155 research outputs found
Measuring the quantum statistics of an atom laser beam
We propose and analyse a scheme for measuring the quadrature statistics of an
atom laser beam using extant optical homodyning and Raman atom laser
techniques. Reversal of the normal Raman atom laser outcoupling scheme is used
to map the quantum statistics of an incoupled beam to an optical probe beam. A
multimode model of the spatial propagation dynamics shows that the Raman
incoupler gives a clear signal of de Broglie wave quadrature squeezing for both
pulsed and continuous inputs. Finally, we show that experimental realisations
of the scheme may be tested with existing methods via measurements of Glauber's
intensity correlation function.Comment: 4 pages, 3 figure
On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
We consider two families of commuting Hamiltonians on the cotangent bundle of
the group GL(n,C), and show that upon an appropriate single symplectic
reduction they descend to the spectral invariants of the hyperbolic Sutherland
and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The
duality symplectomorphism between these two integrable models, that was
constructed by Ruijsenaars using direct methods, can be then interpreted
geometrically simply as a gauge transformation connecting two cross sections of
the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex
Strong relative intensity squeezing by 4-wave mixing in Rb vapor
We have measured -3.5 dB (-8.1 dB corrected for losses) relative intensity
squeezing between the probe and conjugate beams generated by stimulated,
nondegenerate four-wave mixing in hot rubidium vapor. Unlike early observations
of squeezing in atomic vapors based on saturation of a two-level system, our
scheme uses a resonant nonlinearity based on ground-state coherences in a
three-level system. Since this scheme produces narrowband, squeezed light near
an atomic resonance it is of interest for experiments involving cold atoms or
atomic ensembles.Comment: Submitted to Optics Letter
The Maupertuis principle and canonical transformations of the extended phase space
We discuss some special classes of canonical transformations of the extended
phase space, which relate integrable systems with a common Lagrangian
submanifold. Various parametric forms of trajectories are associated with
different integrals of motion, Lax equations, separated variables and
action-angles variables. In this review we will discuss namely these induced
transformations instead of the various parametric form of the geometric
objects
Functional representations of integrable hierarchies
We consider a general framework for integrable hierarchies in Lax form and
derive certain universal equations from which `functional representations' of
particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in
terms of functional equations, are systematically and quite easily obtained.
The formalism genuinely applies to hierarchies where the dependent variables
live in a noncommutative (typically matrix) algebra. The obtained functional
representations can be understood as `noncommutative' analogs of `Fay
identities' for the KP hierarchy.Comment: 21 pages, version 2: equations (3.28) and (4.11) adde
Painleve IV and degenerate Gaussian Unitary Ensembles
We consider those Gaussian Unitary Ensembles where the eigenvalues have
prescribed multiplicities, and obtain joint probability density for the
eigenvalues. In the simplest case where there is only one multiple eigenvalue
t, this leads to orthogonal polynomials with the Hermite weight perturbed by a
factor that has a multiple zero at t. We show through a pair of ladder
operators, that the diagonal recurrence coefficients satisfy a particular
Painleve IV equation for any real multiplicity. If the multiplicity is even
they are expressed in terms of the generalized Hermite polynomials, with t as
the independent variable.Comment: 17 page
Lie point symmetries and first integrals: the Kowalevsky top
We show how the Lie group analysis method can be used in order to obtain
first integrals of any system of ordinary differential equations.
The method of reduction/increase of order developed by Nucci (J. Math. Phys.
37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor
considered. The most striking example we present is the relationship between
Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page
From white elephant to Nobel Prize: Dennis Gaborâs wavefront reconstruction
Dennis Gabor devised a new concept for optical imaging in 1947 that went by a variety of names over the following decade: holoscopy, wavefront reconstruction, interference microscopy, diffraction microscopy and Gaboroscopy. A well-connected and creative research engineer, Gabor worked actively to publicize and exploit his concept, but the scheme failed to capture the interest of many researchers. Gaborâs theory was repeatedly deemed unintuitive and baffling; the technique was appraised by his contemporaries to be of dubious practicality and, at best, constrained to a narrow branch of science. By the late 1950s, Gaborâs subject had been assessed by its handful of practitioners to be a white elephant. Nevertheless, the concept was later rehabilitated by the research of Emmett Leith and Juris Upatnieks at the University of Michigan, and Yury Denisyuk at the Vavilov Institute in Leningrad. What had been judged a failure was recast as a success: evaluations of Gaborâs work were transformed during the 1960s, when it was represented as the foundation on which to construct the new and distinctly different subject of holography, a re-evaluation that gained the Nobel Prize for Physics for Gabor alone in 1971. This paper focuses on the difficulties experienced in constructing a meaningful subject, a practical application and a viable technical community from Gaborâs ideas during the decade 1947-1957
Non-destructive, dynamic detectors for Bose-Einstein condensates
We propose and analyze a series of non-destructive, dynamic detectors for
Bose-Einstein condensates based on photo-detectors operating at the shot noise
limit. These detectors are compatible with real time feedback to the
condensate. The signal to noise ratio of different detection schemes are
compared subject to the constraint of minimal heating due to photon absorption
and spontaneous emission. This constraint leads to different optimal operating
points for interference-based schemes. We find the somewhat counter-intuitive
result that without the presence of a cavity, interferometry causes as much
destruction as absorption for optically thin clouds. For optically thick
clouds, cavity-free interferometry is superior to absorption, but it still
cannot be made arbitrarily non-destructive . We propose a cavity-based
measurement of atomic density which can in principle be made arbitrarily
non-destructive for a given signal to noise ratio
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