Progress of pair production from vacuum in strong laser fields
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摘要: 随着激光技术的飞快发展，激光强度不断提高，超强外场下真空中正负电子对产生的过程，即能量向质量转化过程，已经成为一个研究热点。主要综述了近几年量子Vlasov方程方法和计算量子场论(数值求解Dirac方程)方法在研究强场下真空中正负电子对产生方面的进展，分别介绍了空间均匀场和空间不均匀场下的粒子对产生的情况。第一种情况主要介绍双脉冲结构振荡电场中电子-正电子对的产生、强双频振荡电场中非微扰电子-正电子对的产生、频率调制的激光场中电子-正电子对的产生和Dirac真空对啁啾外场的快速分辨。第二种情况主要介绍优化空间局域电场提高粒子对的产生率、多个势阱-垒结构的振荡场对粒子对产生的增强、振荡 Sauter 电势中正负电子对产生的问题、操纵Dirac真空以控制其在场诱导下的衰变、作为信息传输介质的Dirac真空还有正负电子对产生中的相干和非相干啁啾机制的转变。
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关键词:
- 强场物理 /
- 正负电子对 /
- 量子Vlasov方程 /
- 计算量子场论
Abstract: With the rapid development of laser technology and the continuous improvement of laser intensity, the process of electron-positron pair creation in vacuum under super strong external field, namely the process of energy conversion to mass, has become a research hot spot. In this paper, we mainly review the progress of quantum Vlasov equation and computational quantum field theory (numerical solution of Dirac equation) in the study of the electron-positron pair production in vacuum under intense laser field in recent years, and introduce two situations of particle pair generation spatially homogeneous field and spatially inhomogeneous field, separally. In the first case, there are electron-positron pair production in oscillating electric fields with double-pulse structure, electron-positron pair generation in the strong dual frequency oscillating electric field, electron-positron pair production in frequency modulated laser fields, and resolving rapidly chirped external fields with Dirac vacuum are introduced. The second case mainly introduces the optimization of spatially localized electric fields for electron-positron pair creation, enhanced pair creation by an oscillating potential with multiple well-barrier structures in space, electron-positron pair production in an oscillating Sauter potential, manipulation of the vacuum to control its field-induced decay and Dirac vacuum as a transport medium for information and transition between coherent and incoherent chirping mechanisms in electron-positron pair production. -
图 1 激光强度随年代的发展与相应的物理研究的发展
Figure 1. The development of laser intensity and the corresponding physical research
图 5 双脉冲结构的振荡电场的一般形式。脉冲的特征体现在它们的频率ωj、强度参数ξj和平台周期数Nj ( j ∈{1, 2})并且具有可变的时间延迟δ[49]
Figure 5. General form of an oscillating electric field with double-pulse structure. The pulses are characterized by their frequency ωj , intensity parameter ξj and number of plateau cycles Nj( j ∈{1, 2}) and have variable time delay δ[49]
图 6 在双脉冲电场中产生的粒子的横向动量分布，其中ξ1=ξ2=1, ω=0.49072m, N1=N2=6，时间延迟δ=0(蓝色实线)或δ=π/2m(灰色虚线曲线)。沿场方向的纵向动量分量py=0[49]
Figure 6. Transversal momentum distributions of particles created in an electric double pulse with ξ1=ξ2=1, ω=0.49072m, N1=N2=6, and time delay δ=0 (blue solid curve) or δ=π/2m (gray dashed curve). The longitudinal momentum component along the field direction vanishes, py=0[49]
图 7 在ξ1=1、ξ2=0.1、N=7、ω=0.49072m的双频电场中产生的电子的纵向动量分布 [见公式（19）]。 黑色实线(红色虚线)曲线是指φ=0 (φ=π/2 )的相对相位。横向动量px=0[49]
Figure 7. Longitudinal momentum distribution of electrons created in a bifrequent electric field with ξ1=1, ξ2=0.1, N=7, and ω=0.49072m [see Eq. (19)]. The black solid (red dashed) curve refersto a relative phase of φ=0 (φ=π/2). The transverse momentumvanishes, px=0[49]
图 8 在双频电场中产生的电子的相位的相位谱Φℓ(p)，其中ξ1=1, ξ2=0.1, N=7, 和ω=0.49072m。左图为Φ1，右图为Φ2[54] (弧度范围为−π≤Φℓ≤π, 如图中颜色所示)
Figure 8. Phase-of-the-phase spectra for the electron created in a bifrequent electric field with ξ1=1, ξ2=0.1, N=7, and ω=0.49072m. Left panel: Φ1; right panel: Φ2 (each measured in rad with −π≤Φℓ≤π, as indicated by the color coding)[54]
图 9 调频电场的傅里叶变换，其中上图的调制参数(ωm, b)为(0.01, 1.52)，下图的调制参数为(0.009, 9.52)。并给出了主频峰值。其他场参数为E0=0.1Ecr，τ =100/m，ω=0.5m[60]
