Exact solutions for stimulated emissions by external sources

The exact solutions for transition amplitudes are derived forstimulated emissions by external sources. More precisely, we obtain the exact expressions for transition amplitudes for the emission of an arbitrary number of particles by the sources when some particles are already present, in the process,prior to the switching on of the external sources. The solutions are given for an arbitrary number of particles with arbitrary configurations (of momenta, spin, etc.) and for particles of spin-0, spin-1/2, massive and massless (photons) spin-1 particles, and massless (gravitons) spin-2 particles. Applications are given as illustrations to the process Ø anything, and, in quantum electrodynamics, to the process e ⁺e^–+ any photons, in thepresence of external sources, where a (virtual) photon decays into the paire ⁺e^–.     

Stimulated emission of relativistic particles by external sources in spacetime

Explicit solutions are derived for transition amplitudes associated with stimulated emission of relativistic particles by external sources inspacetime. More precisely, exact expressions are obtained for transition amplitudes for any process where there are initially, at a given time, an arbitrary number of particles localized in various regions of space, prior to the switching on of an intervening source, and then, finally, at a later time when the intervening source ceases to operate, a given number of particles are found to be localized in various regions of space. The analysis is given for massive particles ofarbitrary integer and half-integer spins. The solutions are obtained by carrying out a unitarity expansion inconfiguration space, where particles travel between emitters and detectors in the presence of an intervening source. Considered as an application is the process: particlearbitrary number of particles, where the latter particles emerge spatially with a cone.     

Temperature-dependent particle production and stimulated emissions by external sources

Exact solutions for transition amplitudes for particle production and stimulated emission by external sources are derived forfinite temperatures. More precisely, we obtain the expressions for amplitudes for the emission of an arbitrary number of particles by the sources, and correspondingstimulated emission processes, when one is dealing with a generalized multiparticle state (rather than the vacuum) at finite temperatures. The solutions are given for spin-0, massive and massless (photons) spin-1, and spin-1/2 particles. As applications, we study the process: photon any photons, in the presence of a strong external electromagnetic current, with the net release of a specified energy, and work out the power radiated by a given electromagnetic current distribution, all at finite temperatures. The latter application includes the radiation emitted by a point charged particle atT 0 as a special case.     

Stimulated emission of photon excitations by external currents in spacetime

The problem of stimulated emission of photon excitations by external currents is studied inspacetime by making use of the concept of localized photon excitations in configuration space. An explicit expression is derived for the amplitude that an arbitrary number of photon excitations are produced and found in arbitrary localized regions in space when there are an arbitrary number of photon excitations prior to the switching on of the intervening current. Considered as an application is the reaction of a photon splitting to any number of photon excitations as the latter emerge spatially within a cone in the presence of a strong external electromagnetic current. This work is a generalization of work dealing with strictly massive particles.     

On the transmission rate of classical information through quantum communication channels

The coding of quantum communication channels in real time is considered as applied to the situation when information is coded into continuous quantum degrees of freedom (into the shape of the amplitude of quantum states with an arbitrary number of photons). It is shown that the nonlocalizability of states in quantum field theory requires that the identity of particles should be taken into account. This, together with the finiteness of the limit speed of propagation, leads to the fact that the formulas for the transmission rate of nonrelativistic communication channels have an asymptotic character; i.e., these formulas are formally valid only when the separation between messages is infinite (when the identity of particles can be neglected) and, hence, when the transmission rate in [bit/message s] is infinitely small. A real-time information capacity of a sequential relativistic quantum communication channel is obtained that takes into account the identity of particles for pure signal states with an arbitrary number of photons. An explicit analytic expression is obtained for the transmission rate of a quantum channel of finite bandwidth for one-photon input states.     

Charged Particle Emission and Detection Sources in Quantum Field Theory and Infrared Photons

A study is carried out of the fundamental roles played by emission and detection sources of charged particles in quantum field theory by incorporating the unavoidable fact that charged particles feel the presence of each other even when they are widely separated at the emission and detection sites due to the long range effect of the electromagnetic interaction. It is shown that the emission and detection sources as amplitudes of emission and detection of charged particles are to have given specific coupling dependent phase factors for a correct formulation of the problem. Composite sources are introduced for emitting and detecting “clusters” of charged particles. Finally a complete cancellation of the so-called relativistic Dalitz phase factor occurs prior to computing transition rates and probabilities. This work generalizes our earlier work (Fortschr. Phys. 34 , 835 (1986)) dealing with the non-relativistic Coulomb problem.     

