations. The frequency of the QI signal is altered by the ratio of γ g to Γ for the cases of non-zero detuning (e.g 0 0 ω − Ω≠ ) . [...]... Three -Pulse Photon Echo Signals of Nile Blue Doped in PMMA, Journal of Physical Chemistry A, Vol.107( 14) , 243 1- 244 1 Ohmori, K., Katsuki, H., Chiba, H., Honda, M., Hagihara, Y., Fujiwara, K., Sato, Y and Ueda, K (2006) Real-Time Observation of Phase-Controlled Molecular WavePacket Interference, Physical Review Letters, Vol.96, 093002 132 Coherence and Ultrashort Pulse Laser Emission Pistolis, G and Malliaris,... lowest energy vibronic band (v’ = 0 for both ν7 and ν15 mode) resolved from the fluorescence excitation spectra 126 Coherence and Ultrashort Pulse Laser Emission T2 42 ± 5 fs 23 ± 3 fs γ-CD / water THF g 180 ± 20 cm-1 270 ± 35 cm-1 Table 2 Best-fit parameter set (homogeneous dephasing time and inhomogeneous linewidth value (FWHM)) obtained from QI signal and steady-state spectra fs pulse γ g +γl e Γ phase... (GVD) 122 Coherence and Ultrashort Pulse Laser Emission of the laser output from the interferometer was compensated by a prism pair The pulse pair from the interferometer was frequency-doubled by a BBO crystal The frequency-doubled pulse pair was reflected by a dichroic mirror (DM) and used to excite a sample molecule, while the fundamental pulse pair transmitted through the DM was used to measure laserfringe... molecule cannot produce unidirectional motion using a linearly polarized laser As shown in Fig 6, on the other hand, from symmetry considerations, the gradient has opposite signs between the (R)- and (S)- motors  142 Coherence and Ultrashort Pulse Laser Emission Fig 6 Scheme for a pump-dump laser- ignition: an (S)-motor (left) and an (R)-motor (right) The time evolution of the molecular motor is determined... panels a, b, and c in Fig 8 show the time evolution of the rotational wave packets created in S0 by applying the pump–dump laser- ignition method We omitted wave packets trapped in the S0 potential well because they do not evolve after the dump pulse is turned off Here, the parameters of pulses used were Ap = Ad = 1010 V/m, Tp = Td =100 fs, tp = 50 fs, 144 Coherence and Ultrashort Pulse Laser Emission td... that rotational directions of randomly oriented motors are opposite in (R)- and (S)-motors If molecules do not have chirality, the angular momentum becomes zero Here, an achiral motor is obtained by substituting a methyl group of the motor with a chlorine atom and its potential becomes symmetric as VR(φ) = VS(φ)  140 Coherence and Ultrashort Pulse Laser Emission Fig 4 Temporal behaviours of the instantaneous... theoretical methods for designing optimal laser pulses One is a local control method and the other is a global control method (Gordon & Fujimura, 2002) Here, “local” means that maximization of the target is carried out at each time Therefore, the 146 Coherence and Ultrashort Pulse Laser Emission Fig 9 Time-frequency-resolved spectra I(ω3,t3) of (R)-2-methyl-cyclopenta-2,4dienecarbaldehyde Reproduced with... molecule 136 Coherence and Ultrashort Pulse Laser Emission Fig 1 Upper panel: a model for unidirectional Brownian motions Lower panel: a model for unidirectional motions of a chiral molecular motor induced by a linearly polarized laser pulse Fig 2 A simplified model for chiral molecular motors, (S)- and (R)-motors, which are mirror images of each other They have two rigid groups, A and B The parameter... The excitation wavelength in this measurement was fixed at 42 2 nm to minimize the effects of change in laser pulse shape Fluorescence was measured at the 0-0 peak that was located at 44 0 nm for bulk solvent and at 45 0 nm for γ-CD, respectively The typical pulse duration was obtained to be 47 fs fwhm at the sample point, assuming a Gaussian pulse All the spectral measurements were performed using a... were: γ g = 100 cm−1 and Γ = 200 cm−1 (for the red curve), γ g = 200 cm−1 and Γ = 100 cm−1 (for the blue curve) The common parameters for the two curves were ω0 = 25000 cm−1 , Ω = 22000 cm−1 , γ l = 100cm−1 , and γ * = 25 cm−1 128 Coherence and Ultrashort Pulse Laser Emission Sample Delay stage Lock-in LCM PD ND Chopper MC λ/2 BS λ/2 ND MC PMT Lock-in 2ω Polarizer ω ω SHG Ti:sapphire Laser DM Spectrometer . Vol. 45 , January 1992, 768-778. Ziman, J. M. (20 04) . Electrons and Phonons, ISBN 0-19-850779-8, Oxford University Press, New York, United States of America. 1 14 Coherence and Ultrashort Pulse Laser. 2002, 144 3 04. Uteza, O. P. et al. (20 04) . Gallium transformation under femtosecond laser excitation: Phase coexistenceand incomplete melting. Physical Review B, Vol. 70, August 20 04, 0 541 08. Yan,. (2001). Dynamics and coherent control of high amplitude optical phonons in bismuth. Physical Review B, Vol. 64, August 2001, 092301. 112 Coherence and Ultrashort Pulse Laser Emission Coherent