140 research outputs found
Overcoming loss of contrast in atom interferometry due to gravity gradients
Long-time atom interferometry is instrumental to various high-precision
measurements of fundamental physical properties, including tests of the
equivalence principle. Due to rotations and gravity gradients, the classical
trajectories characterizing the motion of the wave packets for the two branches
of the interferometer do not close in phase space, an effect which increases
significantly with the interferometer time. The relative displacement between
the interfering wave packets in such open interferometers leads to a fringe
pattern in the density profile at each exit port and a loss of contrast in the
oscillations of the integrated particle number as a function of the phase
shift. Paying particular attention to gravity gradients, we present a simple
mitigation strategy involving small changes in the timing of the laser pulses
which is very easy to implement. A useful representation-free description of
the state evolution in an atom interferometer is introduced and employed to
analyze the loss of contrast and mitigation strategy in the general case. (As a
by-product, a remarkably compact derivation of the phase-shift in a general
light-pulse atom interferometer is provided.) Furthermore, exact results are
obtained for (pure and mixed) Gaussian states which allow a simple
interpretation in terms of the alignment of Wigner functions in phase-space.
Analytical results are also obtained for expanding Bose-Einstein condensates
within the time-dependent Thomas-Fermi approximation. Finally, a combined
strategy for rotations and nonaligned gravity gradients is considered as well.Comment: 14+7 pages including appendices, 9 figures; v2 minor changes, matches
published versio
Conformal Mapping and Bound States in Bent Waveguides
Is it possible to trap a quantum particle in an open geometry? In this work
we deal with the boundary value problem of the stationary Schroedinger (or
Helmholtz) equation within a waveguide with straight segments and a rectangular
bending. The problem can be reduced to a one dimensional matrix Schroedinger
equation using two descriptions: oblique modes and conformal coordinates. We
use a corner-corrected WKB formalism to find the energies of the one
dimensional problem. It is shown that the presence of bound states is an effect
due to the boundary alone, with no classical counterpart for this geometry. The
conformal description proves to be simpler, as the coupling of transversal
modes is not essential in this case.Comment: 16 pages, 10 figures. To appear in the Proceedings of the Symposium
"Symmetries in Nature, in memoriam Marcos Moshinsky
Fractional Talbot effect in phase space: A compact summation formula
A phase space description of the fractional Talbot effect, occurring in a
one-dimensional Fresnel diffraction from a periodic grating, is presented.
Using the phase space formalism a compact summation formula for the Wigner
function at rational multiples of the Talbot distance is derived. The summation
formula shows that the fractional Talbot image in the phase space is generated
by a finite sum of spatially displaced Wigner functions of the source field.Comment: 4 pages, LaTeX. Submitted to Optics Expres
Endoscopic Tomography and Quantum-Non-Demolition
We propose to measure the quantum state of a single mode of the radiation
field in a cavity---the signal field---by coupling it via a
quantum-non-demolition Hamiltonian to a meter field in a highly squeezed state.
We show that quantum state tomography on the meter field using balanced
homodyne detection provides full information about the signal state. We discuss
the influence of measurement of the meter on the signal field.Comment: RevTeX, 10 pages, 1 eps figure with psfig. To appear In Physical
Review A 59 (January 1999
Trapping state restoration in the randomly-driven Jaynes-Cummings model by conditional measurements
We propose a scheme which can effectively restore fixed points in the quantum
dynamics of repeated Jaynes-Cummings interactions followed by atomic state
measurements, when the interaction times fluctuate randomly. It is based on
selection of superposed atomic states whose phase correlations tend to suppress
the phase fluctuations of each separate state. One suggested realization
involves the convergence of the cavity field distribution to a single Fock
state by conditional measurements performed on two-level atoms with fluctuating
velocities after they cross the cavity. Another realization involves a trapped
ion whose internal-motional state coupling fluctuates randomly. Its motional
state is made to converge to a Fock state by conditional measurements of the
internal state of the ion.Comment: RevTeX, 5 pages, four (EPS) figures automatically included through
epsfig. Physical Review A 1998 (accepted for publication) Two references
added to Ref. [8]. No other change. Final version which will appear in
Physical Review
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