Electronic spectrum and wave functions in a double quantum well in a nonharmonic field

A method is proposed for calculating quasi-energies and quasi-energy wave functions of a particle located in a double quantum well under the action of a periodic external field with an arbitrary number of harmonics. The solutions of the Schrödinger equation obtained by this method are valid both in weak and strong fields for any frequencies of the external field and any frequencies of the quantum transition in the system.     

Scattering theory in quantum field theory in configuration space

The recent analysis of the propagation of relativistic particles inspacetime and their localization problem is used to develop scattering theory in quantum field theory inconfiguration space. An explicit functional expression is derived for the underlying transition amplitudes having a consistent probabilistic interpretation. Some of the basic ingredients in the analysis are the functional approach developed earlier for transition amplitudes and the amplitudes for stimulated emission of particles by external sources in spacetime.     

Quantum non-demolition phonon counter with a hybrid optomechnical system

A phonon counting scheme based on the control of polaritons in an optomechanical system is proposed. This approach permits us to measure the number of phonons in a quantum non-demolition (QND) manner for arbitrary modes not limited by the frequency matching condition as in usual photon-phonon scattering detections. The performance on phonon number transfer and quantum state transfer of the counter are analyzed and simulated numerically by taking into account all relevant sources of noise.     

Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

Particle-particle correlation and fluctuations in non-equilibrium Fermi/Bose gases

A theory of fluctuations and correlations in non-equilibrium Fermi and Bose gases is developed. A specific quantum correlation is predicted in non-equilibrium collisional quasi-classical gases, created by collisions between particles. The expressions for correlation sources entering the equation for an equal-time two-particle correlation function are obtained and analyzed. The expressions are valid for arbitrary particle-particle interaction potentials. The possibility of display of the quantum correlation in the macroscopic characteristics of fluctuation phenomena in non-equilibrium gases (e.g., current fluctuations in semiconductors) is discussed. A comparison with correlations in a Lorentz gas is made.     

Charged Particle Emission and Detection Sources and the One-Body and the Many-Body Coulomb Scattering

A detailed study is carried out of the fundamental roles of the emission and detection sources in the one-body and the many-body Coulomb scattering. It is shown that the emission and detection sources, as amplitudes of emission and detection of charged particles, are to have given time-dependent structures for a correct formulation of the problem. The method incorporates the long range effect of the Coulomb field which persists even at large distance separations. Most importantly, composite sources are necessarily introduced for the many-body Coulomb scattering which act as emission and detection sources of “clusters” of charged particles and reflect the physically important fact that charged particles feel the presence of each other even before or after “collisions”. A complete concellation of the so-called Dalitz phase factor naturally follows leading to infra-red finite transition amplitudes (as opposed only of transition probabilities) by a systematic use, in the process, of a unitarity sum with respect to the external sources.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

Theory of irreversible processes in nonequilibrium quantum systems. II. Cluster expansions with contraction for homogenous systems

On the basis of a method developed in a previous paper, a systematic rule for obtaining a symmetrized collision superoperator of the Van Hove generalized master equation including an arbitrary number of particles is given. In the formalism, the quantum statistical effect is taken into account through the use of contractions (internal and external contractions) on the basis of the cluster expansion. As an application of this general rule, a symmetrized collision superoperator including the effect of three-particle collisions is obtained.     

Particle Creation in the Effective Action Method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.     

Application of quantum algorithms to direct measurement of concurrence of a two-qubit pure state

This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.     

Langevin and generalized Langevin types of spontaneous emission of quantum particles

In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.     

A Generalized Talmi-Moshinsky Transformation for 1D Harmonic Oscillator Functions and Interaction Matrix Elements

A generalized Talmi-Moshinsky transformation relating one-dimensional harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate an N-particle matrix element can be transformed into a sum of products of one-dimensional integrals.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

Theory of reflection and absorption of light by low-dimensional semiconductor objects in a strong magnetic field under monochromatic and pulsed excitations

The theoretical principles of reflection and absorption of light by low-dimensional semiconductor objects (quantum wells, quantum wires, quantum dots) under monochromatic and pulsed excitations with an arbitrary pulse shape are developed. A semiconductor object can be placed in a strong constant magnetic field. The normal incidence of light on a quantum well whose width can be comparable to the light wavelength and for which the number of levels of electronic excitations can be arbitrary is considered as an example. An integral equation similar to the Dyson equation is derived for the Fourier components of the electric fields. The solutions to this equation are given for a number of special cases.