Theoretical Study Of Vacuum Polarization And Pair Creation Under Strong Field

Early in the twentieth century, Einstein's mass-energy equation E = mc2 has already revealed the possibility of the conversion between energy and matter. A few decades later, nuclear explosion showed us the power of converting matter into energy. In 1928, the establishment of the relativistic quantum mechanics based on the Dirac equation provided us a theoretical basis about the directly conversion of energy into material from the vacuum. Dirac gave a new definition and description of the physical vacuum. He postulated that the vacuum is full of particles with negative energy, which can be interpreted as the "Dirac Sea". Using this theory, he successfully predicted the existence of antiparticles and he believed that the antiparticles can be understood as a hole in the negative energy continuum. All kinds of inferences, hypotheses and experiments were made about the creation and annihilation of positive and negative particles. Theoretically, in the same year as Dirac's publication, Oskar Klein pointed out that if the electron is scattered by a higher enough barrier, the transmission coefficient would be greater than one according to the Dirac equation. This is the famous Klein paradox. In 1936, Werner Heisenberg related the Klein paradox with the electron-positron pair production caused by a super-strong electric field. In 1951, Schwinger proposed a non-perturbation theory that successfully described the production process of electrons in a strong external field and the long time creation rate. Also, he obtained the threshold of the supercritical electric field, about 1018V/m, which is now known as the Schwinger limit. Experimentally, the famous Chinese physicist Zhongyao Zhao's discovery of the electron pair effect in the lab can be considered as the first experiment of converting the energy(?-rays) into matters(electron-positron pairs) in a nuclear electric field. This experiment provides an important basis for Dirac's vacuum theory. The conversion from light to matter wasn't achieved in laboratory until the 1990 s in the Stanford Linear Accelerator Center, USA. But in this experiment, the real particle is still involved in the pair creation, by colliding of 46.6Ge V electron beam with a super intensity laser pulse(wavelength 532 nm and intensity 1018W/cm2). For realizing the direct conversion energy to matter, we should remove the electron and use the power of the laser only to trigger the pair creation. This topic, which has attracted the attention of scientists for a long time, is important to the theoretical modern physics. In recent years, due to the rapid development of laser technology, the maximum light intensity has advanced to the level of 1023 W / cm2. In order to obtain even powerful laser systems, multinational research centers are under construction. This kind of high power laser equipment will vigorously speed up the research progress in this kind of quantum electrodynamics problem –vacuum breakdown. One of the main objectives of the European ELI project is to build a large ultra-short laser facility to generate electric field, whose strengths are near the Schwinger limit, and thenrealize the production of particles from pure energy. In the coming decades, the laser intensity would be high enough to breakdown the vacuum and produce electron-positron pairs. Therefore, to study the process of creation electron-positron pairs and the associate mechanism under extremely intense laser fields is imminent. In recent years, people have already studied these problems through numerical simulation and analytical methods. This thesis' work uses the new computational quantum field theoretical method to study the pair creation from the vacuum. This new method is based on numerically solving the time-dependent Dirac as well as Klein-Gordon equations and describing the field operator unpertubatively. By simulating different external field configurations, we obtained some new results for the pair creation process:(1) The new complex coordinate rotation method While the computational quantum field theoretical(QFT) method in principle can determine the number of created particle anti-particle pairs for any given of external field potentials, the analysis of the particle dynamics is not always straight forward. For example, when the external field is described by a one-dimensional scalar potential well and if potential depth is lower than a threshold value, bound states from the positive energy can be mixed with the negative energy continuum. The details of the mixing and its signature in pair creation have not been well understood. To understand such a long-time behavior in pair creation, we have used the so-called complex coordinate rotation method. In this method the spatial coordinate x and momentum p are rotated in the complex plain. After these transformations the original Hamiltonian becomes complex. It turns out that the imaginary part of the energy eignvalues can be used to describe the pair creation rate. What is even more surprising is that when there are several bound states dived into the Dirac Sea, the sum of all the imaginary parts of the resonance states' energy describes the pair creation rate. This result is unusual because one would expect the channel with the largest decay rate should dominate the creation process in the long time limit. Our result shows evidence of a non-competing channel mechanism. This result appeared in a recent Phys. Rev. Lett. and was a highlight on the IOP of the Chinese Academy of Sciences website.(2) Description based on instantaneous and quasi-local Lorentz transformations While there are reliable techniques available to compute the pair-creation yield for static force fields, any temporal variation in the field can make a theoretical analysis significantly more difficult. We developed a new description that is based on transforming the system into a co-moving Lorentz frame, in which the relevant high-force regions of the external field are basically at rest and the pair-creation rates can be determined with any static field method. As an testingexample, we firstly considered a time-dependent scalar potential that simply moves shape-invariant with a constant velocity v, V(r,t)=V(r–vt). Here the well-known mass-gap threshold law for static potentials(V0>2mc2) for pair creation translates itself directly to a threshold for the “critical velocity” v of the moving potential(assuming V(r) is sub-critical). In promising preliminary tests for more complicated temporal dependencies(such as the important sinusoidal dependence characteristic of the laser's electric and magnetic field and standing waves) we have begun to examine the practicality and accuracy of this new approach, but more systematic studies are planned.(3) Experimental design through multi-field configuration The third mechanism for controlling pair creation without supercriticality is by using many lasers side by side. Such an investigation is potentially important in guiding future experiments. When subcritical lasers are brought next to each other, quantum mechanical tunneling may cause the overall effective field to be supercritical. We have estimated with hundreds of lasers, the intensity of each laser needs to be only a hundred times weaker to the level of about 1027 W/cm2. This is two orders of magnitude weaker than the Schwinger threshold for pair creation.(4) Magnetic field control of pair creation process In order to provide possible guidance to future laser based pair creation and gain better estimates of possible thresholds that trigger the creation process we have operated on several strategies. We considered magnetic field control, used combined electric fields of different frequencies, and used the multi-field tunneling configuration. The introduction of magnetic field to control pair creation has relied on the knowledge of laser plasma physics, this is a much more challenging task than one dimensional problems because a magnetic field with an electric field will cause the underlying dynamics to execute a complicated three dimensional motion. However, we have been able to orient the magnetic field such that only two spatial dimensions(x and y) are involved. This consideration is crucial to the simplification and thus the progression of this project. Specifically, we orient the magnetic field in the z-direction while it varies its strength in the x-direction but does not vary in the y-direction. The additional electric field is assumed to be pointing along the x-direction and only allowed to vary in the x-direction. With this configuration we have been able to produce some surprising results. The first surprise is the total created number of particle N(t). As we fix the electric and magnetic field strengths and fix spatial width of the electric field while only gradually increasing the spatial width of the magnetic field WB, we find N(t) will be suppressed significantly compared to the case when the magnetic field is absent. What is more surprising is that after a certain threshold, the pair creation can be completelyshut off, and beyond this threshold the pair creation exhibit oscillatory behavior. Along with this discovery, we also studied the details of pair creation suppression before the shutoff takes place. It turns out that the introduction of magnetic field will lead to cyclotron motion in the created particles. When these particles return to the creation zone pair creation will be suppressed due to Pauli principle for electrons. In another work we have extended the study to investigate the magnetic control in a boson system. In that case the returned bosons enhance the pair creation due to the so-called anti-Pauli effect and has been discussed in the past. Finally we were able to make a connection between the long time creation rates with the transmission coefficient of single particle Dirac/Klein Gordon equation. This connection is a successful extension of a conjecture by Hund proposed in the presence of an electric field only.