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The nonanalytic property of metric resulting from the presence of gravitomagnetic monopoles is considered. The curvature tensors, dual curvature tensors, dual Einstein tensor (and hence the gravitational field equation of gravitomagnetic matter) expressed in terms of nonanalytic metric are analyzed. It is shown that the spinor gravitomagnetic monopole may be one of the potential origins of the cosmological constant. An alternative approach to the cosmological constant problem is thus proposed based on the concept of gravitomagnetic monopole., Comment: 5 pages, no figures. Keywords: Gravitomagnetic monopole; Nonanalytic metric; Dual curvature tensors; cosmological constant

The quantum vacuum contribution to Berry's geometric phase of photon fields inside a noncoplanarly curved (coiled) fiber is considered by means of the second-quantization formulation. It is shown that the quantum vacuum Berry's phases of left- and right-handed circularly polarized light have the equal magnitudes but opposite signs, and are therefore eliminated entirely by each other. In order to realize such a novel vacuum effect, a scheme to separate the quantum vacuum Berry's phase of one polarized light from another by using the chiral medium fiber is suggested. We think the present study might be the first treatment for the time evolution of vacuum zero-point energy., Comment: 4 pages, Latex

The phenomenological description of propagation of atomic matter waves inside a curved atom wave guide is presented based on the effective action principle. The evolutions in both temporal and spatial domains for the atomic matter wave in the presence of guiding potential fields (classical and quantized) are considered. The coherent control of three-level atomic matter waves in a wave guide by an external controlling light is briefly discussed. The concepts of {\it atomic matter-wave bandgap structure} in a spatially periodic guiding field ({\it e.g.}, the interior potential of carbon peapod which can trap both atoms and light) and {\it optical lattice bandgap medium} are suggested., Comment: 8 pages, Latex, 0 figure

The su$(n)$ Lie algebraic structure of the Pegg-Barnett oscillator that possesses a finite-dimensional number-state space is demonstrated. The supersymmetric generalization of Pegg-Barnett oscillator is suggested. It is shown that such a supersymmetric Pegg-Barnett oscillator may have some potential applications, {\it e.g.}, the mass spectrum of the charged leptons., Comment: 4 pages, Latex, 0 figure

The theoretical mechanism for realizing the negative refractive index with {\it electromagnetically induced transparency} (EIT) is studied. It is shown that in a three-level dense atomic gas, there is a frequency band in which the EIT medium will exhibit simultaneously negative electric permittivity and magnetic permeability in the optical frequency range, and the atomic gas thus becomes a left-handed material. The expressions for the electric permittivity and the magnetic permeability for the probe frequency is presented. One of the remarkable features of the present novel scheme is such that the obtained EIT left-handed material is {\it isotropic} and may therefore have some potentially important applications in the development of new techniques in quantum optics., Comment: 5 pages, 3 figures, Latex

The adiabatic solutions of Maxwell-Bloch equation governing the three-level EIT medium is presented. The time evolution of the density matrix elements of the EIT system and the probe light is thus investigated by using the adiabatic approximation formulation and the slowly varying envelope condition., Comment: 6 pages, Latex, one figure

More recently, Feigel has considered the quantum vacuum contribution to the momentum of electromagnetic media. However, in Feigel's treatment he did not take into account the relativistic transformation of the optical constants (electric permittivity and magnetic permeability) of moving media. Here it is shown that the effect arising from such a transformation will also provide a quantum vacuum contribution to the velocity of media, in addition to the one derived by Feigel himself., Comment: latex

The Lorentz transformations for the optical constants (electric permittivity, magnetic permeability and index of refraction) of moving media are considered., Comment: 4 pages, 0 figure, latex

The nature of Mashhoon's spin-rotation coupling is the interaction between a particle spin (gravitomagnetic moment) and a gravitomagnetic field. Here we will consider the coupling of graviton spin to the weak gravitomagnetic fields by analyzing the Lagrangian density of weak gravitational field, and hence study the purely gravitational generalization of Mashhoon's spin-rotation couplings., Comment: 4 pages, 0 figure, Latex

