Theory of Atom Optics: Feynman’s Path Integral Approach

The present theory of atom optics is established mainly on the Schrödinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.     

Theory of atom optics: Feynman''s path integral approach (Ⅱ)

In the preceding paper, we discussed eight configurations of particle Fraunhofer diffraction. In this paper, we consider nine configurations of particle Fresnel diffraction, and have derived the wave functions of particles in these configurations. Furthermore, the author presents a new inertial navigator principle. Its devised accuracy is not lower than that of the inertial navigator based on cold atom interferometer. The new inertial navigator is named as ABSE inertial navigator. ABSE is abbreviation for Aharonov-Bohm-Sagnac effect.      

Theory of atom optics: Feynman’s path integral approach (II)

In the preceding paper, we discussed eight configurations of particle Fraunhofer diffraction. In this paper, we consider nine configurations of particle Fresnel diffraction, and have derived the wave functions of particles in these configurations. Furthermore, the author presents a new inertial navigator principle. Its devised accuracy is not lower than that of the inertial navigator based on cold atom interferometer. The new inertial navigator is named as ABSE inertial navigator. ABSE is abbreviation for Aharonov-Bohm-Sagnac effect.     

Lecture Demonstration of Fresnel Diffraction by a Slit and Half-Plane

In the present work, lecture demonstration of Fresnel diffraction by a slit and half-plane with the use of modern scientific means of optical experimentation is described. The developed software allows light diffraction to be modeled on a personal computer depending on the wavelength, slit width, and distance from the slit (half-plane) to the screen and simultaneously a graphic method of calculating the field amplitude with the help of the Cornu spiral to be demonstrated. A photodetector system built around a video camera controlled by a personal computer is used to register an actual diffraction pattern. The experimental intensity distributions are compared with the theory. The integrated approach allows the efficiency of comprehension of complex diffraction phenomena in wave optics to be increased. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 9–15, June, 2005.     

Analytical model of the enhanced light transmission through subwavelength metal slits: Green’s function formalism versus Rayleigh’s expansion

We present an analytical model of the resonantly enhanced transmission of light through a subwavelength nm-size slit in a thick metal film. The simple formulae for the transmitted electromagnetic fields and the transmission coefficient are derived by using the narrow-slit approximation and the Green’s function formalism for the solution of Maxwell’s equations. The resonance wavelengths are in agreement with the semi-analytical model [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)], which solves the wave equations by using the Rayleigh field expansion. Our formulae, however, show great resonant enhancement of a transmitted wave, while the Rayleigh expansion model predicts attenuation. The difference is attributed to the near-field subwavelength diffraction, which is not considered by the Rayleigh-like expansion models. PACS 42.25.Bs; 42.65.Fx; 42.79.Ag; 42.79.Dj     

New Prospects for de Broglie Interferometry

We consider various effects that are encountered in matter wave interference experiments with massive nanoparticles. The text-book example of far-field interference at a grating is compared with diffraction into the dark field behind an opaque aperture, commonly designated as Poisson’s spot or the spot of Arago. Our estimates indicate that both phenomena may still be observed in a mass range exceeding present-day experiments by at least two orders of magnitude. They both require, however, the development of sufficiently cold, intense and coherent cluster beams. While the observation of Poisson’s spot offers the advantage of non-dispersiveness and a simple distinction between classical and quantum fringes in the absence of particle wall interactions, van der Waals forces may severely limit the distinguishability between genuine quantum wave diffraction and classically explicable spots already for moderately polarizable objects and diffraction elements as thin as 100 nm.     

Knife-edge diffraction pattern as an interference phenomenon: An experimental reality

This paper demonstrates that a knife-edge diffraction pattern is, indeed, due to the interference of two superimposing waves: the geometrical wave and the boundary diffraction wave. Within the framework of boundary diffraction wave theory it is shown that this diffraction pattern can easily be broadened in such a manner that a single fringe covers the whole field of view. At this point the system converges to a schlieren diffraction interferometer and could be used for the study of phase objects using diffraction-limited optics. Experimental observations show that the method bears a similarity to that of any known two-beam interferometer, e.g. Mach-Zehnder interferometer. The experimental details have been presented and the results are compared with a two-beam holographic interferometer and a point diffraction interferometer.     

