1、1,FIG. 3. Schematic diagram of the energy levels of the由铯原子内的双光子跃迁图示。6S1/2-8S1/2 two-photon transition in atomic Cs. The two-photon双光子跃迁能量达到了411纳米。transition energy v0 corresponds to 411 nm. The excited atoms激发态原子自发的衰减到7P的低水平，spontaneously decay to the ground level through the 7P level, so以至于双光子跃迁通过
2、荧光信号能够被直接的观测到that the two-photon transitions can be directly observed through themeasurement of the fluorescence signal vfl at ;460 nm. The 6S1/2and the 8S1/2 levels are split into two hyperfine states, but only two这两个水平分裂成两种超精细状态，但是只有两种跃迁是可以transitions are allowed, one from each of the sublevels of
3、 the的，一种是从基态各低能级达到激发态。在实验中，ground state to the corresponding excited state. In the experiment所有的信号都达不到几皮秒，all signals were shorter than a few picoseconds, too short to observe如此之短以至于不能观察到这两个跃迁到次能级的任何动态变any dynamics between the two transitions corresponding to the two化，sublevels. We therefore conside
4、red the ground and excited states as 我们由此认为这两个状态是同一个状态single states.2,where g(v) is the line-shape function. Assuming a wide line这里是线性函数，limit, we have我们假设一个宽的极限，我们有如下公式，which can be shown to yield而它可以得到如下的结果Similarly, in this case for N-photon transitions, 同理，在有N个光子跃迁的时候，我们便得到了这个结果， IN(t)dt. These
5、well-known results simply reflect the那些熟悉的结果很容易折射出这个事实，那就是fact that here TPA and multiphoton transitions depend on theTPA（？）和多光子跃迁决定于激发脉冲，而与相位无关intensity of the exciting pulses and not on their phase as in Eq.(6).3, III. EXPERIMENTAL RESULTS实验结果To demonstrate coherent control with this approach, we为
6、了论证，performed experiments with the 6S1/2-8S1/2 two-photon transitions我们用铯原子的，做双光子跃迁实验of atomic cesium, at a wavelength of 411 nm, induced在飞秒脉冲中心波长为822纳米的情况下，产生了波长为411纳by femtosecond pulses centered at 822 nm, as shown schematically米光谱，正如预测，图示的一样。in Fig. 3. Each of the excited atoms decays spontaneou
7、sly每个处于激发态的原子通过7P态自发的衰减到基态，to the ground level through the 7P level, so that以至于双光子跃迁能够通过双光子荧光直接the two-photon transition can be directly monitored through监测到。the measurement of the two-photon fluorescence TPF! signalat 460 nm.The experimental system, shown in Fig. 4, was similar to在Fig,4 中所用的试验系统和Re
8、f.16. 中使用的相似that described in Ref.16. The setup was composed of a装置由可编程的脉冲整形仪器，一个铯原子气态单元，programmable 4-f pulse shaper 14, a Cs gas cell, a photomultiplier,一个光电倍增光，和一个同步的放大器。and a lock-in amplifier. A mode-locked Ti:sapphire一台钛蓝宝石激光器为铯双光子跃迁产生了31飞秒谱宽laser produced 31 fs FWHM transform-limited sech2的脉
9、冲，经过整形仪器后测量，中心波长为822纳米。intensity pulses, centered at 822 nm, measured at the output可编程的脉冲整形仪器有一对1200线每毫米的光栅of the pulse shaper. The programmable 4-f pulse shaper wascomposed of a pair of diffraction gratings with 1200和一对焦距为100毫米的消色透镜组成。lines/mm and a pair of achromat lenses with a 100 mm focal第一快透镜和
10、光栅在傅里叶平面上输入复杂光谱length. The first lens and grating spatially map the complex脉冲，那里有立体的过滤装置spectrum of the input pulse at the Fourier plane, where aspatial filter was inserted. The second lens and grating reassemble第二块透镜和光栅组成一定结构去产生对时间进行修改the spectral components to form a modified timeshaped后的脉冲，pulse.
11、 A programmable one-dimensional liquidcrystal一个可编程的液晶体空间光调节器SLMspatial light modulator SLM! array SLM-256, CRI!,由电脑控制的128个独立结构组成，composed of computer-controlled 128 discrete elements, was被放在整形器的傅里叶平面上，placed at the Fourier plane of the shaper, and was used as a用来只让特定相位的脉冲透过。dynamic filter for spectr
12、al phase manipulation of the pulses.每单元的宽度是97毫米而且各单元之间的间隔是3毫米。The width of each pixel is 97 mm and the interpixel gap is整形后的脉冲用焦距为50的透镜聚焦在气态铯原子团3 mm. The shaped output pulses were focused using a lens上，而且在460纳米的荧光信号被光电倍增仪器with a 50 mm focal length into the Cs gas cell, and the和放大器所检测到。fluorescence s
13、ignal at ;460 nm was detected by the photomultiplier1P28, Hamamatsu! and a lock-in amplifier.FIG. 4. Experimental arrangement for two-photon transitions inCs gas. The programmable 4-f pulse shaper was composed of a pair可编程脉冲整形装置由一对每毫米1200条线的衍射光栅，和一of diffraction gratings with 1200 lines/mm, and a pa
14、ir of achromat对焦距是100毫米的消色透镜组成lenses with a 100-mm focal length. A programmable onedimensional一个可编程的，由电脑控制各部分的SLM（空间光调节器）被SLM with 128 computer controlled discrete elements放在整形仪器的傅里叶变换平面，was placed at the Fourier plane of the shaper, and was used as a它用作动态的控制只透过特定的脉冲。dynamic filter for spectral phase manipulation of the pulses. The经过整形后的脉冲通过焦距长度为50毫米的透镜后shaped output pulses were focused using a lens with a 50 mm focal聚焦于气态铯原子团上。length into the Cs gas cell. The fluorescence signal at ;460 nm波长为460纳米的荧光信号被光电接收器和放大器所检测到。was detected by the photomultiplier and the lock-in amplifier.4,
