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Cerenkov Radiation in Presence of Squeezed Electromagnetic Vacuum

Peter A. Meleshenko, Hang Thi Nguyen, Vladimir A. Gorlov, Михаил Евгеньевич Семенов, A. F. Klinskikh

Published Jan 1, 2015• 0 citations
Publisher

Abstract

In this work we investigate the Cerenkov radiation in the case of motion of a charged particle on a background of the squeezed electromagnetic vacuum. Using the quantum approach (time dependent perturbation theory) we obtain the explicit expression for the Cerenkov radiated power. The analysis of the obtained expression shows that in contrast to the \classical case (where the Cerenkov radiation is a spontaneous process) the Cerenkov radiation in the squeezed vacuum has an induced character. The expression for radiated power contains two terms, namely the flrst term corresponds to radiation power, while the second one corresponds to absorption power. 1. INTRODUCTION Cerenkov efiect (1) have a long history but it remains relevant in relation to the difierent areas of application of such a phenomena (the wide list of publication on this subject takes place, see, e.g., (2{4) and related references). The expression for the radiated power was obtained by solving the equations of classical electrodynamics in the medium. A large number of studies have been devoted to other aspects of the Cerenkov efiect. They concern the extension to the case of magnetic media, a detailed analysis of radiation in crystals, the role of boundaries, etc. The classical theory of spontaneous Cerenkov efiect is fairly accurate, however the quantum analysis gives a more complete understanding of the phenomenon. Moreover, the quantum approach is most useful when considering the motion of a charged particle in a dielectric medium in the external electromagnetic wave. The radiation in this case has an induced nature and quantum approach gives a better understanding of the physical nature of phenomena. Creation of powerful sources of electromagnetic radiation initiated extensive research in the area of particle-fleld interaction. The squeezed states of light (5) play an important role in such researches. These states generalize the well-known class of coherent states and are characterized by the fact that the uncertainty of one of the canonical variables of the electromagnetic fleld is less than in a conventional coherent state. The squeezed states are important in such areas as optical communication, interferometry, nonlinear optics, the detection of gravitational waves, etc. It should also be noted that the squeezed states are objects of purely quantum nature. So the description of the motion of a charged particle on a background of the squeezed vacuum can be performed using the quantum fleld theory only. This problem is of great practical interest (new sources of electromagnetic radiation such as free-electron lasers and Cerenkov lasers). In this work we investigate the Cerenkov radiation in the case of motion of a charged particle on a background of the squeezed electromagnetic vacuum. Due to \purely quantum nature of the squeezed vacuum we use the quantum approach, namely the time dependent perturbation theory.

