636 research outputs found

### 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

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