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.
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.
Electromagnetic radiation by accelerated charges is a fundamental process in physics. Here, we introduce a quantum-optical framework for controlling the emission of radiation of an electron in an intense laser field via squeezed vacuum states. By engineering the quantum fluctuations of the emission modes, we demonstrate that the probability of nonlinear Compton scattering can be significantly enhanced or suppressed through tunable squeezing amplitude and angle. We show numerically that our predictions are experimentally accessible with current squeezing technologies, establishing a new paradigm for quantum control in high-intensity light-matter interactions.
The stimulated Compton scattering of photons between two oppositely propagating coherent lights by a relativistic electron moving along the same line is studied analytically. The system is described in a moving frame so that the electron becomes nonrelativistic and the frequencies of the two lights coincide. Except for the replacement of the static wiggler by a propagating light, our system is essentially the same as a free-electron laser working in the Compton regime and described in the usual Bambini-Renieri frame. The Q representation of two-mode coherent states is adopted to describe the radiation fields, and the electron states are expressed in terms of plane waves. A perturbative solution, with the quantum recoil of the electron as the perturbation parameter, of the time evolution of the system is carried out far beyond the first order. It demonstrates that two nonclassical effects, i.e., squeezing and photon antibunching, occur as results of the scattering. It also confirms once more the fact that quantum recoils play the exclusive role in generating such nonclassical photon states. A very important improvement in the present treatment is that the electron part of the density matrix is traced out before the calculation of the squeezing effect. As a result, it is found that there is no squeezing if the initial state is a vacuum. This is, perhaps, a significant new discovery. Many-electron effects are ignored in the present study.
We develop a fully quantized theory of nonlinear Compton scattering driven by a single-mode quantum field. Exact quantum-Volkov states retain pump depletion, back-action, and final-state correlations through displaced or squeezed-displaced Fock-state ladders. A finite Fock-state pump produces discrete photon-transfer edges and a terminal spectral cutoff. In the bright, weakly depleted regime, the exact theory reduces to a Wigner-function weighted-average of scattering probabilities evaluated at fixed complex field amplitudes, with ordinary and generalized Bessel functions describing the harmonic structure for circular and linear polarization, respectively. For squeezed coherent light, the squeezing angle controls the high-energy emission through photon-number fluctuations.
Quantum-electrodynamic processes that take place in the presence of a squeezed electromagnetic field are discussed. Integral formulas are derived that make it possible to express the probability of any process in a squeezed electromagnetic field in terms of the probability of the same process in a classical electromagnetic field. The main laws that govern processes of first order in the fine-structure constant as functions of the number of photons involved and the quantum fluctuations are examined. Tunneling formulas for the probability of a photon producing an electron-positron pair in a strong squeezed field are derived. Also, resonant electron-electron scattering is examined and the scattering cross section as a function of the statistical properties of the field (the way the field has been squeezed) is investigated. It is found that the quantum fluctuations of the squeezed electromagnetic field give rise to an increase in the scattering cross section, with the probability of the process in a phase-squeezed electromagnetic field always being higher than the probability of the process in an amplitude-squeezed electromagnetic field.
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.
An atomic electron, in the vacuum of photons, can emit and reabsorb photons of any frequency. Such processes give rise to well known radiative corrections (Lamb—shift, g — 2, natural width of excited states...). We review in this paper similar effects which can be induced by the interaction of an atomic electron with an incident electromagnetic wave, and we try to get some physical insight in radiative processes by comparing these two types of « spontaneous » and « induced » effects. Optical pumping methods have been very useful for studying how atoms are perturbed by optical or RF photons. The Zeeman sublevels of an atomic ground state are broadened and shifted by a resonant or quasiresonant optical irradiation. The corresponding light-shifts (or « Lamp-shifts » as A. Kastler called them) are due to virtual absorptions and reemissions of incident photons. Another example of an induced effect is the modification of the magnetic properties of an atomic level due to a high frequency non resonant RF irradiation. The Larmor precession is slowed down and becomes anisotropic. The two previous examples correspond to two situations leading to simple calculations. For a resonant or quasiresonant excitation, a single atomic transition needs to be considered. Non perturbative treatments can be given which include the effect of the atom field coupling to all orders. For example, the « dressed atom » approach allows a unified treatment of various effects such as light shifts, Autler-Townes doublets resonance fluorescence triplets... On the other hand, for a high frequency irradiation, all atomic transitions must be included. It is possible in this case to derive an effective hamiltonian describing, to lowest order in the fine structure constant α, how electronic energy levels are perturbed in the presence of N photons ω. The remaining part of the paper is devoted to the analysis of such a situation. The terms of the effective hamiltonian proportional to the number N of incident photons correspond to the induced effects. They can be fully interpreted in semiclassical terms and they describe how the slow motion of the electron in the external static fields is modified by the high frequency vibration in the incident monochromatic wave. For example, the vibrating electron averages the static potential over a finite length, the angular oscillation of the spin reduces the effective magnetic moment. The remaining terms, which are independent of N, exist even in the vacuum of photons (N = 0) and describe the contribution of the mode ω to spontaneous radiative corrections. It is possible to split them into two parts. The first one has the same structure as the N-dependent terms, with N replaced by 1/2. It describes the corrections due to the vibration of the electron in vacuum fluctuations which have a spectral power density ħω/2 per mode. The second part represents the effect of radiation reaction, i.e. the interaction of the electron with its self field. Such an interpretation is confirmed by a Heisenberg equations approach where the total force acting upon the electron is split into two physical (i.e. hermitian) parts representing respectively the effect of the vacuum « free » field and the effect of the « source » field produced by the electron itself. These considerations are finally applied to the problem of the positive sign of g - 2. The g-factor can be written as 2 ωL/ωc, where ω L is the Larmor frequency of the spin and ωc the cyclotron frequency of the charge for an electron in a weak static field B 0. In the absence of radiative corrections, g = 2, and ω L = ωc. To lowest order in 1/c (order zero), radiation reaction slows down ωc but not ωL (a charge is more coupled to its self field than a magnetic moment). The effect of vacuum fluctuations appears only at order 2 in 1/c and corresponds to relativistic and magnetic effects which slow down both ωL and ωc. Therefore, it appears that, in the non relativistic domain, the main effect is a reduction of ωc by radiation reaction and this explains why 2 ωL/ωc becomes larger than 2. A complete relativistic calculation (to all orders in 1/ c, but to lowest order in α) does not change this conclusion since the contribution of non relativistic modes (ħω < mc2) is predominant in the integral giving g — 2.