The standard model in cavity quantum electrodynamics. I. General features of mode functions for a Fabry-Perot cavity

Abstract

In the present and the accompanying paper a justification of the standard model of cavity quantum electrodynamics is given in terms of a quasi-mode theory of macroscopic canonical quantization. The coupling of the cavity quasi-mode to external quasi-modes is treated for the representative case of the three-dimensional Fabry-Perot cavity. The general form of the travelling and trapped mode functions for this cavity are derived in this paper and the mode-mode coupling constants are calculated in the accompanying paper. The slow dependence of the coupling constants with the mode frequency difference demonstrates that the conditions for Markovian damping of the cavity quasimode are satisfied. As also discussed in the accompanying paper, the interaction of radiative atoms with cavity quasi-modes is associated with reversible energy exchanges between atom and cavity and represented by Rabi coupling constants. The interaction of radiative atoms located within the cavity with sideways travelling external quasi-modes involves slowly varying coupling constants and is associated with irreversible spontaneous emission dampling. The basic processes represented in the standard cavity quantum electrodynamics model and the associated coupling constant and decay rates thereby follow from the quasi-mode theory.     

Frozen geometric discord in dissipative cavity quantum electrodynamics system

We investigate the dynamics of geometric quantum correlations for certain decoherence channels and discuss the necessary conditions for the existence of frozen geometric discord. As illustrative examples, we study the phenomenon of double sudden transitions in geometric discord for a system consisting of two noninteracting atoms inserted in two independent dissipative cavities and how the initial state parameters and decay rate of dissipative cavities affect the frozen time during which the geometric discord remains constant. We also explore the dynamics of geometric discord between two noninteracting atoms trapped in a common dissipative cavity and find that the geometric discord exhibits sudden transition between classical and quantum decoherence. Moreover, a nonzero stationary geometric discord can arise in both the independent cavity case and common cavity case.     

Quasi mode theory of macroscopic canonical quantization in quantum optics and cavity quantum electrodynamics

Abstract

A macroscopic, canonical quantization of the EM field and radiating atom system in quantum optics and cavity QED involving classical, linear optical devices, based on expanding the vector potential in terms of quasi mode functions is presented. The quasi mode functions approximate the true mode functions for the device, and are obtained by solving the Helmholtz equation for an idealized spatially dependent electric permittivity function describing the device. The Hamiltonian for the EM field and radiating atom system is obtained in multipolar form and the quantum EM field is found to be equivalent to a set of quantum harmonic oscillators, one oscillator per quasi mode. However, unlike true mode theory where the quantum harmonic oscillators are uncoupled, in the quasi mode theory they are coupled and photon exchange processes can occur. Explicit expressions for the coupling constants are obtained. The interaction energy between the radiative atoms and the quantum EM field depends on the amplitudes of the quasi mode functions at the positions of the radiating atoms, similar to that for the true mode approach. The simpler forms for the quasi mode functions enable the atom-field interaction energy to be written in a form in which the atoms are only coupled to certain types of modes—for example cavity quasi modes, which are large inside the optical cavity. In such cases the escape of energy from excited atoms in the cavity can be pictured in quasi mode theory as a two step process—the atom de-excites and creates a photon in a cavity quasi mode, the photon in the cavity quasi mode is then lost and appears as a photon in an external quasi mode. In this process the first step occurs via the atom-cavity quasi mode interaction, the second through coupling between cavity and external quasi modes. This may be contrasted with the true mode approach, where the excited atom loses its energy and the photon is created in one of the true modes. As all true modes have non-zero amplitudes outside as well as inside the cavity, the escape of energy from excited atoms in the cavity is seen as a one step process. An application of the quasi mode theory to the quantum theory of the beam splitter is outlined. The unitary operator used to describe this device is a scattering operator, relating initial and long time values of annihilation, creation operators for pairs of incident and reflected modes, interpreted here as quasi modes.     

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

Abstract

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be ‘guessed’ from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.     

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics. II. Application to reflection and refraction at a dielecric interface

Abstract

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.     

Variation in the constants in an extended standard model. Part I. Determining the constants and estimating possible variations

The constants in the extended standard model are considered, which includes gravitational interaction and massive neutrinos. The accuracy is compared in determining the coupling constants on various energy scales, and theoretical estimates are given for the possible time variations. __________ Translated from Izmeritel'naya Tekhnika, No. 8, pp. 3–7, August, 2008.     

Model for quantum scattering of rotons. II. Two-dimensional interaction

A speculative roton Hamiltonian is used to calculate scattering cross sections in the two-dimensional problem. For the hard-cylinder interaction, one gets the same result as that obtained by the usual wave scattering in the high-energy limit. The variational calculation for the roton-vortex interactionP ·v _s yields the temperature-independent momentum-transfer cross section _T 8 Å, improving the results obtained before by other methods.     

General formalism of interaction of a three-level atom with cavity fields in the Kerr-like medium

Abstract

A general formalism of a three-level atom interacting with one-mode or two-mode cavity fields in a Kerr-like medium is presented. Dynamic behaviours of the atomic occupation probabilities and the transfer phenomena are investigated numerically in two typical cases. Our results show that the transfer phenomena may depend on the initial conditions.     

