Harmonic Enhancement Mechanism of a Superposition State Atom Irradiated by Short Pulses

We investigate the high-order harmonic generation （HHG） of a model atom whose initial state is prepared in a superposition of its ground state and an excited state irradiated by different duration laser pulses. Compared to the HHG generated from an atom whose initial state is in its ground state, its conversion efficiency obtains some enhancement. The enhancement originates from the higher ionization rate （rather than the ionization yield） of the atom with superposition initial state.     

啁啾脉冲辐照下始于原子迭加态的高次谐波发射

本文研究了一维初态为基态与第一激发态等权线性迭加态的模型原子在不同正啁啾激光脉冲辐照下的高次谐波发射谱。数值结果表明,谐波谱平台的截止位置随啁啾系数的增大大幅度的展宽。采用SMT(simple man’s theory)仔细分析了各啁啾激光场辐照下电子的动力学行为,阐明了谐波谱平台随啁啾系数增大而展宽的机制。     

High-order harmonic generation spectrum of an excited one-dimensional Coulomb atom in an intense laser field

Response of the wave packet of a one-dimensional Coulomb atom to an intense laser field is calculated using the symmetrized split operator fast Fourier method. The high-order harmonic generation (HHG) of the initial state separately being the ground and excited states is presented. When the hardness parameter \alpha in the soft Coulomb potential V(x)=-1/\sqrt{x^2+\alpha} is chosen to be small enough, the so-called hard Coulomb potential V(x)=-1/|x| can be obtained. It is well known that the hard one-dimensional Coulomb atom has an unstable ground state with an energy eigenvalue of $\sim0.5$ and it has no states corresponding to physical states in the true atoms, and has the first and second excited states being degenerate. The parity effects on the HHG can be seen from the first and second excited states of the hard one-dimensional Coulomb atom. The HHG spectra of the excited states from both the soft and hard Coulomb atom models are shown to have more complex structures and to be much stronger than the corresponding HHG spectrum of the ground state of the soft Coulomb model with $\alpha=2$ in the same laser field. Laser-induced non-resonant one-photon emission is also observed.     

相干叠加态高次谐波发射的时间行为分析

本文研究了一维模型分子离子(初态为基态和一个激发束缚态叠加的相干态)在超强超短激光脉冲作用下的谐波发射谱.我们发现在高次谐波谱平台区域出现了周期性的结构变化.我们利用小波变换对谐波谱进行了暂态时间频率分析,结果表明该谐波结构产生的原因是由电离电子返回母离子时与不同束缚态复合而产生的谐波光脉冲之间相干叠加.同时采用半经典计算,对所得到的计算结果进行了分析,验证了我们的结论.     

Theoretical Study of High-Order Harmonic Generation From a Coherent Superposition State in a Chirp-Free Pulse Combined with a Chirped Control Pulse

In this paper, we theoretically investigate high-order harmonic generation (HHG) from a helium atom prepared in a coherent superposition state in a two-color laser field. Numerical results show that the emission efficiency of the harmonic spectrum in a coherent superposition state is enhanced by approximately eight orders of magnitude compared with the case of the ground state. In addition, the effect of the initial population of the excited state on the HHG is presented to reveal the physical origin of the enhancement of HHG. By adjusting the laser parameters of the driving pulse, such as the chirping parameter, the relative phase, and the intensity of the driving pulse, an ultrabroad continuum with a width of 275 eV can be observed. Finally, an isolated 12-as pulse is generated after phase compensation.     

Generation of intense water window X-ray pulses by superposition of an initial state of the helium atom driven by a three-color field

We theoretically study the generation of high-order harmonics and attosecond pulses from the superposition of an initial state in helium atom driven by a three-color laser field. It is shown that when the initial state is chosen to be a single electronic state, due to the rapid depletion of the ground state, the efficiency of the spectral continuum will be decreased as the initial state increases. When the initial state is chosen to be the coherent superposition of the ground state and an arbitrary excited state, the efficiency of the spectral continuum can be enhanced compared to that from the single initial state. Further, with the optimization of the three-color laser beam, not only can the harmonic cutoff be extended to the water window X-ray region but also the spectral continuum is contributed by the single harmonic emission peak with the dominant short quantum path. Consequently, two combinations of the laser parameters can be found to generate the water window spectral continuum. By properly superposing some harmonics on the spectral continuum, a number of intense water window pulses with the duration of sub-35 as can be produced.     

