Theoretical simulation of the photoassociation process for NaCs

We investigate the two-step association process of NaCs using the time-dependent wave packet method.Ground state atoms can be photoassociated to the low vibrational levels of the ground state for an NaCs molecule by the two-step association.The time-dependent Schro¨dinger equation of the association process is solved within a three-state model and the wave packet is propagated with the "split operator-Fourier transform" scheme and the rotating-wave approximation(RWA).The vibrational population distribution of the ground state can be obtained by projecting the wave packet to every vibrational level of the ground state.The results not only show that for NaCs achievement of photoassociation production is accompanied by the photodissociation of the higher vibrational molecules,but also show that the vibrational distribution in lower vibrational levels of the ground state changes with the laser parameters.     

Control of photoassociation reaction F+H→HF with ultrashort laser pulse

The laser-induced vibrational state-selectivity of product HF in photoassociation reaction H+F$\rightarrow$HF is theoretically investigated by using the time-dependent quantum wave packet method. The population transfer process from the continuum state down to the bound vibrational states can be controlled by the driving laser. The effects of laser pulse parameters and the initial momentum of the two collision atoms on the vibrational population of the product HF are discussed in detail. Photodissociation accompanied with the photoassociation process is also described.     

Theoretical study of the influence of intense femtosecond laser field on the evolution of the wave packet and the population of NaRb molecule

Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the population of ground and double-minimum electronic states of the NaRb molecule. For the different laser wavelengths, the evolution of the wave packet of 6{ }^1\Sigma ^ + state with time and internuclear distance is different, and the different laser intensity brings different influences on the population of the electronic states of the NaRb molecule. One can control the evolutions of wave packet and the population in each state by varying the laser parameters appropriately, which will be a benefit for the light manipulation of atomic and molecular processes.     

The effect of field modulation on the vibrational population of the photoassociated NaK and its dynamics

This paper presents calculation results for the photoassociation of a NaK molecule with a two-color modulated laser and gives a detailed analysis about them.For the two-step photoassociation process in intense fields,the effect of two-color modulated laser parameters,such as relative phase,envelope period,and laser intensity,on the population of the molecular electronic state can be obtained by solving the time-dependent Schrodinger equation through the quantum wave packet method.The numerical simulation shows not only that the influence of laser parameters on the vibrational distribution presents some regularity,but also that a higher population in the ground electronic state can be realized through adjusting these laser parameters.     

Photoassociation of NaRb with an asymmetric laser pulse

We investigate the photoassociation dynamics of cold NaRb molecule controlled by an asymmetric laser pulse called slowly-turned-on and rapidly-turned-off (STRT) laser pulse. This new shaped laser pulse has a remarkable merit, compared with the typical Gauss-type pulses, so that we can efficiently associate molecules with the state expected instead of going back to the continuum state. Using the three-state model, we solve the quantum mechanical equation with the “split operator-Fourier transform” method under the rotating-wave approximation (RWA) in propagation of the wave packet. By the projection of the obtained wave function onto each vibrational state, we can get the vibrational population of the ground electronic state. The results reveal that, with the STRT laser pulse, an efficient photoassociation process can be achieved and the vibrational distribution in the ground state can be controlled by the laser parameters.     

Stopping a vibrational wave packet with laser-induced dipole forces

Intense near-infrared laser pulses can generate laser-induced dipole forces that are strong enough to influence or control vibrational motion of a small molecule. Generally, the force acts to pull the molecule apart. Our numerical simulations show that, by applying the laser-induced dipole force at an appropriate time within one vibrational period, the wave packet motion of H+2 or D+2 can be accelerated or decelerated. Using the wave packet formed by the rapid ionization of H2 or D2, we also show that it is possible to move the vibrational population almost entirely to the v=0 state. Coherent cooling of the molecular vibrational motion can be achieved.     

Control of de-excitation to selected vibrational levels in the ground state of NaH molecule using two broadband ultrashort pulses

We show that the de-excitation to different vibrational levels of the ground state in NaH molecule can be controlled by using two delayed ultrashort pulses (4 fs Gaussian). A vibrational wave packet generated on the excited A¹Σ⁺ state by the first pulse is de-excited back to the ground state by a second pulse after a time delay. The cross-section for de-excitation of the wave packet to different vibrational levels of the ground electronic state can be controlled by controlling the delay time between the two pulses as well as by choosing a pulse duration much shorter than the vibrational period of the molecule, such that the de-excited wave packet remains localized in the Franck–Condon region of a particular vibrational level of the ground state. Hence, the de-excitation to a particular vibrational level can be enhanced by suppressing that in others. In spite of the large bandwidth of the pulse which includes nine vibrational levels of the upper state and five vibrational levels of the ground state, one can selectively de-excite the molecule to any one or two vibrational levels of the ground state by carefully choosing the delay time between the pulses and the pulse duration. We are designing the wave packet in the ground state by two short pulses and selectively distributing the population in one or two levels at various values of the delay time. In light molecules having small vibrational period, this selectivity in de-excitation to one or two vibrational levels in the ground state can be achieved only by using ultrashort (4 fs) pulses in the presence of which the localization of the wave packet in the Franck–Condon region of the vibrational levels are particularly possible. It has been shown that the de-excitation cross-section to a particular vibrational level oscillates with delay between the pulses which can be realized as a time-dependent quantum gate.     

