On mechanical motion damping of a magnetically trapped diamagnetic particle

We discuss eddy-current-induced limitations of the attenuation of mechanical motion of a diamagnetic particle trapped by an inhomogeneous magnetic field in the Earth's gravitational potential. We show that the mechanical frequency of the particle oscillation is independent on the particle properties and is proportional to the free fall acceleration constant, similarly to the classical mechanical pendulum. The frequency can be used to measure the gravity field. The eddy-current induced attenuation constant does not depend on the mass of the particle and reduces with the particle volume. The quality factor of the mechanical motion can be as high as 10⁹ and is comparable with the attenuation due to interaction of the particle with incompletely evacuated air. A possibility of usage of the particle as a quantum mechanical system is discussed.     

Inertial and gravitational mass in quantum mechanics

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.     

A new type of quantum interferometer for gravitational wave detection

We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave. In particular, a gravitational wave with amplitude h = 10⁻²³ will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion.     

Is gravitational mass of a composite quantum body equivalent to its energy?

We define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.     

Remarks concerning the notion of free fall in axiomatic space-time theory

The notion of free fall plays a central role in EPS axiomatics. A constructive procedure for the detection of freely falling gravitational monopoles has been elaborated by Coleman and Korté. This was done in order to eliminate the vagueness of the primitive notion of free fall from spacetime theory. In this paper it is shown that neither the gravitational monopoles nor their free fall can be detected by the proposed procedure alone, without using physical laws beyond the mentioned spacetime theories. For this purpose, two examples of geodesic directing fields in a Schwarzschild space time are presented, one for particles obeying a special Lorentz-force equation and one for objects obeying Papapetrou's spinning particle equation. Two possibilities are discussed to overcome the difficulties of the constructive procedure.     

Bound states of a gravitational soliton and a test particle

Classical and quantum bound states of a test particle in the regular gravitational field of a gravitational soliton are investigated. The quantum spectrum is very similar to that of a Newtonian atom, except for the absence ofs orbitals.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

The electrostatic and gravitational field of spherically symmetric objects

The electrostatic and gravitational fields of an extended spherically symmetric object is presented. The limit to a point-like object is discussed for Born-Infeld type of electrodynamics and it is shown, that the extreme Reissner-Nordstrøm field, where no event horizon occurs, is unphysical.     

Resonance spectroscopy of gravitational states of antihydrogen

We study a method to induce resonant transitions between antihydrogen ( \(\bar {H}\) ) quantum states above a material surface in the gravitational field of the Earth. The method consists in applying a gradient of magnetic field which is temporally oscillating with the frequency equal to a frequency of a transition between gravitational states of antihydrogen. Corresponding resonant change in a spatial density of antihydrogen atoms can be measured as a function of the frequency of applied field. We estimate an accuracy of measuring antihydrogen gravitational states spacing and show how a value of the gravitational mass of the \(\bar {H}\) atom can be deduced from such a measurement.     

Approximate Real–Time Visualization of a Quantum Transition by Means of Continuous Fuzzy Measurement

For the detection of gravitational waves the quantum mechanical properties of the detector have to be taken into account. Not all gravitational wave detectors allow a quantum nondemolition (QND) measurement. Continuous weak or fuzzy measurements are an alternative to study the evolution of a quantum mechanical system under the influence of an external field. In the present paper we investigate this alternative by applying it to a simplified system. We numerically simulate continuous fuzzy measurements of the oscillations of a two-level atom subjected to a resonant external light field. We thereby address the question whether it is possible to measure characteristic features of the evolution of a single quantum system in real time without relying on a QND scheme. We compare two schemes of continuous measurement: continuous measurement with constant fuzziness and with fuzziness changing in the course of the measurement. Because the sensitivity of the two-level atom to the influence of the measurement depends on the state of the atom, it is possible to optimize the continuous fuzzy measurement by varying its fuzziness.     