It is shown that the valency electrons in rapidly rotating C_{60} molecules acquire an Aharonov-Carmi (A-C) phase shift, which is proportional to the molecular angular velocity flux enclosed by the matter wave of valency electrons on the C_{60} molecular shell. The energy shift of the valency electrons due to both the molecular rapid rotation and the molecular A-C phase shift is calculated., Comment: 3 pages, 0 figure, latex

The elimination of decoherence of a multiphoton two-state quantum system by using an appropriate external driving field is considered. The multiphoton process caused by the noise field has a supersymmetric Lie algebraic structure. The time-evolution equations for the off-diagonal elements of the density operator of the two-state system are derived in the interaction picture. A simple explicit formula is given for the time-dependent external driving field used to eliminate the decoherence of the multiphoton two-state system., Comment: 6 pages, 2 figures

General formulae for the transient evolution of the susceptibility (absorption) induced by the quantum interference effect in a four-level N-type EIT medium is presented. The influence of the signal light on the transient susceptibility for the probe beam is studied for two typical cases when the strength of the coupling beam is much greater or less than that of the signal field. An interesting level reciprocity relationship between these two cases is found., Comment: 8 pages+3 figures, Latex

Three weak gravitational effects associated with the gravitomagnetic fields are taken into account in this paper: (i) we discuss the background Lorentz transformation and gauge transformation in a linearized gravity theory, and obtain the expression for the spin of gravitational field by using the canonical procedure and Noether theorem; (ii) we point out that by using the coordinate transformation from the fixed frame to the rotating frame, it is found that the nature of Mashhoon's spin-rotation coupling is in fact an interaction between the gravitomagnetic moment of a spinning particle and the gravitomagnetic fields. The fact that the rotational angular velocity of a rotating frame can be viewed as a gravitomagnetic field is demonstrated; (iii) a purely gravitational generalization of Mashhoon's spin-rotation coupling, i.e., the interaction of the graviton spin with the gravitomagnetic fields is actually a self-interaction of the spacetime (gravitational fields). In the present paper, we will show that this self-interaction will also arise in a non-inertial frame of reference itself: specifically, a rotating frame that experiences a fluctuation of its rotational frequency (i.e., the change in the rotational angular frequency) will undergo a weak self-interaction. The self-interaction of the rotating frame, which can also be called the self-interaction of the spacetime of the rotating frame, is just the non-inertial generalization of the interaction of the graviton spin with the gravitomagnetic fields., Comment: 8 pages, 0 figure, Latex. It is a supplement to the paper: Purely gravitational generalization of spin-rotation couplings, J.Q. Shen, Phys. Rev. D vol.70: 067501 (2004)

This paper demonstrates that there is much similarity in the mathematical formalisms between the optical constants of artificial electromagnetic media (such as chiral media, left-handed media, photonic crystals and EIT media) and some physical phenomena in field theory, including general relativity, quantum mechanics, energy band theory, etc. The significance of such comparisons lies in that: (i) the unification in mathematical descriptions shows that many physical phenomena and effects, which seem to have no connections between them, actually share almost the same mathematical structures; (ii) it can provide clue to us on suggesting more new effects which is similar in mathematical descriptions to the familiar phenomena in other areas., Comment: 7 pages, Latex