Partially coherent Fresnel diffraction by a slit aperture. IV. Effect of the phase term in the coherence function

A formula was derived in paper 1 of the this series for investigating the Fresnel diffraction field of a slit aperture when the mutual coherence function of the illumination contains a quadratic phase term. That formula is applied to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source. The phase term has a big effect on the features of Fresnel diffraction.     

The Theory of (Exclusively) Local Beables

It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.     

Are quantum wave packets observable? Sokolov effect: puzzling generation of 2p states in the 2s hydrogen beam passing trough a wide metal slit

The observation of excitation of 2p states in a collimated 2s hydrogen beam passing through a wide metal slit with no direct contacts or electric field applied (Sokolov effect) up to now has had no reasonable explanation. A solution presented in this paper is formulated within the standard quantum-mechanical framework with a consecutive wave packet treatment of the atomic center-of-mass wave function. It is found that a very weak interaction of the beam diffraction halo with the slit, though negligible for center-of-mass motion, coherently affects the intrinsic state of an atom in the beam and efficiently induces transitions. High sensitivity of this interference phenomena may be used to measure transverse coherence length of the beam.Received: 25 March 2003, Published online: 15 July 2003PACS: 03.65.-w Quantum mechanics     

Directly recording diffraction phenomena in time domain

By making use of a new technique for measuring the complete spatiotemporal electric field of light with micrometer spatial and femtosecond temporal resolution, we directly demonstrate the formation of the so-called boundary diffraction wave and Arago’s spot, as well as the superluminal propagation of a “diffraction-free” pulse. We believe that such spatiotemporally resolved measurements and the time-domain treatment of diffracting waves not only turn out to be useful for modern physical optics, especially in micro- and meso-optics, but also significantly aid in the understanding of diffraction phenomena in general.     

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.     

Structure of boundary diffraction wave revisited

The physically appealing boundary diffraction wave theory which suggests that diffraction patterns arise due to interference of an undisturbed (geometrical) wave and the boundary diffraction wave generated by edge of the diffracting aperture, simplifies the solution of diffraction problems by reducing the Fresnel–Kirchhoff surface integral into a line integral over the illuminated boundary of the diffracting aperture. The present work reports experimental investigations carried out on the structure of the boundary diffraction wave. It has been shown that the boundary diffraction wave is continuous behind the diffracting aperture and apparently there does not exist any discontinuity at the geometrically light to shadow transition boundary, as is required by the theory. PACS 42.25.-p; 42.25.Fx; 42.25.Hz     

Classical and Non-relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter.     

Diffraction of the wave packet of a three-level Λ atom in the field of a multifrequency standing light wave

The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997)     

Scattering of waves by an aperture in an impedance screen

The transmission and diffraction of waves by an aperture in an impedance screen is investigated. The Senior's solution of the scattering problem of waves by an impedance half-plane is transformed into a physical optics type integral. The obtained method is applied to the transmission problem of waves by a slit in an impedance screen. The results are compared with the aperture problem in black and conducting screens numerically.     

Optodynamic description of a linear momentum transfer from a laser induced ultrasonic wave to a rod

We present a new optodynamic experimental technique to measure the linear momentum obtained by a rod during a nanosecond laser pulse ablation of the rod’s front face on the basis of the displacement due to an ultrasonic wave reflection at its rear end. With the help of a simple theory, we explained the step-like motion of the rod’s free end. This theory conforms well with the general shape of the measured displacement history curve. The acquired momentum can be directly estimated by measuring the height of a step from the step-like motion of the rod’s end. Measurements based on an arm-compensated Michelson interferometer also enabled us to follow the attenuation of an ultrasonic wave and so to determine the characteristic attenuation time. This quantity plays a major role in the transfer of linear momentum from within the initial ultrasonic wave to the final net uniform motion of the specimen. PACS  52.38.Mf; 43.35.Yb; 43.35.Cg