Photoassociation reaction of OH molecules through reverse ladder transition

Photoassociation via reverse ladder transition controlled by two and four laser pulses is investigated using the time-dependent quantum wave packet method. The calculated results show that the amplitudes of the pulses have an enormous effect on the target population and total yield of association. For the target state with a high energy level, the population of background states can reduce the state-selectivity. Although, the total yield of association is decreased, the four pulses can induce the population transferring to low vibrational levels, and the state-selectivity of the target state is high.     

Controlling vibrational wave packet motion with intense modulated laser fields

Intense, nonresonant laser fields produce Stark shifts that strongly modify the potential energy surfaces of a molecule. A vibrational wave packet can be guided by this Stark shift if the laser field is appropriately modulated during the wave packet motion. We modulated a 70 fs laser pulse with a period on the time scale of the vibrational motion (approximately 10 fs) by mixing the signal and idler of an optical parametric amplifier. We used ionization of H2 or D2 to launch a vibrational wave packet on the ground state of H2(+) or D2(+). If the laser intensity was high as the wave packet reached its outer turning point, the Stark shift allowed the molecule to dissociate through bond softening. On the other hand, if the field was small at this critical time, little dissociation was measured. By changing the modulation period, we achieved control of the dissociation yield with a contrast of 90%.     

NaLi分子飞秒含时光电子能谱的理论研究

运用三态模型和含时波包方法,研究了NaLi分子处于强飞秒抽运-探测激光场中的波包动力学过程和时间分辨光电子能谱,并且揭示了飞秒激光脉冲参数与NaLi分子光电子能谱之间的关系.研究发现:对于不同的激光波长,波包的振动周期是不同的,而且随着抽运-探测脉冲延迟时间的不同,NaLi分子光电子能谱的谱峰高度和位置发生变化;当λ1=352 nm并且?t=400 fs时,外阱中相应的光电离信号(0.5 eV处)明显强于内阱中相应的光电离信号(1.35 eV处).计算结果表明,NaLi分子激发态41Σ+上波包动力学的一些信息能够通过其光电子能谱反映出来.这些结果可以为实验上实现分子的光控制以及量子操控过程提供一些有价值的参考信息,并为进一步的理论研究提供重要依据.     

Theoretical Study of the Influence of Femtosecond Laser Wavelength on the Evolution of a Double-Minimum Electronic Excited State Wave Packet for NaRb

Employing the two-state model and the time-dependent wave packet method, the influence of femtosecond laser wavelength on the evolution of the double-minimum electronic excited state wave packet is numerically investigated. For different laser wavelengths, evolutions of the double-minimum electronic excited state wave packet with time and internuclear distance are different. One can control the evolution of the wave packet by varying the laser wavelength appropriately, which will benefit the light manipulation of atomic and molecular processes. Furthermore, study of the dynamics of the NaRb molecule may yield clues to creating an ultracold molecule.     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释。通过分析文中的直观图像,研究了波包的动力学过程。结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的。     

Formation of ground-state vibrational wave packets in intense ultrashort laser pulses

The formation of coherent vibrational wave packets in the electronic ground state of neutral molecules in intense ultrashort laser pulses and their subsequent detection by means of recently developed pump-probe experiments are discussed. The wave packet formation is due to the pronounced dependence of the strong-field ionization rate on the internuclear distance. This leads to a deformation of the initial wave function due to an internuclear-distance dependent depletion. The phenomenon is demonstrated with a time-dependent wave packet study for molecular hydrogen.     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释.通过分析文中的直观图像,研究了波包的动力学过程.结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的.     

处理NaCs光解离问题的两种方案比较

利用含时波包动力学方法中的劈裂算符-傅里叶变换传播方案和切比雪夫多项式展开方案研究了NaCs分子的光吸收截面，并对由这两种方案计算得出的结果进行了比较.结果表明劈裂算符-傅立叶变换传播方案能更好地展示光吸收截面的中间动力学信息，而在研究初始波包与光吸收截面的关系时，由切比雪夫多项式展开方案获得的结果则更直观.利用后一方案计算的从基态 不同振动态跃迁到激发态 上相应的光吸收截面的结果表明，初始波包对光吸收截面有一定的影响，所有振动态的吸收截面均表现出谐振行为，即每一个振动态吸收截面最小值的个数恰好等于基态振动态波函数节点的个数，这种节点映射行为与映射原理相符合.     

