Tunable beam displacer

We report the implementation of a tunable beam displacer, composed of a polarizing beam splitter (PBS) and two mirrors, that divides an initially polarized beam into two parallel beams whose separation can be continuously tuned. The two output beams are linearly polarized with either vertical or horizontal polarization and no optical path difference is introduced between them. The wavelength dependence of the device as well as the maximum separation between the beams achievable is limited mainly by the PBS characteristics.Comment: 3 pages, 2 figure

Rolling of asymmetric disks on an inclined plane

In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the common misconception that the instantaneous point of contact of the rolling body with the plane can be used to evaluate the angular momentum $\mathbf L$ and the torque $\boldsymbol\tau$ in the equation of motion $d\mathbf L/dt = \boldsymbol\tau$. To obtain the correct equation of motion, the "phantom torque" or various rules that depend on the motion of the point about which $\mathbf L$ and $\boldsymbol\tau$ are evaluated were discussed. In this paper, I consider asymmetric disks rolling down an inclined plane and describe the most basic way of obtaining the correct equation of motion; that is, to choose the point about which $\mathbf L$ and $\boldsymbol\tau$ are evaluated that is stationary in an inertial frame

Optical analog of Rabi oscillation suppression due to atomic motion

The Rabi oscillations of a two-level atom illuminated by a laser on resonance with the atomic transition may be suppressed by the atomic motion through averaging or filtering mechanisms. The optical analogs of these velocity effects are described. The two atomic levels correspond in the optical analogy to orthogonal polarizations of light and the Rabi oscillations to polarization oscillations in a medium which is optically active, naturally or due to a magnetic field. In the later case, the two orthogonal polarizations could be selected by choosing the orientation of the magnetic field, and one of them be filtered out. It is argued that the time-dependent optical polarization oscillations or their suppression are observable with current technology.Comment: 10 pages, 10 figure

Riccati parameter modes from Newtonian free damping motion by supersymmetry

We determine the class of damped modes \tilde{y} which are related to the common free damping modes y by supersymmetry. They are obtained by employing the factorization of Newton's differential equation of motion for the free damped oscillator by means of the general solution of the corresponding Riccati equation together with Witten's method of constructing the supersymmetric partner operator. This procedure leads to one-parameter families of (transient) modes for each of the three types of free damping, corresponding to a particular type of %time-dependent angular frequency. %time-dependent, antirestoring acceleration (adding up to the usual Hooke restoring acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y}, where \gamma is the family parameter that has been chosen as the inverse of the Riccati integration constant. In supersymmetric terms, they represent all those one Riccati parameter damping modes having the same Newtonian free damping partner modeComment: 6 pages, twocolumn, 6 figures, only first 3 publishe

Atom laser dynamics in a tight-waveguide

We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. During the time evolution the density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir.Comment: 6 pages, 5 figures, to be published in the Proceedings of the 395th WE-Heraeus Seminar on "Time Dependent Phenomena in Quantum Mechanics ", organized by T. Kramer and M. Kleber (Blaubeuren, Germany, September 2007

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

Dynamics of an Inelastic Gravitational Billiard with Rotation

The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries, where we include rotational effects and additional forms of energy dissipation. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. The simulations demonstrate that the parabola has stable, periodic motion, while the wedge and hyperbola (at high driving frequencies) appear chaotic. The hyperbola, at low driving frequencies, behaves similarly to the parabola; i.e., has regular motion. Direct comparisons are made between the model's predictions and previously published experimental data. The value of the coefficient of restitution employed in the model resulted in good agreement with the experimental data for all boundary shapes investigated. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.Comment: 11 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1103.443

Unsuitability of the moving light clock system for the Lorentz factor derivation

The moving light clock system was analyzed with respect to the orientation of the wavefront of the light pulse observed in the moving and stationary frames of reference. The plane wavefront of the light pulse was oriented horizontally in both the frames. The wavefront observed in the stationary frame was not perpendicular to the direction of the light pulse propagation. This showed different characteristics of the light pulse than that assumed in the Lorentz factor derivation. According to the horizontal orientation of the wavefront, velocity c was determined as the vertical component of the light pulse motion observed in the stationary frame. Application of this velocity distribution in the Lorentz factor derivation showed the same travel time for the light pulse observed in the moving and stationary frames of reference. The moving light clock system was therefore found to be unsuitable for the Lorentz factor derivation and illustration of time dilation, and shown to illustrate the relativity of the observation of light rather than the relativity of time.Comment: 4 pages, 5 figure