Quantum theory of transition radiation and transition pair creation

A theory of the transition radiation and the transition pair creation is developed in the frame of QED. The spectral-angular distributions of probability of the transition radiation and of the transition pair creation are found. The total energy losses of an electron and the total probability of pair creation by a photon are calculated and analyzed. Features of radiation and pair creation processes in a superdense medium (typical for white dwarfs) are discussed.     

Quantum detection and estimation theory

A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the place of the probability density functions of conventional statistics. The optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented. Quantum estimation theory seeks best estimators of parameters of a density operator. A quantum counterpart of the Cramér-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates. Applications at present are primarily to the detection and estimation of signals of optical frequencies in the presence of thermal radiation.This paper was prepared under grant NGR-05-009-079 from the National Aeronautics and Space Administration.     

Quantum Tunneling Radiation of Kerr-NUT Black Hole

Based on particles in a dynamical geometry, extending the Parikh ＇s method of quantum tunneling, radiation, we deeply investigate the quantum tunneling radiation of Kerr-NUT bhck hole. When self-gravitating action, energy conservation, and angular momentum conservation are taken into account, the emission rate of the particle on the event horizon is related to the change of Bekenstein-Hawking entropy and the emission spectrum is not precisely thermal, but is consistent with an underlying unitary theory.     

Quantum Communication in Rindler Spacetime

A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. We study the impact of this Davies-Fulling-Unruh noise on communication, particularly quantum communication from an inertial sender to an accelerating observer and private communication between two inertial observers in the presence of an accelerating eavesdropper. In both cases, we establish compact, tractable formulas for the associated communication capacities assuming encodings that allow a single excitation in one of a fixed number of modes per use of the communications channel. Our contributions include a rigorous presentation of the general theory of the private quantum capacity as well as a detailed analysis of the structure of these channels, including their group-theoretic properties and a proof that they are conjugate degradable. Connections between the Unruh channel and optical amplifiers are also discussed.     

Quantum theory of the Raman effect

A quantum mechanical analysis is made of higher order processes in Raman scattering. In particular the examples of coupled Stokes and Antistokes radiation and the generation of 1st and 2nd Stokes radiation are considered. All fields, electromagnetic and phonons, are quantized and the Schrödinger equation for the system is solved exactly. This completely quantum mechanical approach eliminates discrepancies which occur when linearization procedures such as the parametric approximation are employed. The theory applies to both stimulated and spontaneous Raman scattering.     

Contrasting Classical and Quantum Vacuum States in Non-inertial Frames

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories.     

Quantum theory of light propagation in a fluctuating laser-active medium

The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.     

Quantum Limits on the Entropy of Bandlimited Radiation

Physical limits on the amount of information carried by bandlimited waveforms radiated in one and three dimensions are considered. It is shown that the entropy of radiation can achieve the Bekenstein bound using a “burst” of energy, whose density vanishes as the radiating system expands. In comparison, black body radiation of infinite bandwidth achieves the same entropy scaling, that is proportional to the volume of the space, but requires an energy density that remains constant as the system expands. Rather than following the standard statistical physics approach of counting the number of eigenstates of the Hamiltonian of the quantum wave field, our derivation first considers an optimal subspace approximation, and then determines the number of bits that are required to represent any waveform in the space spanned by this representation with a minimum quantized energy error. This favors a geometric interpretation where the complexity of state counting is replaced by the one of determining the minimum cardinality covering of the signal space by high-dimensional balls, or boxes, whose size is lower bounded by quantum constraints. All derivations are given for both deterministic and stochastic settings.     

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.     

腔光力学系统中的量子测量

腔光力学系统近年来迅猛发展, 在精密测量、量子传感等方面已展现出重要的应用价值. 特别是与微纳技术和冷原子技术结合后, 这一系统正发展成为研究量子测量与量子操控的理想平台. 本文首先综述腔光力学在量子测量, 尤其是量子测量基础理论研究方面的进展; 然后分析腔光力学系统中的量子测量原理; 最后介绍我们近来在这方面的研究进展, 并通过我们设计的一系列新颖的基于腔光力学系统的量子测量方案来具体展示该系统在量子测量、量子操控等方面的潜在应用.     

Quantum theory of self-induced transparency

It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon theory. In this paper we quantize the electromagnetic field and compute some quantum effects by using known results from the sine-Gordon quantum field theory. In particular, we compute the intensity of spontaneously emitted radiation using the thermodynamic Bethe ansatz with boundary interactions.     

Quantum beats in stimulated electronic raman scattering of ultrashort laser pulses

A theory of quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.     

Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect

We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.     

Quantum theory of a dissipative oscillator

The nonlinear equation of dissipative quantum mechanics is considered in the relaxation-time approximation. It is shown that the steady current-free state does not change when dissipation is taken into account; in particular, there is no ground-state damping, and the zero energy is conserved. A solution is obtained to the problem of the excitation of a harmonic oscillator, serving as a model of single-mode radiation in an open resonator; the solution obtained describes the evolution of the oscillator from an arbitrary steady state under the action of a constraining force. Transition probabilities between the oscillator steady states are calculated. The results are found to be in agreement with the classical theory of damping oscillations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–105, September, 1978.     

Quantum statistical properties of higher-order non-linear optical processes

We study the quantum statistical properties of radiation in higher-order parametric processes and higher harmonic generation. Adopting the Heisenberg picture, we use the short-time approximation to solve the Heisenberg equations and to calculate the quantum characteristic functions and quasi-distributions. The lossy mechanism is included with or without rotating terms. We show that the statistical properties of radiation involved in these non-linear optical processes are described by the model of the superposition of coherent and chaotic fields with correlated components in this approximation. Generalizations of the well-known conservation laws for the number operators are derived. We show for parametric processes that the pumping mode has tendency to be coherent while the signal modes are obtaining a noise. In the higher-harmonic generation, the basic radiation is losing its coherence proportionally to its intensity while the generated higher-harmonic radiation has tendency to be coherent.The part of this paper devoted to thek-th harmonic generation describes a portion of the Diploma Work.     

Quantum theory of laser cooling: Statistical description of the process dynamics

A dynamic theory of coherent X-ray radiation generated in a periodic layered medium by a relativistic electron multiply scattered by target atoms has been developed. The expressions describing the spectral–angular characteristics of parametric X-ray radiation and diffracted transition radiation are derived. Numerical calculations based on the derived expressions have been performed.     

Quantum vacuum radiation spectra from a semiconductor microcavity with a time-modulated vacuum Rabi frequency

We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Quantum calculations in a unique rest frame

The distribution of astronomical redshifts and the cosmic background radiation define a unique inertial reference frame. This paper contains an investigation of questions concerning quantum theory which arise with the introduction of a unique rest frame into spacetime. The Mössbauer effect, photon pair production, and photoelectric effect are treated together with photon scattering by a moving reflector and the Compton effect. Dirac's 1928 quantum theory of electrons is shown to yield its well-known energy spectrum for the hydrogen atom independently of the velocity of the atom relative to the rest frame.1. Address for the academic year 1990–91: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602, USA.