A new scheme of realizing the nonadiabatic conditional geometric phase shift via a noncoplanar (and coiled) fiber system is presented in this Letter. It is shown that the effective Hamiltonian that describes the interaction of polarized photons with the fiber medium is just the Wang-Keiji type of Hamiltonian. This, therefore, means that the coiled fiber system may be an ideal implementation of realizing the nonadiabatic geometric phase gates for the topological quantum computation. The remarkable feature of the present method is that it can automatically meet the conditions and requirements proposed in the Wang-Keiji scheme: (i) in the coiled fiber system, the dynamical phase of photon wavefunction caused by the interaction Hamiltonian automatically vanishes; (ii) the Wang-Keiji requirement for the parameters in the Wang-Keiji Hamiltonian can be exactly satisfied automatically in the fiber system; (iii) the conditional initial state can be easily achieved by manipulating the initial wave vector of polarized photons. Due to these three advantages, the coiled fiber system may be a potentially practical way of achieving the nonadiabatic conditional geometric phase shift (and hence the nonadiabatic geometric quantum gates)., Comment: 4 pages, Latex

A phenomenological description of time evolution of atomic matter waves inside a spiral shaped atomic-wave guide is presented in this report. We study three related topics: (i) the effective Hamiltonian and the time-development equation governing the matter waves; (ii) wavefunctions describing the matter waves in the noncoplanar atom guide; (iii) showing that such wavefunctions obtained is just the eigenstates of the atomic momentum operator. It is believed that both the idea and the results presented here may have relevance to some fundamental problems of atom optics., Comment: 3 pages, Latex. Submitted to PRA for publication as a brief report

The oscillator algebra of Pegg-Barnett (P-B) oscillator with a finite-dimensional number-state space is investigated in this note. It is shown that the Pegg-Barnett oscillator possesses the su($n$) Lie algebraic structure. Additionally, we suggest a so-called supersymmetric P-B oscillator and discuss the related topics such as the algebraic structure and particle occupation number of supersymmetric P-B oscillator., Comment: 4 pages, Latex

In this note we show the existence of the hyperbolical geometric quantum phase that is different from the ordinary trigonometric geometric quantum phase. Gravitomagnetic charge (dual mass) is the gravitational analogue of magnetic monopole in Electrodynamics; but, as will be shown here, it possesses more interesting and significant features, {\it e.g.}, it may constitute the dual matter that has different gravitational properties compared with mass. In order to describe the space-time curvature due to the topological dual mass, we construct the dual Einstein's tensor. Further investigation shows that gravitomagnetic potentials caused by dual mass are respectively analogous to the trigonometric and hyperbolic geometric phase. The study of the geometric phase and dual mass provides a valuable insight into the time evolution of quantum systems and the topological properties in General Relativity., Comment: 3 pages, Latex

This paper is devoted to investigating the physically interesting optical and electromagnetic properties, phenomena and effects of wave propagation in the negative refractive index materials, which is often referred to as the {\it left-handed media} in the literature. This paper covers a wide range of subjects and related topics of left-handed media such as many mathematical treatment of fundamental effects ({\it e.g.}, the reflection and the refraction laws on the interface between LH and RH media, the group velocity and energy density in dispersive materials, the negative optical refractive index resulting from a moving regular medium, the reversal of Doppler effect in left-handed media, the reversal of Cerenkov radiation in left-handed media, the optical refractive index of massive particles and physical meanings of left-handed media, the anti-shielding effect and negative temperature in left-handed media, {\it etc.}), and their some applications to certain areas ({\it e.g.}, three kinds of compact thin subwavelength cavity resonators (rectangular, cylindrical, spherical) made of left-handed media, the photon geometric phases due to helicity inversions inside a periodical fiber made of left-handed media, {\it etc.})., Comment: 44 pages, Latex

In the present paper we investigate the restriction conditions for three kinds of cavity resonators ({\it i.e.}, the rectangular, cylindrical, spherical resonators). It is shown that the layer of materials with negative optical refractive indices can act as a phase compensator/conjugator, and thus by combining such a layer with another layer made of the regular medium one can obtain a so-called compact thin subwavelength cavity resonator., Comment: seven pages, Latex, 0 figure

