1,171 research outputs found
Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
It is known that actions of field theories on a noncommutative space-time can
be written as some modified (we call them -modified) classical actions
already on the commutative space-time (introducing a star product). Then the
quantization of such modified actions reproduces both space-time
noncommutativity and usual quantum mechanical features of the corresponding
field theory. The -modification for arbitrary finite-dimensional
nonrelativistic system was proposed by Deriglazov (2003). In the present
article, we discuss the problem of constructing -modified actions for
relativistic QM. We construct such actions for relativistic spinless and
spinning particles. The key idea is to extract -modified actions of the
relativistic particles from path integral representations of the corresponding
noncommtative field theory propagators. We consider Klein-Gordon and Dirac
equations for the causal propagators in such theories. Then we construct for
the propagators path-integral representations. Effective actions in such
representations we treat as -modified actions of the relativistic
particles. To confirm the interpretation, we quantize canonically these
actions. Thus, we obtain the Klein-Gordon and Dirac equations in the
noncommutative field theories. The -modified action of the relativistic
spinning particle is just a generalization of the Berezin-Marinov
pseudoclassical action for the noncommutative case
Complementarity and the uncertainty relations
We formulate a general complementarity relation starting from any Hermitian
operator with discrete non-degenerate eigenvalues. We then elucidate the
relationship between quantum complementarity and the Heisenberg-Robertson's
uncertainty relation. We show that they are intimately connected. Finally we
exemplify the general theory with some specific suggested experiments.Comment: 9 pages, 4 figures, REVTeX, uses epsf.sty and multicol.st
Single-particle nonlocality and entanglement with the vacuum
We propose a single-particle experiment that is equivalent to the
conventional two-particle experiment used to demonstrate a violation of Bell's
inequalities. Hence, we argue that quantum mechanical nonlocality can be
demonstrated by single-particle states. The validity of such a claim has been
discussed in the literature, but without reaching a clear consensus. We show
that the disagreement can be traced to what part of the total state of the
experiment one assigns to the (macroscopic) measurement apparatus. However,
with a conventional and legitimate interpretation of the measurement process
one is led to the conclusion that even a single particle can show nonlocal
properties.Comment: 6 pages, 5 figure
Afshar's Experiment does not show a Violation of Complementarity
A recent experiment performed by S. Afshar [first reported by M. Chown, New
Scientist {\bf 183}, 30 (2004)] is analyzed. It was claimed that this
experiment could be interpreted as a demonstration of a violation of the
principle of complementarity in quantum mechanics. Instead, it is shown here
that it can be understood in terms of classical wave optics and the standard
interpretation of quantum mechanics. Its performance is quantified and it is
concluded that the experiment is suboptimal in the sense that it does not fully
exhaust the limits imposed by quantum mechanics.Comment: 6 pages, 6 figure
Quantum Cryptography Using Single Particle Entanglement
A quantum cryptography scheme based on entanglement between a single particle
state and a vacuum state is proposed. The scheme utilizes linear optics devices
to detect the superposition of the vacuum and single particle states. Existence
of an eavesdropper can be detected by using a variant of Bell's inequality.Comment: 4 pages, 3figures, revte
Atom gratings produced by large angle atom beam splitters
An asymptotic theory of atom scattering by large amplitude periodic
potentials is developed in the Raman-Nath approximation. The atom grating
profile arising after scattering is evaluated in the Fresnel zone for
triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It
is shown that, owing to the scattering in these potentials, two
\QTR{em}{groups} of momentum states are produced rather than two distinct
momentum components. The corresponding spatial density profile is calculated
and found to differ significantly from a pure sinusoid.Comment: 16 pages, 7 figure
Teleportation of a quantum state of a spatial mode with a single massive particle
Mode entanglement exists naturally between regions of space in ultra-cold
atomic gases. It has, however, been debated whether this type of entanglement
is useful for quantum protocols. This is due to a particle number
superselection rule that restricts the operations that can be performed on the
modes. In this paper, we show how to exploit the mode entanglement of just a
single particle for the teleportation of an unknown quantum state of a spatial
mode. We detail how to overcome the superselection rule to create any initial
quantum state and how to perform Bell state analysis on two of the modes. We
show that two of the four Bell states can always be reliably distinguished,
while the other two have to be grouped together due to an unsatisfied phase
matching condition. The teleportation of an unknown state of a quantum mode
thus only succeeds half of the time.Comment: 12 pages, 1 figure, this paper was presented at TQC 2010 and extends
the work of Phys. Rev. Lett. 103, 200502 (2009
Low-noise AlGaAsSb avalanche photodiodes for 1550 nm light detection
Avalanche photodiodes (APD) can improve the signal to noise ratio in applications such as LIDAR, range finding and optical time domain reflectometry. However, APDs operating at eye-safe wavelengths around 1550 nm currently limit the sensitivity because the APDs’ impact ionization coefficients in the avalanche layers are too similar, leading to poor excess noise performance. The material AlGaAsSb has highly dissimilar impact ionization coefficients (with electrons dominating the avalanche gain) so is an excellent avalanche material for 1550 nm wavelength APDs. We previously reported a 1550 nm wavelength AlGaAsSb SAM APD with extremely low excess noise factors, 1.93 at a gain of 10 and 2.94 at a gain of 20. Using a more optimized design, we have now realized an AlGaAsSb SAM APD with a lower dark current (7 nA at a gain of 10 from a 230 μm diameter APD), a higher responsivity (0.97 A/W) and a lower excess noise (1.9 at a gain of 40), compared to our previous SAM APD. Noise-equivalent-power (NEP) measurements of our APD with a simple transimpedance amplifier circuit produced an NEP 12 times lower than a state-of-the-art APD under identical test conditions, confirming the advantage of low-noise AlGaAsSb SAM APDs
Direct measurement of optical quasidistribution functions: multimode theory and homodyne tests of Bell's inequalities
We develop a multimode theory of direct homodyne measurements of quantum
optical quasidistribution functions. We demonstrate that unbalanced homodyning
with appropriately shaped auxiliary coherent fields allows one to sample
point-by-point different phase space representations of the electromagnetic
field. Our analysis includes practical factors that are likely to affect the
outcome of a realistic experiment, such as non-unit detection efficiency,
imperfect mode matching, and dark counts. We apply the developed theory to
discuss feasibility of observing a loophole-free violation of Bell's
inequalities by measuring joint two-mode quasidistribution functions under
locality conditions by photon counting. We determine the range of parameters of
the experimental setup that enable violation of Bell's inequalities for two
states exhibiting entanglement in the Fock basis: a one-photon Fock state
divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced
in the process of non-degenerate parametric down-conversion.Comment: 18 pages, 7 figure
Notes on a paper of Mess
These notes are a companion to the article "Lorentz spacetimes of constant
curvature" by Geoffrey Mess, which was first written in 1990 but never
published. Mess' paper will appear together with these notes in a forthcoming
issue of Geometriae Dedicata.Comment: 26 page
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