中国计量科学研究院建成量子化霍尔电阻标准

国际计量委员会推荐，1990年1月1日起在世界范围内启用量子化霍尔电阻标准代替使用了几十年的电阻实物基准。中国计量科学研究院经过十几年的努力，在2003年建成了量子化霍尔电阻标准。课题组自主研制了能满足实际量值传递工作要求的量子化霍尔器件，并建成了高精度的低温电流比较仪，以把量子化霍尔电阻量值传递到日常检定工作中使用的十进电阻值。课题成果中有多项独创性的成就。目前所建量子化霍尔电阻标准的不确定度为10^-10量级，达到国际领先水平。     

Rayleigh wave interaction with inhomogeneities—Part II: The buried cavity and inclusion

The elastodynamic interaction between an explosively generated Rayleigh pulse and a buried imperfection such as a cavity or an inclusion in a half plane is investigated. Dynamic photoelasticity was employed to obtain full field information for data analysis. Measurements of the stress distribution along the free boundary of the half plane and the cavity and along the cavity/inclusion interface have been made. Results show that fractures occur for shallow as well as for deeper burial depths initiating from the cavity boundary.     

A scheme for a conditional quantum phase gate using a bimodal cavity and a ladder-type three-level atom

A scheme is proposed to implement a two-qubit conditional quantum phase gate for the intracavity field using a single ladder-type three-level atom driven by two modes in a high-Q cavity. The quantum information is encoded on the Fock states of a bimodal cavity. The averaged fidelity of the gate can be expected to reach 99.86%.     

Variation of constants in the extended standard model. Part 2. Experimental constraints on the possible variations

The paper discusses possible signs of time variation in the constants for the extended standard model. Existing experimental constraints on the magnitude of the changes are given in order to allow for the possible effects on the metrological characteristics of primary standards for the units of physical quantities. Translated from Izmeritel'naya Tekhnika, No. 9, pp. 15–19, September, 2008.     

Two-level atom and multichromatic waves in a lossless cavity

Abstract

In this paper, we shall examine a generalized version of the Jaynes-Cummings model in which a two-level atom moves in a lossless cavity and is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that both the motion of the atom and the photon conversion between multichromatic waves are dynamically correlated. Using the semiclassical approximations introduced in a previous paper, we obtain the equations which describe the dynamics of this quantum system and discuss the solutions in several special cases. In particular, we point out that the motion of the atom may be controlled by the electromagnetic modes, and vice versa, that is the amplitudes and phases of the electromagnetic fields in the cavity may also be determined by the position of the atom.     

The velocity field in quantum hydrodynamics

In the usual form of quantum hydrodynamics the velocity field is defined in terms of the inverse density operator ^–1(x). It is found that this inverse does not exist. An unambiguous velocity field can, however, be constructed without the use of ^–1(x) by requiring that its Fourier components be canonical conjugates to the corresponding Fourier components of the density operator when the system is in a box with periodic boundary conditions. This velocity field has at mostN nonzero Fourier components whereN is the number of particles in the system; it satisfiesj(x)=1/2[(x)v(x)+v(x)(x)]; it has the proper behavior under galilean transformations; and the corresponding classical field is uniquely determined at theN particle positions, where it is equal to the particle velocity, and is a smooth interpolating field between these points. The velocity is not defined uniquely at positions where there are no particles, but this is a reflection of the atomicity of the system—a field uniquely defined at each point in space would represent a continuum with an infinity of degrees of freedom. The commutation relations of the velocity field with itself and with the current density are derived and found to be similar but not identical to those given by Landau.Based on work performed under the auspices of the U.S. Atomic Energy Commission     

The constants of the standard model and the possible reduction in their number on changing to grand unification models

Some methods of determining the constants of the Standard Model, the values of the constants established at the present time, and the dependence of the coupling constants of the strong, electromagnetic and weak interactions on the characteristic energy of the process are presented. Possible generalizations of the Standard Model, which lead to a reduction in the number of fundamental constants, are considered. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 3–7, March, 2007.     

Anisotropy of electron-phonon interaction spectra in a magnetic field and quantum interference effects in antimony point contacts

Peculiarities of point-contact spectra behavior of antimony are investigated in a magnetic field. It turns out that the singularities in the spectra can both decrease and increase depending not only on orientation of the contact axes with respect to the crystallographic axis of Sb and the magnetic field vector, but also on the ratio between the contact diameter, the Larmour radius of the charge carriers and their mean free path. The spectrum sign inversion for a dirty contact that is due to electron state delocalization as a result of electronphonon interaction is detected. It means that point-contact spectroscopy is possible in highly disordered materials when the quantum localization is significant.     

A cohesive micromechanic fatigue model. Part II: Fatigue-creep interaction and Goodman diagram

A Cohesive Micromechanic Fatigue Model (CMFM), which identifies a chemical reaction between a broken chain and its neighbor as the main micro-scale source of fatigue failure has been developed recently. The successive chain breakages which control the damage evolution were characterized by the statistical strength distribution of the chains and the probability of the neighbor to break. The model explained the power law S-N curve for high cycle fatigue and the endurance limit phenomenon.

In this study, the basic concept is expanded by defining two kinds of breakage sources for the neighbors. A dynamic type, associated with the local transient disturbance, occurring during breakage, and a static type, related to the relative motion between adjacent chains. The first is dominated by the strain at the breaking point and leads to a creep like macro response. The second is a function of the maximum strain difference experienced during unloading, which causes fatigue failure.

The interaction between the two mechanisms gives a total macro response which depends on both the mean and the alternate stress. Results provide a theoretical explanation to the empirical “Goodman diagram” and to the low cycle fatigue behavior. The effect of different probability functions for the chemical reaction was studied. An activation type was found most suitable for predicting the macro response, and a Weibull distribution has been used. All material parameters which were introduced on the microscale, have a direct, uncoupled outcome on the macro response.     

A quantum loop in magnetic field and a quantum interference rectifier

The electron transport in a curvilinear quantum wire exposed to a magnetic field was studied. A possible design of the quantum interference rectifier is suggested.