We study the quantum-vacuum geometric phases resulting from the vacuum fluctuation of photon fields in Tomita-Chiao-Wu noncoplanar curved fibre system, and suggest a scheme to test the potential existence of such vacuum effect. Since the signs of the quantum-vacuum geometric phases of left- and right- handed (LRH) circularly polarized light are just opposite, the total geometric phases at vacuum level is inescapably absent in the fibre experiments performed previously by other authors. By using the present approach where the fibre made of gyroelectric media is employed, the quantum-vacuum geometric phases of LRH light cannot be exactly cancelled, and may therefore be achieved test experimentally., Comment: 3 pages, Latex

In this paper, we assume that the observer is fixed in a comoving frame of reference with $g_{00}=\frac{\lambda}{\Lambda}$, where $\lambda$ and $\Lambda$ denote the comoving parameter and the cosmological constant, respectively. By using the {\it comoving suppression mechanism} and {\it Mach's principle} (the latter of which is used to determine the comoving parameter $\lambda$), we calculate the vacuum energy density of quantum fluctuation field in the above-mentioned comoving frame of reference. It is shown that in such a comoving frame of reference, the cosmological constant will greatly decrease by many orders of magnitude (if Mach's principle is applied to this calculation, then it will be shown that $\Lambda$ is reduced by about 120 orders of magnitude). Additionally, we briefly discuss the related topics such as the varying observed speed of light ($\frac{{\rm d}c}{{\rm d}t}={\mathcal O}(10^{-9}{\rm m/s}^{2})$) and the mystery of anomalous acceleration ($\sim 10^{-9}{\rm m/s}^{2}$) acquired by the Pioneer 10/11, Galileo and Ulysses spacecrafts., Comment: 4 pages, Latex

The elimination of decoherence of two-state quantum systems interacting with a thermal reservoir through an external controllable driving field is discussed in the present paper. The restriction equation with which the external controllable driving field should agree will be derived. Based on this, we obtain the time-development equation of the off-diagonal elements of density operator in the supersymmetric multiphoton two-state quantum systems, which is helpful for studying the polarization evolution in this two-state quantum model., Comment: 5 pages, Latex

This note is devoted to the detailed mathematical treatment of the coupling of graviton spin to gravitomagnetic fields. The expression (i.e., $\sim g_{0m}\dot{g}_{0n}(\partial_{m}g_{0n}-\partial_{n}g_{0m})$) for the graviton spin-gravitomagnetic (S-G) coupling in the Lagrangian/Hamiltonian density of the weak gravitational fields is presented in this note., Comment: 4 pages, Latex. This paper presenting the trivial and lengthy calculations only serves as the supplement to a paper entitled "The purely gravitational generalization of spin-rotation couplings" (by J.Q. Shen): Phys. Rev. D vol.70: 067501 (2004)

This note discusses the motion of a charged particle in the magnetic dipole field and a modified Barut's lepton mass formula. It is shown that a charged particle in the magnetic dipole filed has no bound states, which means that Barut's lepton mass formula may have no physical basis., Comment: 4 pages, no figures, Latex

Gravitomagnetic charge that can also be referred to as the {\it dual mass} or {\it magnetic mass} is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low-motion weak-field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the dual relationship between the dynamical theories of gravitomagnetic charge (dual mass) and gravitoelectric charge (mass) is also taken into account in the present paper., Comment: 20 pages, Latex (There are some minor revisions made to the published paper)

The optical refractive index of a moving regular medium is calculated by using the Lorentz transformation in this note. It is shown that in some velocity region of medium moving relative to the initial frame K, the moving medium may possess a negative index of refraction measured by the observer fixed at the frame of reference K., Comment: 2 pages, Larex

This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way., Comment: 4 pages, Latex

We investigate the oscillator algebra of the Pegg-Barnett oscillator with a finite-dimensional number-state space and show that it possesses the su($n$) Lie algebraic structure. In addition, a so-called supersymmetric Pegg-Barnett oscillator is suggested, and the related topics such as the algebraic structure and particle occupation number of the Pegg-Barnett oscillator are briefly discussed., Comment: 5 pages, Latex

