Dušan Arsenović

Electromagnetic energy flow lines as possible paths of photons

Motivated by recent experiments where interference patterns behind a grating are obtained by accumulating single photon events, we provide here an electromagnetic energy flow-line description to explain the emergence of such patterns. We find and discuss an analogy between the equation describing these energy flow lines and the equation of Bohmian trajectories used to describe the motion of massive particles.

Should particle trajectories comply with the transverse momentum distribution

Abstract.The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.

Semi-classical quantization of the magnetic top

SummaryThe magnetic top (A. O. Barut, M. Bozić and Z. Marić:Ann. Phys. (N.Y.),214, (1992) 53) is quantized using the Bohr-Sommerfeld-Einstein (BSE) and the Einstein-Brillouin-Keller (EBK) quantization methods. It has been previously quantized by canonical, Schrödinger (A. O. Barut, M. Bozić and Z. Marić:Ann. Phys. (N.Y.),214, (1992) 53) and path-integral methods (A. O. Barut and I. Duru:Phys. Lett. A,158, (1991) 441). By comparing the exact wave functions with the semi-classical ones, it is concluded that the usual conditions of quantization should be modified in order to allow for half-integer values of canonical angular momentum (spin). This modification requires to abandon the condition of single-valuedness of wave functions. We justify this using Pauli’s and the Reiss argumentation that single-valuedness of wave functions does not follow from basic quantum-mechanical postulates and that a certain kind of multi-valued (i.e. path-dependent) wave functions cannot be excludeda priori.

Coherent processes in electromagnetically induced absorption: a steady and transient study

A perturbation method was used to solve optical Bloch equations (OBEs) for the transition Fg=1→Fe=2, in order to describe the role of ground-level Zeeman coherences in the formation of electromagnetically induced absorption (EIA). A narrow Lorentzian peak, centered at zero value of the scanning magnetic field, appears in the analytical expression of the second-order correction of a density-matrix element for ground-level Zeeman coherences, (ρg−1, g+1)x2. Through analytical expressions for lower-order corrections of density-matrix elements, we were able to establish clear relations between the narrow Lorentzian in (ρg− 1, g+1)x2 and higher-order corrections of optical coherences, i.e. EIA. We see from analytical expressions that these two resonances have opposite signs and that EIA becomes electromagnetically induced transparency (EIT) in the limit of low efficiency of spontaneous transfer of coherences from excited-level to ground-level Zeeman sublevels. The transient behavior of EIA follows the time evolution of (ρg− 1, g+1)x2. After the coupling laser is turned on, both the Lorentzian peak in (ρg− 1, g+1)x2 and EIA reach steady state via over-damped oscillations.

Enhancement of electromagnetically induced absorption with elliptically polarized light - laser intensity dependent coherence effect

Using the (2)S(1/2)F(g) = 2 --> (2)P(3/2)F(e) = 3 transition in (87)Rb vapor at room temperature, we study effect of the laser light polarization on the electromagnetically induced absorption (EIA). This work extends the recent study of the behavior of the EIA as a function of the laser ellipticity (Brazhnikov et. al., JETP Lett. 83, 64, 2006). We have shown that such behavior strongly depends on the laser power. For the low laser power EIA amplitude has maximum for linearly polarized light, while for high laser power elliptically polarized light of ellipticity 15-20 degrees generates maximum of the EIA amplitude. EIA width varies slowly with the laser ellipticity at lower laser power, and much stronger at higher laser power. Through our theoretical model we attributed observed results to combined effect of the laser ellipticity and power on the population of ground state Zeeman sublevels.

Is the classical law of the addition of probabilities violated in quantum interference

We analyse and compare the positive and negative arguments on whether quantum interference violates the classical law of the addition of probabilities. The analysis takes into account the results of recent interference experiments in neutron, electron and atom optics. Nonclassical behaviour of atoms was found in atomic experiments where the measurements included their time of arrival and space distribution. We determine probabilities of elementary events associated with the nonclassical behaviour of particles in interferometers. We show that the emergence of the interference pattern in the process of accumulation of such elementary events is consistent with the classical law of the addition of probabilities.

Trajectory-based interpretation of Young's experiment, the Arago–Fresnel laws and the Poisson–Arago spot for photons and massive particles

We present a trajectory-based interpretation of Youngs experiment, the Arago–Fresnel laws and the Poisson–Arago spot. This approach is based on the equation of the trajectory associated with the quantum probability current density in the case of massive particles, and the Poynting vector for the electromagnetic field in the case of photons. Both the form and properties of the evaluated photon trajectories are in good agreement with the averaged trajectories of single photons observed recently in Youngs experiment by Steinbergs group at the University of Toronto. In the case of the Arago–Fresnel laws for polarized light, the trajectory interpretation presented here differs from interpretations based on the concept of ‘which-way’ (or ‘which-slit’) information and quantum erasure. More specifically, the observers information about the slit that the photons went through is not relevant to the existence of interference; what is relevant is the form of the electromagnetic energy density and its evolution, which will model consequently the distribution of trajectories and their topology. Finally, we also show that the distributions of end points of a large number of evaluated photon trajectories are in agreement with the distributions measured at the screen behind a circular disc, clearly giving rise to the Poisson–Arago spot.

On non-vanishing amplitude of Hanle electromagnetically induced absorption in Rb.

Amplitude and linewidts of the Hanle EIA, obtained from transmission of the laser locked to closed F(g) ? F(e) = F(g) +1 transitions in (85)Rb and(87)Rb, have maximum values at few mW/cm2. Amplitude of the EIA reaches steady value different from zero for higher laser intensities, even for laser intensities of 40 mW/cm(2). Theoretical model of EIA, for the same atomic system as in the experiment, show that the laser intensity, at which maximum of amplitudes and widths occur, depends on the laser detuning. For smaller laser detuning of a few tens of MHz, EIA has a maximum and then vanishes at higher laser intensities. For larger laser detuning of the order of hundreds MHz (but still in the range of Doppler broadening) amplitude of the EIA has very broad maximum and remains above zero for intensities above 40 mW/cm(2). Such theoretical results indicate that Hanle absorption peak remains in the experimental results, regardless of the laser intensities, due to Doppler effect.

Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis

The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.

Simplified model of low energy x-ray backscattering

The reflection of x-rays from a half space is studied within the framework of a model that assumes multiple isotropic scattering of photons without energy loss. An exactly solvable analytical expression for the angular distribution of reflected photons is derived. The range of validity of the model was determined by the Monte Carlo simulation thereby incorporating energy loss and angular dependences. For water as a scatterer, in the energy range from 10 to 60 keV, which is often used in x-ray diagnostics, the two approaches differ by at most 5%. The analytic results, confirmed by the Monte Carlo simulation, show that the angular distribution of reflected photons for energies greater than 30 keV--where multiple scattering events dominate--may be represented by a cosine law, within a few per cent of accuracy.