Autler-Townes Splitting in Photoelectron Spectrum of Three-Level Li2 Molecule in Ultrashort Pulse Laser Fields

The Autler-Townes （AT） splitting in femtosecond photoelectron spectrum of three-level Li2 molecules is theoretically investigated using time-dependent quantum wave packet method. With proper femtosecond laser pulses, three peaks of the AT splitting can be observed in the photoelectron spectrum. The AT splitting stems from rapid Rabi oscillation caused by intense ultrashort laser pluses. The effects of laser parameters on the molecular ionization dynamics are also discussed.     

处理NaCs光解离问题的两种方案比较

利用含时波包动力学方法中的劈裂算符-傅里叶变换传播方案和切比雪夫多项式展开方案研究了Na Cs分子的光吸收截面,并对由这两种方案计算得出的结果进行了比较.结果表明劈裂算符-傅立叶变换传播方案能更好地展示光吸收截面的中间动力学信息,而在研究初始波包与光吸收截面的关系时,由切比雪夫多项式展开方案获得的结果则更直观.利用后一方案计算的从基态X1∑+不同振动态跃迁到激发态B1∑+上相应的光吸收截面的结果表明,初始波包对光吸收截面有一定的影响,所有振动态的吸收截面均表现出谐振行为,即每一个振动态吸收截面最小值的个数恰好等于基态振动态波函数节点的个数,这种节点映射行为与映射原理相符合.     

Non-adiabatic transition in C2H5OH+ on a light-dressed potential energy surface by ultrashort pump-and-probe laser pulses

We experimentally investigate how parameters of ultrashort laser pulses such as the pulse width and wavelength could induce changes in the dynamics of vibrational wave packets on the light-dressed-potential energy surface (LD-PES) of C₂H₅OH⁺ using a pump-and-probe pulse excitation scheme. The probability of non-adiabatic transition at 800 nm from the singly ionized ground state to the repulsive excited state leading to C–O bond breaking is enhanced when a probe laser pulse is delayed by ～180 fs. At this pulse delay, on the other hand, C–C bond breaking is significantly suppressed. Therefore, the deformation of LD-PES is considered to change the direction of the wave packet traveling originally along the C–C stretching into the direction along the C–O stretching. This non-adiabatic transition leading to the redirection of the dissociating wave packet is found to occur more efficiently at the probe laser wavelengths at 400 nm than at 800 nm. The critical pulse delay is still ～180 fs even at 400 nm.     

Wave packet dynamics in different electronic states investigated by femtosecond time-resolved four-wave-mixing spectroscopy

This paper reviews results on wave packet dynamics investigated by means of femtosecond time-resolved four-wave-mixing (FWM) spectroscopy. First, it is shown that by making use of the various degrees of freedom which are offered by this technique information about molecular dynamics on different potential-energy surfaces can be accessed and separated from each other. By varying the timing, polarization, and wavelengths of the laser pulses as well as the wavelength of the detection window for the FWM signal, different dynamics are coherently excited and probed by the nonlinear spectroscopy. As a model system we use iodine in the gas phase. These techniques are then applied to more-complex molecules (gas phase: benzene, toluene, a binary mixture of benzene and toluene; solid state: polymers of diacetylene matrix-isolated in single crystals of monomer molecules). Here, ground-state dynamics are investigated first without any involvement of electronically excited states and then in electronic resonance to an absorption transition in the investigated molecules. Signal modulations result which are due to wave packet motion as well as polarization beats between modes in different molecules. Phase and intensity changes yield information about intramolecular vibrational energy redistribution, population decay (T₁), phase relaxation (T₂), and coherence times. Received: 12 October 1999 / Published online: 13 July 2000     

利用多光子跃迁控制基态HF分子布居转移

采用波包动力学方法研究了HF分子基电子态的多光子跃迁. 激光场由两束频率比为1:2的重合红外脉冲构成. 态|0,0>作为初始态, 态|4,0>与态|4,2>分别作为目标态. 计算结果表明, 通过选取不同的共振频率, 可以控制布居跃迁至不同的目标态. 两束脉冲间的初相位差可以控制布居转移概率. 当初相位差为π/2的偶数倍时, 布居转移概率为最大值. 当初相位差为π/2的奇数倍时, 布居转移概率为最小值. 初相位差对于态|4,0>的布居影响大于态|4,2>. 关键词： 多光子跃迁 初相位 布居转移 波包