We show that the solution obtained by Bekkar {\it et al.} in their comment [Phys. Rev. A {\bf 68}, 016101 (2003)] on Guedes's work of solving the quantum system with a time-dependent linear potential is still {\it not} the {\it general} one of the Schr\"{o}dinger equation. It is concluded that Bekkar {\it et al.}'s solution (corresponding to the linear Lewis-Riesenfeld invariant) and our solution (corresponding to the quadratic-form Lewis-Riesenfeld invariant) presented here will constitute together a complete set of solutions (general solutions) of the time-dependent Schr\"{o}dinger equation of the system under consideration., Comment: 2 pages, Latex

This note considers two related topics regarding the {\it self-induced charge current} in the experiments detecting photon rest mass: (i) the effective rest mass, $(0.3\sim 1)\times 10^{-54}$ Kg, of photons arising from the ions in the secondary cosmic ray is compared to Luo {\it et al.}'s new upper limit on photon rest mass ($1.2\times 10^{-54}$ Kg); (ii) there are two main classes of experiments to detect photon rest mass based respectively on the Amp\`{e}re-Maxwell-Proca equation and the Lagrangian (or Hamiltonian) density of electromagnetically interacting system., Comment: 3 pages, Latex

This note is concerned with the connections between the conformal group and the quantum states of photons. It is shown that there exist analogies between the photonic quantum states and the conformal group, namely, the time-development operator (with a free Hamiltonian), displacement and squeezing operators of the vacuum state corresponds to the dilatation, translation, proper Lorentz transformations, respectively, and that the three quantum states of photons ({\it i.e.}, Fock state, coherent state and squeezed state) in quantum optics thus bear some analogy to the above three transformations in the conformal group. Based on this comparison, we argue by analogy that if the phase transformation operators acting on a vacuum state (hence the Fock state, coherent state and squeezed state are generated) are truly exactly analogous to the conformal transformations, then a fourth quantum state of photons (referred to as the {\it conformal state}), which corresponds to the {\it special conformal} transformation (acceleration transformation) and will therefore be of special physical interest, can be suggested., Comment: 4 pages, Latex

By making use of the Lewis-Riesenfeld invariant theory, the solution of the Schr\"{o}dinger equation for the time-dependent linear potential corresponding to the quadratic-form Lewis-Riesenfeld invariant $I_{\rm q}(t)$ is obtained in the present paper. It is emphasized that in order to obtain the general solutions of the time-dependent Schr\"{o}dinger equation, one should first find the complete set of Lewis-Riesenfeld invariants. For the present quantum system with a time-dependent linear potential, the linear $I_{\rm l}(t)$ and quadratic $I_{\rm q}(t)$ (where the latter $I_{\rm q}(t)$ cannot be written as the squared of the former $I_{\rm l}(t)$, {\it i.e.}, the relation $I_{\rm q}(t)= cI_{\rm l}^{2}(t)$ does not hold true always) will form a complete set of Lewis-Riesenfeld invariants. It is also shown that the solution obtained by Bekkar {\it et al.} more recently is the one corresponding to the linear $I_{\rm l}(t)$, one of the invariants that form the complete set. In addition, we discuss some related topics regarding the comment [Phys. Rev. A {\bf 68}, 016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63}, 034102 (2001)] and Guedes's corresponding reply [Phys. Rev. A {\bf 68}, 016102 (2003)]., Comment: six pages; Latex; I think that this paper will be a supplement to the recent comment [Phys. Rev. A {\bf 68}, 016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63}, 034102 (2001)] and Guedes's reply to Bekkar {\it et al.}'s comment

