Quantummechanical solutions of the laser masterequation I

The masterequation for the statistical operatorW of a Laser mode andA active two-level atoms 1 is solved by using the coherent state representation 2 of the lightfield. The ansatz forW represents the most general symmetrical coupling of the light mode to all atoms and therefore contains the full influence of quantum fluctuations of the atomic system on the light mode. The system of equations can be solved practically exactly in the stationary case and leads to a photon number distribution in the laser valid for arbitrary pumping. This distribution agrees with that found by a Fokker-Planck equation 3 for not too high pumping and approaches the Poisson distribution for very high pumping. The smooth transition of the inversion from σ₀ (below threshold) to σ (above threshold) can also be calculated.     

Quantummechanical solutions of the laser masterequation. II

A Fokker-Planck equation for a distribution function over the macroscopic observables of the laser essentially equivalent to that recently obtained byRisken,Schmid andWeidlich is derived from the fundamental quantummechanical laser masterequation. The general method used is the expansion of the statistical operator in a complete set of projection operators of the atoms and the lightfield. The assumptions leading from the microscopic equation of motion to the macroscopic semiclassical Fokker-Planck equation are explicitly introduced and discussed.     

Quantum mechanical masterequation and Fokker-Planck equation for the damped harmonic oscillator

For the statistical operator of the damped harmonic oscillator a Masterequation is given in operator form describing both inelastic and elastic, purely phase destroying processes. By expressing the statistical operator in the diagonal representation with respect toGlauber's coherent states the Masterequation is transformed into a Fokker-Planck equation forGlauber's quasiprobability distribution function. The general solution of this Fokker-Planck equation is calculated. It is shown how the solution of a Masterequation can be used for calculating correlation functions and expressions are given for the amplitude and intensity correlation functions which are in complete formal agreement with the corresponding classical formulae.     

The time dependent solution of the masterequation for a laser system

Calculations of the cross sections for collision-induced transitions between Zeeman sublevels of excited alcali atoms are proposed, which are independent from dynamical models. 1. Supposing that the spin of the valence electron does not flip, the transition matrix, describing collision-induced deorientation of the orbital angular momentum, is analysed considering invariance principles only. Consequently the cross sections for depolarizing collisions are given by two dynamical parameters. 2. The full transition matrix, describing deorientation of the orbital angular momentum as well as of the spin of the valence electron, is analysed in the same way. In this general case the depolarizing cross sections are given by six dynamical parameters.     

Quantum mechanical calculation of multi-time-correlation functions and its application to the laser theory

Quantum mechanical multi-time-correlation functions are derived and applied to laser theory. The correlation functions for the laser field amplitudes and intensities are calculated. Far above the threshold region the latter correlation function shows damped oscillations.     

Quantum mechanical computers

The physical limitations, due to quantum mechanics, on the functioning of computers are analyzed. Editor's note: This article, which is based on the author's plenary talk presented at the CLEO/IQEC Meeting in 1984, originally appeared in the February 1985 issue ofOptics News. It is here reprinted with kind permission of Professor Feynman andOptics News.     

Quantum mechanical tunnelling

It was shown earlier that during quantum mechanical tunnelling, a microscopic particle has a distributed probability of emission about its original energy and is not constrained to be field-emitted only at its initial energy. Such an energy distribution process appears obvious on the quantum theory of observation and measurement which relates the energy of a microscopic particle with the time required for its determination through the Heisenberg’s uncertainty relation. Here, an account of the tunnelling theory based upon the latter is presented. The consequent analysis gives rise to a spectrum in the energy of the transmitted electrons and also yields a method to estimate the tunnelling time as well as the tunnelling current density across an arbitrary barrier.     

He-CO散射截面的量子力学研究

采用精确度较高的密耦方法(Close-Coupling)计算了He-CO碰撞的散射截面,能量从5meV～70meV,计算结果与M.Keil等的实验结果(64meV)基本相符,研究表明:势能的零点能位置、势阱深度、势阱位置、排斥势强度以及势能在势阱附近的方向性都对散射截面有较大的影响.     

Quantum theory of the two-photon laser

We start from a master equation for the density operator of the atoms and the field mode, and apply the operator method of adiabatic elimination of the atomic variables, recently developed by Haake and Lewenstein for the usual single mode laser, to the case of a degenerate two-photon laser. A Fokker-Planck equation for the Wigner distribution function of the lightfield and its steady state solution are derived. With a Gaussian approximation to the solution, analytical and numerical results on the photon statistics are calculated.     

Quantum mechanical interaction-free measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.     

Quantum mechanical calculations of the HCN-HNC isomerization

Ab initio calculations using a minimum basis of Slater orbitals have been carried out on the molecules HCN and HNC with optimization of geometry. The predicted geometry of HNC is compatible with an observed radio-emission line which has been attributed to this molecule. The reaction profile for the internal migration of the proton has been calculated. The transition state is approximately T shaped with an activation energy from HNC of 251 kJ/mole.     

Quantum electrodynamics in a laser and the electron laser collision

Quantum electrodynamics in a laser is formulated, in which the electron–laser interaction is exactly considered, while the interaction of an electron and a single photon is considered by perturbation. The formulation is applied to the electron– laser collisions. The effect of coherence between photons in the laser is therefore fully considered in these collisions. The possibility of γ-ray laser generation by use of this kind of collision is discussed.     

Quantum mechanical calculation of the carbine valent zone

Results of a quantum mechanical calculation of the valent states of carbine are presented. A comparison is performed with data from spectroscopic experiments studying the valent states of this modification of solid carbon.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 65–68, July, 1989.     

经典守恒定律的量子力学推导

从量子力学出发,推出了经典动量守恒定律和能量守恒定律,并讨论了在微观领域经典守恒定律适用的条件.     

Quantum mechanical version of the classical Liouville theorem

In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from |z>to|sz-rz*> corresponds to the motion from a point z(q,p) to another point sz-rz* with |s|2-|r|2=1.The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics.     

Quantum mechanical evolution of relativistic particles

This is a tentative theory of quantum measurement performed on particles with unspecified mass. For such a particle, the center of the wave packet undergoes a classical motion which is a precious guide to our approach. The framework is manifestly covariant and a priori nonlocal. It allows for describing an irreversible process which lasts during a nonvanishing lapse of time. The possibility to measure a dynamical variable in an arbitrary slate is discussed. Our picture is most satisfactory if we focus on free particles and constants of the motion. Two-particle systems and measurement of individual observables in a correlated slate are considered.     

Quantum description of free electrons in the laser

The fully quantum mechanical theory of the free electron laser is formulated in the moving frame introduced by the authors. The laser and wiggler fields are taken to be at their classical limit and quantum effects of the electron motion are considered. The Schrodinger equation is written down and solved for the unsaturated gain and momentum distribution. The results are found to be closely related to the corresponding expressions from a fully classical theory.     

Quantum mechanical stability approach to the Coulomb quasipotential

The critical coupling constant characterizing the stability behaviour of the Coulomb quasipotential has been evaluated as α ? α_c = 2. The present stability approach is based on the quantum-mechanical controllability requirement of the dispersion shifts due to the interactions. The dispersions characterizing the Coulomb quasipotential have been established suitably within the high-energy euclidian region.