DOI
10.2532/piers150129173009

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In this work we investigate the Cerenkov radiation in the case of motion of a charged particle on a background of the squeezed electromagnetic vacuum. Using the quantum approach (time dependent perturbation theory) we obtain the explicit expression for the Cerenkov radiated power. The analysis of the obtained expression shows that in contrast to the \classical case (where the Cerenkov radiation is a spontaneous process) the Cerenkov radiation in the squeezed vacuum has an induced character. The expression for radiated power contains two terms, namely the flrst term corresponds to radiation power, while the second one corresponds to absorption power. 1. INTRODUCTION Cerenkov efiect (1) have a long history but it remains relevant in relation to the difierent areas of application of such a phenomena (the wide list of publication on this subject takes place, see, e.g., (2{4) and related references). The expression for the radiated power was obtained by solving the equations of classical electrodynamics in the medium. A large number of studies have been devoted to other aspects of the Cerenkov efiect. They concern the extension to the case of magnetic media, a detailed analysis of radiation in crystals, the role of boundaries, etc. The classical theory of spontaneous Cerenkov efiect is fairly accurate, however the quantum analysis gives a more complete understanding of the phenomenon. Moreover, the quantum approach is most useful when considering the motion of a charged particle in a dielectric medium in the external electromagnetic wave. The radiation in this case has an induced nature and quantum approach gives a better understanding of the physical nature of phenomena. Creation of powerful sources of electromagnetic radiation initiated extensive research in the area of particle-fleld interaction. The squeezed states of light (5) play an important role in such researches. These states generalize the well-known class of coherent states and are characterized by the fact that the uncertainty of one of the canonical variables of the electromagnetic fleld is less than in a conventional coherent state. The squeezed states are important in such areas as optical communication, interferometry, nonlinear optics, the detection of gravitational waves, etc. It should also be noted that the squeezed states are objects of purely quantum nature. So the description of the motion of a charged particle on a background of the squeezed vacuum can be performed using the quantum fleld theory only. This problem is of great practical interest (new sources of electromagnetic radiation such as free-electron lasers and Cerenkov lasers). In this work we investigate the Cerenkov radiation in the case of motion of a charged particle on a background of the squeezed electromagnetic vacuum. Due to \purely quantum nature of the squeezed vacuum we use the quantum approach, namely the time dependent perturbation theory.
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
This chapter reviews the classical description of radiation. It describes how classical electromagnetic radiation interacts with a quantum mechanical particle. The general rule is that, even though the wave functions and the electromagnetic potentials change with the gauge, all physically observable quantities are independent of the gauge. The chapter also describes the process of the absorption of light by a system in terms of the effect of an external classical electromagnetic field on the system. The total emission rate is the sum of the induced and the spontaneous rates. Spontaneous emission is just the quantum mechanical version of the classical phenomenon of radiation from an accelerating charge. A very important consequence of the fact that the electromagnetic field is quantized is that there are vacuum fluctuations of the field, analogous to the zero point motion of a harmonic oscillator. Einstein gave a simple statistical argument to determine the rate at which spontaneous emission takes place.
The propagation of C\ifmmode \breve{}\else \u{}\fi{}erenkov radiation through a medium in which the population of two energy levels is inverted has been studied. The population inversion is represented by an imaginary part of the index of refraction of the medium at the resonance frequency. The resonant atoms are embedded in a host medium which has the shape of a slab of finite width LLL and dielectric constant ${\ensuremath{\epsilon}}_{h}$, which is real and varies slowly for frequencies close to the resonance frequency of the embedded atoms. It is assumed that the host medium and the embedded atoms inside the slab behave as an isotropic noncrystalline medium. The slab is covered by a mirror on each of its surfaces and the medium outside the slab and the mirrors has dielectric constant ${\ensuremath{\epsilon}}_{1}$ (${\ensuremath{\epsilon}}_{1}=1$ for vacuum). While each individual charged particle can stimulate coherent emission by different resonant atoms, the phase of radiation which is due to different particles is uncorrelated. It is shown, however, that radiation of high intensity in the direction of the C\ifmmode \breve{}\else \u{}\fi{}erenkov cone can be produced by highcurrent particle beams. Exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. Using the method of stationary phase approximate expressions are derived for the C\ifmmode \breve{}\else \u{}\fi{}erenkov fields as well as the radiated energy in the foward and backward direction, far away from the slab.
When an electron is accelerated, it emits radiation. In the relativistic quantum realm the elementary radiation process is the emission of a single photon, a process known as nonlinear Compton scattering in the case of an electron moving in the presence of a strong electromagnetic wave. This process is typically described within the Furry picture, where the electromagnetic wave is described as a classical background field and the electron-positron field is quantized in the presence of that background field. Equivalently one can quantize the electron-positron field in the vacuum but then the photon emission process is described as a transition from an initial state to a final state both featuring, apart from the electron (the initial state) and the electron and the photon (the final state), the same coherent state of photons appropriately related to the electromagnetic wave. Here, we consider a more general situation where the initial and the final state feature the same squeezed coherent state. Then, we specialize to the case where the coherent state corresponds to a plane-wave field and the mostly populated modes of the coherent state are also squeezed. We show that, when quantum fluctuations induced by the squeezing in the coherent field are negligible, a condition well satisfied at available squeezing levels, the squeezing effects effectively reduce to a frequency modulation of the plane-wave field corresponding to the coherent state. By means of numerical examples we show that at already available squeezing levels the emission spectrum of nonlinear Compton scattering and the total photon yield can be altered significantly. Analytical explanations of the main numerical results are also provided.
A theory is developed for the interaction of coherent electromagnetic (EM) radiation with a free electron gas and for the influence of the plasma on the photon statistics of the radiation field. Two important possibilities for generating squeezed states are shown: Squeezed states can be generated by the interaction of a one-mode laser with a plasma in a cavity; squeezed states can be generated by transmitting coherent radiation through the plasma. The maximal squeezing of the radiation obtained in the latter case is equal to the reciprocal of the dielectric constant of the plasma. Inside the plasma the EM field is represented by quasiphotons. Their dispersion relations are derived by using Bogoliubov transformations together with a self-consistency requirement for the motion of the electrons interacting with these quasiphotons. The squeezing processes are found to be strong when the frequency of the radiation is a little above the plasma frequency. By adding a constant magnetic field in the direction of propagation of the EM wave different amounts of squeezing are obtained for right- and left-circularly polarized EM waves.
In this chapter we shall be using the formalism of Chapter 4 to describe some properties of the quantized free electromagnetic field, emphasizing the analogies and differences with classical electromagnetism. The analogies explain why classical optics was so successful, to the extent that, even though light was not quantized, it was able to describe almost all known optical phenomena up until the 1970s. The differences highlight typical quantum behaviour, with no classical equivalent, which lies at the heart of modern quantum optics. The chapter begins by presenting formal ways of describing the main components of quantum optics experiments, namely, photodetectors and semi-reflecting mirrors. One can then understand homodyne detection, used to measure field quadrature components, even at optical frequencies for which no detector is fast enough to follow the oscillations of the field itself. Section 5.2 deals with the quantum vacuum where, in contrast to the classical vacuum, radiation has properties, in particular, fluctuations, with which one can associate physical effects. We then discuss in Section 5.3 some quantum radiation states in the simple case where a single mode l of the field is excited (non-vacuum). We introduce the idea of a quasiclassical state, or coherent state, used to make the link with classical optics. We shall also study other states, those with a definite number of photons, or squeezed states, which exhibit typically quantum properties, quite inconceivable in classical electromagnetism, and we shall show how these properties can be understood by reference to the Heisenberg relations, with an extremely useful graphical representation.