This paper is concerned with the connection between density matrix method, supersymmetric quantum mechanics and Lewis-Riesenfeld invariant theory. It is shown that these three formulations share the common mathematical structure: specifically, all of them have the invariant operators which satisfies the Liouville-Von Neumann equation and the solutions to the time-dependent Schr\"{o}dinger equation and/or Schr\"{o}dinger eigenvalue equation can be constructed in terms of the eigenstates of the invariants., Comment: 4 pages, Latex

Three related topics on the quantum-vacuum geometric phases in a noncoplanarly curved optical fiber is presented: (i) a brief review: the investigation of vacuum effect and its experimental realization; (ii) the sequence of ideas of geometric phases in the fiber; (iii) three derivations of effective Hamiltonian that describes the wave propagation of photon field in a curved fiber., Comment: 5 pages, Latex; The present paper is a supplement to the paper: arXiv: quant-ph/0309007 (entitled: An experimental realization of quantum-vacuum geometric phases by using the gyrotropic-medium optical fiber). It is a supplement to the paper: Quantum-vacuum geometric phases in the noncoplanarly curved fiber system, J.Q. Shen, The European Physical Journal D, vol. 30: 259-264 (2004)

The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal product procedure is considered in the present Letter. In order to investigate this physically interesting geometric phases at quantum-vacuum level, we suggest an experimentally feasible scheme to test it by means of a noncoplanarly curved fiber made of gyrotropic media. A remarkable feature of the present experimental realization is that one can easily extract the nonvanishing and nontrivial quantum-vacuum geometric phases of left- and/or right- handed circularly polarized light from the vanishing and trivial total quantum-vacuum geometric phases., Comment: 4 pages, Latex

In this Letter the expression for the refractive index of de Broglie wave in the presence of a potential field is obtained and based on this, the physical meanings of negative index of refraction is revealed. We demonstrate that the electromagnetic wave propagation in a left-handed medium with negative refractive index behaves just like that of antiphotons, which is required of the complex vector field theory. It is believed that the complex vector field theory is helpful in considering the wave propagation and photonic band gap structure in the left-handed medium photonic crystals with a periodicity in negative and positive index of refraction., Comment: 11 pages, Latex

The contribution of self-induced charge currents of metamaterial media to photon effective rest mass is discussed in detail in the present paper. We concern ourselves with two kinds of photon effective rest mass, i.e., the frequency-dependent and frequency-independent effective rest mass. Based on these two definitions, we calculate the photon effective rest mass in the left-handed medium and the 2TDLM media, the latter of which is described by the so-called two time derivative Lorentz material (2TDLM) model. Additionally, we concentrate primarily on the torque, which is caused by the interaction between self-induced charge currents in dilute plasma (e.g., the secondary cosmic rays) and interstellar magnetic fields (ambient cosmic magnetic vector potentials), acting on the torsion balance of the rotating torsion balance experiment., Comment: 11 pages, Latex

An experimentally feasible realization of testing quantum-vacuum geometric phases of photons by using a gyrotropic-medium optical fibre via Casimir's effect is proposed., Comment: 2 pages, Latex

Some physically interesting properties and effects of wave propagation in biaxially anisotropic left-handed materials are investigated in this paper. We show that in the biaxially gyrotropic left-handed material, the left-right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media. It is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left-handed media we will present a different geometric phase that is independent of the cone angles. The extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left- and right- handed (LRH) media is also studied in detail by using the Lewis-Riesenfeld invariant theory. Some interesting applications (e.g., controllable position-dependent frequency shift, detection of quantum-vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left-handed media is briefly discussed., Comment: 18 pages, 0 figure, Latex

Neutron spin can be coupled to the Earth's rotating frequency. Once if the Earth's rotating frequency is time-dependent, then the neutron will acquire a Berry's topological phase (cyclic adiabatic geometric phase). So, a potential method to investigate the Earth's time-varying rotating frequency by measuring the phase difference between geometric phases of neutron spin polarized vertically down and up is proposed., Comment: 1 page, Latex