Figure 9. The Fourier transform of the frequency modulated electric field, where the values of modulation parameter (ωm, b) are (0.01, 1.52) for the upper panel and (0.009, 9.52) for the lower panel. And the values of dominant frequency peaks are shown. Other field parameters are E0=0.1Ecr, τ =100/m, ω=0.5m[60]
图 11 产生的电子-正电子对数密度随场频率ω变化的曲线。振荡结构与n光子吸收阈值有关。上面曲线对应E0=0.1Ecr，下面曲线对应E0=0.01Ecr。其他场参数为τ=100/m。注意这里没有调频，即b=0[60]
Figure 11. The number density of created electron-positron pairs as a function of field frequency ω. The oscillating structures are related to the n-photon thresholds. The upper line corresponds to E0=0.1Ecr and the lower line corresponds to E0=0.01Ecr. Other field parameters are τ =100/m. Note that there is no frequency modulation, i.e., b=0[60]
图 12 (a)啁啾电场脉冲的E(t)随时间变化示意图。(b)不同时刻的Page-Lampard谱SPL(ω, t)，对应的啁啾参数为ω0=2c2和b=c2。最下面图是E(t)的传统谱ST(ω)[62]
Figure 12. (a) Sketch of the temporal behavior of the chirped electric field pulse E(t) used in this work. (b) The Page-Lampard SPL(ω,t) spectrum taken at different time for E(t) with ω0=2c2 and b=c2. The bottom graph is the traditional spectrum ST(ω) of E(t)[62]
图 13 (a)生成的正电子数|Cp;u(t)|2的能量谱的时间导数等值线图，这是正电子能量ep的函数。(b)外加电场E(t)的Page-Lampard谱SPL(ω,t)。其他参数为Ton=0.01 a.u., Toff=0.01 a.u., T=0.025 a.u., ω0=2c2和b=c2, E0=0.005c3[62]
Figure 13. (a) Contour plot of the temporal derivative of the energy spectrum of the created number of positron |Cp;u(t)|2 as a function of the positron energy ep. (b) The Page-Lampard spectrum SPL(ω,t) of the external electric force field E(t). Other parameters are Ton=0.01 a.u., Toff=0.01 a.u., T=0.025 a.u., ω0=2c2 and b=c2, E0=0.005c3[62]
图 17 势阱时空结构的等高线图。面板(a)用于φ=0，面板(b)用于φ=π/2，面板(c)用于φ=π，面板(d)用于φ=3π/2。时间设置为t=50π/c2。其他参数为D0=10λc, V0=2.53c2和ω0=0.04c2，空间大小为L=2.5[72]
Figure 17. Contour profile plot of the spacetime structure of the potential well. Panel (a) is for φ=0, panel (b) is for φ=π/2, panel (c) is for φ=π, and panel (d) is for φ=3π/2. The simulation time is set to t=50π/c2. Other parameters are D0=10λc, V0=2.53c2, and ω0=0.04c2, the spatial size is L=2.5[72]
图 23 空心圆圈表示产生的正电子数密度N(E, t)的增长，为了比较，实线是根据方程式（32）的预测。发送者场的显示脉冲持续时间为10−3个原子单位[84]
Figure 23. The open circles show the growth of the number density of created positrons N(E, t). For comparison, the solid line is the prediction according to Eq. (32). The displayed pulse durations of the sender’s field are in 10−3 atomic units[84]
图 24 在与啁啾的外部电场相互作用过程中产生的电子能量的增长图。L=2.4 a.u., 其他参数为b=300c2, ω=2.8c2,τ=5.325×10–4 a.u., t1=0.004 a.u.和F0=5c3[87]
Figure 24. The growth of the energy of the created electrons during the interaction with a chirped external electric field. L=2.4 a.u. and the other parameters are b=300c2, ω=2.8c2, τ=5.325×10–4 a.u., t1=0.004 a.u. and F0=5c3[87]
图 25 在与啁啾的外部场相互作用时所产生的电子总能量的增长。L=2.4 a.u.，场参数为V0=5c2, W=0.5/c, D=0.6 a.u.和b=300c2, ω=2.8c2, τ=5.325×10–4 a.u.和t1=0.004 a.u.[87]
Figure 25. The growth of the total energy of the created electrons during the interaction with a chirped external field. L=2.4 and the other parameters are V0=5c2, W=0.5/c, D=0.6 a.u.and b=300c2, ω=2.8c2, τ=5.325×10–4 a.u. and t1=0.004 a.u.[87]
表 1 三种HPLS光束在ELI-NP上的工作参数[19]
Table 1. Operational parameters of the three HPLS beam lines at ELI-NP [19]
PHPLS/PW ELP/J I0max/(W·cm−2) flp/Hz operational in 10 150～225 1023 0.017 2021 1 15～25 5.6×1021 1 2020 0.1 1.5～2.5 2.2×1020 10 2020 
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表 2 不同调制参数组的粒子对数密度(ωm, b)，见图10中标注的点[60]
Table 2. The number density for different selected sets of modulation constants (ωm, b)，see the points marked in Fig. 10 [60]
(ωm, b) number density A (0, 0) 1.04×10−7 B (0.010, 1.52) 2.00×10−6 C (0.009, 9.52) 7.63×10−9 D (0.023, 2.24) 6.10×10−7 E (0.096, 0.96) 9.89×10−8 F (0.022, 8.64) 2.03×10−5
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