HYPER: A Satellite Mission in Fundamental Physics Based on High Precision Atom Interferometry

The article presents the HYPER project, a proposal for a satellite mission on precision matter-wave interferometry. For the mission several scientific objectives are under investigation, for which atom interferometers proved on ground to be a true complementary and competitive alternative for classical concepts: The application of atom interferometers as gyroscopes, the measurement of the gravitational acceleration (including tests of the universality of the free fall of atoms) and the precise determination of the fine-structure constant. The paper focuses on the use of cold-atom gyroscopes to map the Lense-Thirring effect close by the Earth and reports on results of recent feasibility studies of the European Space Agency. HYPER requires new concepts of compact, high-resolution matter-wave gyroscopes, which are better adapted to the use in satellite based experiments. The article will give a concise overview of the status and strategies in the field.     

Displacement-noise-free gravitational-wave detection

We present a new idea that allows us to detect gravitational waves without being disturbed by any kind of displacement noise, based on the fact that gravitational waves and test-mass motions affect the propagations of light differently. We demonstrate this idea by analyzing a simple toy model consisting of three equally-separated objects on a line. By taking a certain combination of light travel times between these objects, we construct an observable free from the displacement of each object, which has a reasonable sensitivity to gravitational waves.     

Deterrents to a Theory of Quantum Gravity

As shown previously, quantum mechanics directly violates the weak equivalence principle in general, and thus indirectly violates the strong equivalence principle in all dimensions. The present paper shows that quantum mechanics also directly violates the strong equivalence principle unless it is arbitrarily abetted in hindsight. Vital domains are shown to exist in which quantum gravity would be non-applicable. There are classical subtleties in which the strong equivalence principle appears to be violated, but is not. Neutron free fall interference experiments in a gravitational field are examined, as is Galileo's falling body assertion and the misconception it leads to.     

玻色-爱因斯坦凝聚态的结构理论研究系列之一:玻色-爱因斯坦凝聚态的复合表示理论

针对近零温度下玻色-爱因斯坦凝聚态的特点,建立了复合原子表示模型.提出了复合原子的概念,研究发现复合原子具有一定的零点半径与结合能,得出了相应的表达式.认为该物态作为一个宏观量子态的说法具有相对性,应该据研究角度而定.同时,给出了二个分离的玻色-爱因斯坦凝聚态之间产生1/R型作用势的几种情况,为同类实验提供了理论依据.     

Repulsive gravitational effect of a quantum wave packet and experimental scheme with superfluid helium

We consider the gravitational effect of quantum wave packets when quantum mechanics, gravity, and thermodynamics are simultaneously considered. Under the assumption of a thermodynamic origin of gravity, we propose a general equation to describe the gravitational effect of quantum wave packets. In the classical limit, this equation agrees with Newton’s law of gravitation. For quantum wave packets, however, it predicts a repulsive gravitational effect. We propose an experimental scheme using superfluid helium to test this repulsive gravitational effect. Our studies show that, with present technology such as superconducting gravimetry and cold atom interferometry, tests of the repulsive gravitational effect for superfluid helium are within experimental reach.     

Gravitational Perturbations on Local Experiments in a Satellite: The Dragging of Inertial Frame in the HYPER Project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Thirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.     

Quantum experiments with macroscopic mechanical objects

Recent achievements in the isolation of macroscopic mechanical objects from a heat bath make it possible to implement quantum measurements with such systems. In this case, either a free mass or an oscillator can be used as a test object. The advantage of the first variant is in significantly longer relaxation times achieved for free masses. The advantage of the second variant is in the absence of restrictions on the limiting measurement accuracy associated with internal losses in the meter. This restriction can be bypassed, retaining a long relaxation time typical of free masses, if a test oscillator with a ponderomotive electromagnetic rigidity is used. Estimates show that the potential sensitivity of this test body for the modern level of technology may be considerably higher than the standard quantum limit.     

Chimera states in an ensemble of linearly locally coupled bistable oscillators

Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.