迭加态原子高次谐波发射的选频提高

本文研究了由体系的基态和较高激发态迭加形成的原子在强激光场作用下的高次谐波发射.观察电离波包的演化过程,阐明了谐波发射效率提高的原因.在给定入射激光条件下,通过选择不同的激发态,可以实现对谐波发射的控制.     

Strengthened Hyper-Raman Lines with the Coherent Superposition State

High-order harmonic generations from a one-dimensional Coulomb potential atom are calculated with the initial state prepared as a coherent superposition between its ground and first excited states. When the energy difference of the two states is small, we can choose proper laser pulse such that the first excited state can be excited only to other bound states instead of being ionized. We show that only the hyper-Raman lines are observable instead of the harmonics. The energy difference of the ground and the first excited state can be deduced from the highest peak of the hyper-Raman lines. We further show that the similar results can be obtained by using a combination of two laser pulses with different frequencies interacting with the atom initially at the ground state.     

High-intensity molecular harmonic generation without ionization

We theoretically investigate high-order harmonic generation from H + 2 in an infrared laser field.Our numerical simulations show that a highly efficient plateau structure exists in the molecular harmonic spectrum.Under the action of the infrared laser pulse,the bound electronic wave packet in a potential well has enough time to tunnel through the effective potential barrier,which is formed by the molecular potential and the infrared laser field,and then recombine with the neighboring nucleus emitting a harmonic photon.During the entire dynamic process,because the wave packet is mainly located in the effective potential,the diffusion effect is of no significance,and thus a highly efficient harmonic plateau can be achieved.Specifically,the cut-off frequency of the plateau is linearly scaled with the peak amplitude of the infrared laser electric field,which may open another route to examine the internuclear distance of the molecule.Furthermore,one may detect the molecular bond lengths using the harmonic plateau.     

High-order harmonic transient grating spectroscopy in a molecular jet

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.     

Isolated ultrashort attosecond pulse generation from a coherent superposition state in a few-cycle chirped laser pulse

We theoretically demonstrate an efficient method for producing an isolated ultrashort attosecond pulse by high-order harmonic generation in an intense few-cycle chirped laser pulse. Our simulation calculations show that the harmonic spectrum reveals an ultrabroad extreme ultraviolet supercontinuum when the initial state is prepared in a coherent superposition of the ground and first excited states. It is also shown that the method can enhance the short quantum path and eliminate the long one, and then an isolated 23-attosecond pulse is produced. By properly adjusting the chirp parameter, a clean single attosecond pulse as short as 11 attoseconds is directly obtained.     

利用三束中红外空间非均匀激光场产生超长平台区

数值研究了氦离子在三束中红外激光场下发射高次谐波以及阿秒脉冲的特点. 计算结果表明, 通过适当调节三束激光场的延迟时间和相位角, 不仅谐波发射的截止能量得到了延伸, 而且单一的量子路径也被选择出来对谐波发射起作用, 随后通过适当的引入空间非均匀参数,谐波截止能量得到了进一步扩展,形成了一个超长的1773eV的平台区. 并且我们发现当选择氦离子的基态和第一激发态为叠加初始态时,谐波的强度被增强了4-6个数量级. 最后, 通过叠加谐波谱上的谐波, 可获得一系列脉宽为32as左右的阿秒X射线光源. 并且这些光源的强度比氦离子基态作为初始态时增强了4-6个数量级.     

利用三束中红外空间非均匀激光场产生超长平台区

数值研究了氦离子在三束中红外激光场下发射高次谐波以及阿秒脉冲的特点. 计算结果表明, 通过适当调节三束激光场的延迟时间和相位角, 不仅谐波发射的截止能量得到了延伸, 而且单一的量子路径也被选择出来对谐波发射起作用, 随后通过适当的引入空间非均匀参数,谐波截止能量得到了进一步扩展,形成了一个超长的1773eV的平台区. 并且我们发现当选择氦离子的基态和第一激发态为叠加初始态时,谐波的强度被增强了4-6个数量级. 最后, 通过叠加谐波谱上的谐波, 可获得一系列脉宽为32as左右的阿秒X射线光源. 并且这些光源的强度比氦离子基态作为初始态时增强了4-6个数量级.     

Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave

We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave,and particularly calculate the atomic inversion of the wave packet.A general method of calculation is presented.The results are interesting.For example,if the wave packet is very narrow or /and the interaction is very strong,no matter the atom is initially in its ground state or excited state,the atomic inversion approaches zero as time approaches infinity.If the atom is initially in its ground state and excited state with the probability 1/2 respectively,and if the momentum density is an even function,then the atomic inversion equals zero at any time.     

High-order harmonic generation in nitrogen molecules with subpicosecond visible dye-laser pulses

An experimental study of high-order harmonic generation in nitrogen molecules (N₂) has been made using intense visible (616 nm) dye-laser pulses, where the harmonic radiation up to the 21st order is observed. The harmonic distribution represents a plateau that is preceded by an intensity minimum at the 7th order. The harmonic generation characteristics were atomic-like. It has been found that there are some similarities in the high-order harmonic generation characteristics for N₂ and Ar, including the highest-order harmonics, harmonic distributions, and the influence of the multiphoton ionization on the high-order harmonic generation. These similarities are reasonably attributed to the energetic correspondence of excited levels and ionization potentials. It is pointed out that the ac Stark shift of excited levels and ionization potentials plays an important role also in the high-order harmonic generation in N₂.     

Resonance-Radiation Force Exerted by a Circularly Polarized Light on an Atomic Wave Packet

We study the behaviour of an atomic wave packet in a circularly polarized light, and especially give the calculation of the radiative force exerted by the circularly polarized light on the atomic wave packet under the resonance condition. A general method of the calculation is presented and the result is interesting. For example, under the condition that the wave packet is very narrow or/and the interaction is very strong, no matter whether the atom is initially in its ground state or excited state, as time approaches to infinity, the resonance-radiation force exerted by the light on the atom approaches to zero. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is a even function, then the resonance-radiation force exerted by the light on the atom is equal to zero.     

Decoding the electron dynamics in high-order harmonic generation from asymmetric molecular ions in elliptically polarized laser fields

The high-order harmonic generation from an asymmetric molecular ion is theoretically investigated based on the Born-Oppenheimer model with two-dimensional electron dynamics. It is shown that the harmonic intensity changes periodically in elliptically polarized laser fields. The periodical character is ellipticity-dependent. By establishing the physical image, the periodicity of the harmonic intensity can be ascribed to the contributions of the ground state and the excited state. Furthermore, the electron dynamics from different electronic states can be selected via combining the elliptically polarized laser field with a static electric field. The harmonics dominated either by ground state or excited state are emitted once in an optical cycle in the combined laser field.     

Multi-photon resonance enhanced super high-order harmonic generation

This paper proposes highly charged ions pumped by intense laser to produce very high order harmonics.Numerical simulations and full quantum theory of Ne 9+ ions driven by laser pulses at 1064 nm in the power range of 10 9 W/cm 2 ～ 10 15 W/cm 2 show that the emission spectrum corresponds to the electronic transitions from the excited states to the ground state,which is very different from the spectrum of general high-order harmonic generation.In such situation,harmonic order as high as 1000 can be obtained without producing lower order harmonics and the energy conversion efficiency is close to general high order harmonic generation of hydrogen atom in the same laser field.     

Control of the supercontinuum spectrum bandwidth and emission efficiency for intense-isolated sub 40-as pulse generation by using a coherent superposition of states

We present a systematic study for generation of intense and short single as pulse in pre-excited He-ionic medium with the use of a same-frequency laser field synthesis. By preparing He+ ions in a coherent superposition of the ground and excited states, a depth of spectral modulation efficiently decreases and the efficiency of harmonic plateau increases. By means of optimizing the laser parameters, the broadband XUV supercontinuum achieve by the superposition state scheme. It shows that by increasing the harmonic order of the supercontinuum, emission efficiency increases. The detailed view shows that the short-trajectory contributes to each supercontinuous harmonic and long-trajectory fully suppresses. Finally, by superposing some properly selected harmonics from optimal spectrum, an intense and almost transform-limited isolated 38-as pulse can be generated without phase compensation. A single isolated 5-as pulse can be achieved after phase compensation. These results are explained by using classical and quantum time-frequency analyses.     

High-order harmonic generation in sub-one-cycle regime

We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle.It is found that the switching term of the laser field may have an obvious influence on the cutoff,intensity or plateau structure of the high-order harmonic spectrum.Generally speaking,the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.