Shenzhen Double Tenth Technology on laser wave packet generation Shenzhen Double tenth technology on laser wave packet generation  

A diatomic molecule is taken as an example to show that the molecule excites from the ground state vibrational level of its electron ground state to the first excitation  

The process of states.  The molecular potential energy curve is shown in FIG. 1.11.  The potential energy curve in the figure is based on Born-  

Oppenheimer approximation, that is, the nucleus of the molecule moves much slower than the electron, so it can  

To express the potential energy of the electron as a function of the distance between nuclei.  The corresponding vibrational energy levels are also in the potential energy curve  

Is given.  The potential energy curve of an electron is represented by the harmonic oscillator potential functions V1 (R), ji (R) and ji (R).  Assume that  

The initial state X of the molecule before excitation.  The ground state vibrational energy level located in the ground state of an electron, the mode square of its wave function  

Shown in Figure 1.11.  The electron configuration of the first excited state is different from that of the ground state  

Slightly larger, this difference is typical of molecular features, indicating that changes in electron configuration affect atomic interactions  

To use.  

Figure 1.11 potential energy curves of diatomic molecules with three characteristic electronic states V1 (R), V2 (R) and fly (R)  

The resonance potential of the electronic state keeps the nucleus in a bound state and causes the emergence of vibrational energy levels in the potential well.  The ultra-fast spectral information of the system can be obtained through the following routes  

Path acquisition: the first short pulse laser excites the molecule from the ground state to the intermediate state V2 (R) and forms a wave packet on the potential energy curve of V2 (R).  

And it oscillates over time.  The motion of the wave packet is measured by a second pulsed laser into 2, which excites the intermediate state to a third electronic state  

On V3 (R) · The third electron state can be measured by laser-induced fluorescence method  

After absorbing the photon, the ground state molecule is electrically charged and carries out vertical jump between potential energy curves according to Franck-Condon principle  

Transition, that is, the change of electron state configuration is much faster than the nuclear motion, in the process of electron transition, the nuclear motion is considered to be "frozen"  

Knot "state.  If the excitation light is monochromatic, only one vibrational level is excited in the first excitation state energy curve  

To send.  If short pulse excitation is used and the laser spectrum is wide enough, more than one wood characteristic state may be activated  

At the same time, the coherent superposition state is formed, namely wave packet W (t).  The energy difference between the ground state and the first excited state in the figure (according to potential  

Calculated at the minimum of the energy curve) is 1577 OCm-1 (about 2eV).  The reduced mass and ground state are used with the first  

The interval of the vibrational energy level in the excited state (W = 1.9x1O13Hz, equivalent to the oscillation period of 333FS) is the iodine molecule  

Quite. 

FIG. 1.12 (a) shows the probability fractions of wave packets prepared at the excited state V2 (R) with different excitation pulse widths  

W (t) 12, the pulse width of gaussian linear excitation light from top to bottom is 42fS, 167fs and 667fs respectively (corresponding to  

1/8, 1/2, and 2x periods of 12 molecules).  The wave packet and ground state excited by 1/8 of the pulse width of molecular vibration period can be seen  

The wave packet}Xol9_ '} on the potential energy curve of Vi (R) is close, as expected by eq. (1.28) and eq. (1.30)  

Like that.  If the excitation pulse width is increased, the shape of the wave packet gradually deviates from}Xol9 ', but becomes more and more like a single  

Probability distributions of wave functions for wood eigenstates (see chapter 2).  In the above example, the wavelength and ground state of the excited light are selected  

The energy gap between Vi (R) and the fifth wood eigenstate (P5) of the excited state V2(R) matches, and the wave function of the wood eigenstate  

As shown in Figure 1.12 (a), the laser pulse width (667fs) used is long enough to make the equation  

(1-33), so the excited wave packet is the same as}(p512).  Unlike the 42FS pulse width, 167FS laser in  

The excited states generated by V2 (R) potential energy (the above two excited states are linear superpositions of wood eigenstates), pulse  

The laser excitation with a width of 667FS is a stable state and does not evolve with time.  If you sweep the excitation frequency  

The absorption spectrum of the molecule can be obtained.  Due to the limitation of time - energy uncertainty principle, spectral resolution  

The rate depends on the pulse width of the scanning laser.  This dependence is contained in Cil "equation ((1.27)], absorption spectrometer  

Arithmetic is simply the sum of the modulo squares of a series of numbers:  

Figure 1.12 Probability distribution of wave packet prepared at the excited state V2 (R) with different excitation pulse width!  W (t) "and its absorption spectrum  

(a) Calculation of the wave packet generated by the excitation of molecules from the ground state to the electron excited state by the pulse width of 42Fs, I6 and 66, respectively  

The wave packet and the wave function of the ground state excited by a pulsed laser with a pulse width of 42fS.  Xo12(dotted line) is very close;  (b) Apply the foregoing  

Absorption spectra measured by laser with different pulse width  

Absorption spectra determined by excitation with different pulse width are shown in Figure 1.12 (b), indicating that the shorter the laser pulse,  

The lower the spectral resolution.  The 42fS pulse width corresponds to a spectral resolution of 353cm-1 (FWHM), while the long pulse  

Light (667fs) corresponds to a resolution of 22cm-1 (F \THM), and each spectral line corresponds to some Xo'(Pi,  

The transition.  Long pulse light excitation is seen, corresponding to the frequency-resolved spectrum, since only one wood characteristic state is excited  

To view the action of Al I] YN package.  And to azazon the opposite vein.  

The pulse excites a coherent superposition of wood eigenstates on V2 (R),  

The motion can be used for dynamic measurement.  

Especially by dividing the people, but the field ten days scepter  

The wave packet is on the V2 (R) potential energy curve