Preparation of double ten technology wave packet and excitation pulse width  

In the above description of the wave function, only the characteristics of the wide spectrum of laser pulse are used  

Investigate the effect of laser pulse width on the preparation and evolution of wave packet.  In practice, the pulse width and frequency of ultrashort pulses  

The width of spectrum affects the properties of wave packet and its evolution.  The motion of the wave packet has some characteristics of classical particle motion  

Therefore, the spatial resolution of molecular structure can be obtained by real-time observation of wave packet motion.  The points  

The order of magnitude of the typical atomic velocity is ioooom/s (=o. by fs), so for the excitation whose pulse width is LOFS  

Light has the spatial resolution of the original motion.  

It is considered that the pulsed laser acting on the ground state Xo with wood characteristic energy of E station causes the system to transition to (PO' CPS '(P2)  

The corresponding energy of the wood characteristic state is Eo, El, E., etc.  The first order micro applied to the system by the electric field  

Perturbation theory, and the transition probability from ground state to excited state can be deduced under the condition of near resonant transition.  pulse  

The laser electric field can be expressed by a Gaussian function:  

Where, A is the product factor including the pulsed laser electric field vibration I interval and the electric dipole transition moment, i.e., A=5"E, and  

+Pn1Xo> is the so-called Franck-Condon factor, which represents the initial state and the excited state in the case of electron vertical transition  

The wave function overlap integral between (see chapter 2).  The integral of (1.26) is the Fourier function of the Gaussian  

After transformation to  

Is the Bohr frequency.  In the limit condition of ultrashort pulse action ((T--) o), CLL =A< CPL, JXO >, indicating that over  

The limit of short pulse action is equivalent to franck-Condon transition.  Produced by ultrashort pulses of laser light  

The excited state can be expressed as  

Note that the wave function of the initial state can also be expressed as the basis function of the excited wood eigenstate wave function a-11:  

It can be seen that when the ultra-short pulse laser (Delta function form) is applied to the system, the potential energy surface of the upper energy level  

On the formation of the wave packet and the ground state wave function form exactly the same excited state wave function (except constant factors), however  

The wave packet is obviously not the wood eigenwave function of the excited state, but the coherent superposition state.  As the wave packet evolves,  

The phase relation of each wood characteristic state disappears with time, and the evolution process of wave packet function is expressed as 

For the above unsteady states, quantum mechanical observable physical quantities such as position and momentum also change with time.  

Take the nuclear spacing R of diatomic molecules for example, the quantum mechanical expected value of nuclear spacing is  

The starting position, for the iodine molecule, corresponds to a vibration period of about 333fs o given by the equation in FIG. 1.10  

(1.31) The expected value of calculated R (t) over time.  The dotted lines in the figure are harmonic oscillators described by classical mechanics  

Locus of nucleus spacing change: The other three curves were 1/8 (42fs), 1/2 (167fs) and 2 times of pulse width respectively  

(667FS) excitation wave packet corresponding to nuclear spacing change trajectory of pulse laser with vibration period.  As shown in Figure 1.10,  

When the pulse width is 1/8, the motion trajectory of the wave packet excited is similar to that of the classical harmonic oscillator: the pulse width is 2  

The equilibrium values of the wave packet trajectories excited by period-doubling and the distance between nuclei are close to each other and cannot be used in wave packet dynamics  

Measure, in fact, that in this case, only one wood characteristic state is excited.  

The evolution dynamics of the upper energy state wave packet generated by the 42FS pulse is very similar to the trajectory of the classical particles in the harmonic oscillator potential well.  pulse  

The upper energy wave packet generated by the pulse with a width of 66 valence does not show oscillatory motion because the wave packet formed resembles a single intrinsic energy in a potential well  

level  

When the excitation light is a long pulse (frequency resolved spectrum), there is T and Co, and the equation (  

Take the following form:  

C11 = A < CPN} x0 > s (W11 - W) (1.32)  

Where 8 (6)11-6)) is Delta function except frequency.  Is equal to (I) has a non-zero value, and is everywhere else  

Zero.  Therefore, only when the excitation frequency is exactly matched with the energy difference between the energy level N and the ground state energy level, can it be excited,  

When this condition is satisfied, only a wood characteristic energy} K is excited, while physical observable such as momentum and space valence W  

The expected value of phi doesn't change with time.  For the excitation light pulse width in the intermediate state, as long as T is small enough to ensure  

Exp b (GJ11-GJO) 2CXT2/4]>>O, then more than one wood characteristic state will be excited.  

Using Fourier transform relations that satisfy energy and time, it is obvious that the longer the excitation pulse, the higher the energy state  

The closer the wave packet of is to a single steady-state wood characteristic state: similarly, the shorter the excitation pulse, the more spectrum it covers  

The wave packet formed in the upper energy state is closer to the initial wave function of the ground state, and there is wave packet evolution dynamics.