Sagnac Effect of Gödel's Universe

We present exact expressions for the Sagnac effect of Gödel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Gödel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.     

Modeling and simulation of polarization errors in Sagnac fiber optic current sensor

Sagnac fiber optic current sensor (S-FOCS) is a kind of optical interferometer based on Sagnac structure, optical polarization states of sensing light wave in Sagnac fiber optic current sensor are limited. However, several factors induce optical polarization error, and non-ideal polarized light waves cause the interference signal crosstalk in sensor, including polarizer, quarter-wave retarder, splice angular, birefringence and so on. With these errors, linearly polarized light wave in PM fiber and circularly polarized light wave in sensing fiber become elliptically polarized light wave, then, nonreciprocal phase shift induced by magnetic field of the current is interrupted by wrong polarization state. To clarify characteristics of optical polarization error in fiber optic current sensor, we analyze the evolution process of random optical polarization state, linear optical polarization state and circular optical polarization state in Sagnac fiber optic current sensor by using Poincare sphere, then, build optical polarization error models by using Jones matrix. Based on models of polarization state in Sagnac fiber optic current sensor, we investigate the influence of several main error factors on optical polarization error characteristics theoretically, including extinction ratio in polarizer, phase delay in quarter-wave retarder, splice angular between quarter-wave retarder and polarization maintaining fiber. Finally, we simulate and quantify nonreciprocal phase shift to be detected in fiber optic current sensor related with optical polarization errors. In the end, we demonstrate S-FOCS in test. The results show that transfer matrix errors are induced by inaccurate polarization properties during polarization state conversion, then, the stability and accuracy of the S-FOCS are affected, and it is important to control the polarization properties at each step of the polarization state conversion precisely.     

A Direct Kinematical Derivation of the Relativistic Sagnac Effect for Light or Matter Beams

The Sagnac time delay and the corresponding Sagnac phase shift, for relativistic matter and electromagnetic beams counter-propagating in a rotating interferometer, are deduced on the ground of relativistic kinematics. This purely kinematical approach allows to explain the universality of the effect, namely the fact that the Sagnac time difference does not depend on the physical nature of the interfering beams. The only prime requirement is that the counter-propagating beams have the same velocity with respect to any Einstein synchronized local co-moving inertial frame.     

Interferometry with Ca atoms

Separated field excitation of a calcium atomic beam using four traveling laser fields represents two distinct atom interferometers utilizing the internal degrees of freedom of the atoms. Phase shifts between the atomic partial waves have been realized by phase shifts of the laser wave fields, by the ac-Stark shift, and by rotation of the interferometer (Sagnac effect). One particular interferometer can be selected by interaction of the atomic waves with extra laser fields. We furthermore report on the preparation of a laser cooled and deflected calcium atomic beam that can be utilized to largely increase the sensitivity of the interferometer.     

Internal structure of a classical spinning electron

A classical model of the spinning electron in general relativity consisting of a rotating charge distribution with Poincaré stresses is set up. It is made out of a continuous superposition of thin charged shells with differential rotation. Each elementary shell is maintained in stationary equilibrium in the gravitational field created by the others. A class of interior solutions of the Kerr-Newman field is thus obtained. The corresponding stress-energy tensor naturally splits into the sum of two terms. The first one is the Maxwell tensor associated to a rotating charge distribution, and the second one corresponds to a material source having zero energy density everywhere, no radial pressure, and an isotropic transverse stress. These negative pressures or tensions are identified with the cohesive forces introduced by Poincaré to stabilize the Lorentz electron model. They are shown to be the source of a negative gravitational mass density and thereby of the violation of the energy conditions inside the electron.     

The Generalized Stefan-Boltzmann Law of Slowly Changing Kerr-Newman Black Hole

Using the entropy density near the event horizon of Kerr-Newman black hole, the instantaneous radiation energy flux and the instantaneous radiation power of the slowly changing Kerr-Newman black hole have been studied. It is found that the thermal radiation of the Kerr-Newman black hole always satisfies the generalized Stefan-Boltzmann law and is affected by the gravitational field, the electromagnetic field around the black hole and the change of black hole event horizon. But the rate of the change of the event horizon usually makes very little affect on the instantaneous radiation energy flux and radiation power. Only when the rate of the change of the event horizon approaches to the light speed, it can make obviously affect on them.     

A nonstationary generalization of the Kerr-Newman metric

A new metric depending on three arbitrary parameters is presented by the method of complex coordinate transformations. It gives the gravitational field of a radiating rotating charged body. The metric is algebraically special of Petrov type II according to classification of the Weyl tensor, with a twisting, shear-free, null congruence identical to that of the Kerr-Newman metric. The new metric bears the same relation to the Kerr-Newman metric as the Bonner-Vaidya metric does to the Reissner-Nordstrom metric.     

计算光在引力场中偏折的新方法

利用光的量子论,能量守恒及弱等效原理得出电磁波传播在几何近似下,光线在引力场中的偏转角和波矢的关系. 利用引力场中电磁波方程,在弱场近似下给出了一般的计算光线偏转角度的方法. 具体计算了Schwarzchild引力场中光线的偏折及Kerr-Newman引力场中光线的偏折. 关键词： 引力场 电磁波方程 能量守恒 弱场近似     

Coupled-resonator-induced transparency in two microspheres as the element of angular velocity sensing

We proposed a two-coupled microsphere resonator structure as the element of angular velocity sensing under the Sagnac effect.We analyzed the theoretical model of the two coupled microspheres,and derived the coupled-resonatorinduced transparency(CRIT) transfer function,the effective phase shift,and the group delay.Experiments were also carried out to demonstrate the CRIT phenomenon in the two-coupled microsphere resonator structure.We calculated that the group index of the two-coupled sphere reaches n_g = 180.46,while the input light at a wavelength of 1550 nm.     

延迟线长度对全光纤光学电流互感器的影响

基于法拉第效应的Sagnac干涉仪型光学电流互感器可精确测量电流,因此受到广泛关注。延迟线在典型的串联型电流互感器结构中起到不可或缺的作用,其长度变化会影响系统输出,从而有可能使解调出的法拉第相移引入误差。通过对琼斯矩阵得出的理想系统输出进行理论分析与数值仿真实验,研究了延迟线长度变化对尺度因子的影响。研究结果表明,在一定条件下,延迟线长度失匹配会使尺度因子误差超过0.2%,而温度变化导致的延迟线光程变化产生的尺度因子误差不够明显。因此,建议在采用典型的串联型Sagnac结构及该解调方案时,延迟线长度最好与调制圆频率相匹配,如有特殊需求,实际长度与匹配长度的偏差不要超过50m,或者将所有器件整合在一起,采用专用线传输。     

Coriolis force and Sagnac effect

The optical Sagnac effect is considered, when the fictitious gravitational field simulates the reflections from the mirrors. It is shown that no contradiction exists between the conclusions of the laboratory and rotated observers. Because of the acting of a gravity-like Coriolis force, the trajectories of coand anti-rotating photons have different radii in the rotating reference frame, while in the case of equal radii the effective gravitational potentials for the photons have to be different.     

Phase properties of a Jaynes-Cummings model with Stark shift and Kerr medium

Phase properties of the field interacting with a two-level atom in a lossless cavity Jaynes-Cummings model, taking into account the level shifts produced by Stark effect with an additional Kerr medium for one-mode are studied using the phase formalism of Pegg and Barnett. It is shown in particular that phase properties of the field reflect the collapse and revival phenomena. The results for the time evolution of the phase probability distribution and the phase fluctuations are obtained. The effect of Stark shift on the phase properties in both the absence and presence of a Kerr medium is analyzed. Phase localization is found for certain choice of the parameters. Received: 27 March 1998 / Revised: 8 June 1998 / Accepted: 9 June 1998     

Neutron interference in the Earth’s gravitational field

This work relates to the famous experiments, performed in 1975 and 1979 by Werner et al., measuring neutron interference and neutron Sagnac effects in the earth’s gravitational field. Employing the method of Stodolsky in its weak field approximation, explicit expressions are derived for the two phase shifts, which turn out to be in agreement with the experiments and with the previously obtained expressions derived from semi-classical arguments: these expressions are simply modified by relativistic correction factors.     

Neutrino Oscillations in the de Sitter and the Anti-de Sitter Space-Time

General expressions of the neutrino oscillation phase in the generally static space-time with spherical symmetry are given. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. We find that a blue shift of the oscillation length takes place when the neutrino travels out of the gravitational field. Then, we discuss the variation of the oscillation length influenced by the cosmological constant. In the de Sitter space-time, the positive cosmological constant prolongs the oscillation length. And, in the anti-de Sitter space-time, the negative cosmological constant shortens it as expected.     

Backward influence of the interference signal from the sensors of physical quantities on the radiation intensity spectrum of a low-coherent source

We consider specific features of optical-circuit operation in the presence of radiation which is returned to the source after having passed an optical path exceeding the initial coherence length of the reference wave when, as was previously assumed, the delay modulation should not influence the oscillation mode. However, experiments with the Michelson and Sagnac fiber interferometers showed that intensity modulation of the interference signal and, therefore, intensity modulation of the source radiation related to the active-medium nonlinearity appear when the interfering waves with the phase-difference modulation return. The revealed effect leads to distortion of a signal at the interferometer output irrespectively of the delay time and can be removed by placing an optical isolator at the source output.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

On the possibility of measuring the gravitational interaction of the neutron with a macroscopic body

The possibility of experimentally observing the gravitational interaction of the neutron with a macroscopic body is discussed. It is shown that the sensitivity of neutron-optics experiments may be one to two orders of magnitude higher than that which is necessary for observing the gravitational effect. Either the deflection of the neutron trajectory in the gravitational field of a heavy attractor or the gravitation-induced shift of the neutron-wave phase can be recorded experimentally.