1,848 research outputs found
Higher order nonclassicalities in a codirectional nonlinear optical coupler: Quantum entanglement, squeezing and antibunching
Higher order nonclassical properties of fields propagating through a
codirectional asymmetric nonlinear optical coupler which is prepared by
combining a linear wave guide and a nonlinear (quadratic) wave guide operated
by second harmonic generation are studied. A completely quantum mechanical
description is used here to describe the system. Closed form analytic solutions
of Heisenberg's equations of motion for various modes are used to show the
existence of higher order antibunching, higher order squeezing, higher order
two-mode and multi-mode entanglement in the asymmetric nonlinear optical
coupler. It is also shown that nonclassical properties of light can transfer
from a nonlinear wave guide to a linear wave guide.Comment: 9 pages 5 figure
Lower order and higher order entanglement in hyperfine manifold modeled as a four-wave mixing process
Possibilities of generation of lower order and higher order intermodal
entanglement in 87Rb 5S-5P-5D hyperfine manifold are rigorously investigated
using Sen-Mandal perturbative technique by showing the equivalence of the
system with the four-wave mixing (FWM) process. The investigation has revealed
that for a set of experimentally realizable/relevant parameters we can observe
lower order and higher order intermodal entanglement between pump and signal
modes, signal and idler modes, and idler and pump modes in a FWM process
associated with the 87Rb 5S-5P-5D hyperfine manifold. In addition, trimodal
entanglement involving pump, signal and idler modes is also reported.Comment: 12 pages, 5 figure
Higher order two-mode and multi-mode entanglement in Raman processes
The existence of higher order entanglement in the stimulated and spontaneous
Raman processes is established using the perturbative solutions of the
Heisenberg equations of motion for various field modes that are obtained using
the Sen-Mandal technique and a fully quantum mechanical Hamiltonian that
describes the stimulated and spontaneous Raman processes. Specifically, the
perturbative Sen-Mandal solutions are exploited here to show the signature of
the higher order two-mode and multi-mode entanglement. In some special cases,
we have also observed higher order entanglement in the partially spontaneous
Raman processes. Further, it is shown that the depth of the nonclassicality
indicators (parameters) can be manipulated by the specific choice of coupling
constants, and it is observed that the depth of nonclassicality parameters
increases with the order.Comment: 9 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1301.028
Interplay between quantum Zeno and anti-Zeno effects in a non-degenerate hyper-Raman nonlinear optical coupler
Quantum Zeno and anti-Zeno effects are studied in an asymmetric nonlinear
optical coupler composed of a probe waveguide and a system waveguide. The
system is a nonlinear waveguide operating under non-degenerate hyper-Raman
process, while both the pump modes in the system are constantly interacting
with the probe waveguide. The effect of the presence of probe on the temporal
evolution of the system in terms of the number of photons in Stokes and
anti-Stokes modes as well as phonon number is quantified as Zeno parameter. The
negative (positive) values of the Zeno parameter in the specific mode are
considered as the signatures of the quantum Zeno (anti-Zeno)effect in that mode
of the system. It is observed that the phase mismatch in Stokes and anti-Stokes
generation processes can be controlled to induce a transition between quantum
Zeno and anti-Zeno effects for both off-resonant and resonant hyper-Raman
process. However, in case of off-resonant hyper-Raman process in the system
waveguide, the frequency detuning parameters can also be used analogously to
cause the desired crossover. Further, the general nature of the physical system
and the perturbative technique used here allowed us to analytically study the
possibilities of observing quantum Zeno and anti-Zeno effects in a large number
of special cases, including situations where the process is spontaneous,
partially spontaneous and/or the system is operated under degenerate
hyper-Raman process, or a simple Raman process.Comment: Dynamics of quantum Zeno and anti-Zeno effect is studied analytically
in a nonlinear optical coupler which is very general in natur
Intermodal entanglement in Raman processes
The operator solution of a completely quantum mechanical Hamiltonian of the
Raman processes is used here to investigate the possibility of obtaining
intermodal entanglement between different modes involved in the Raman processes
(e.g. pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode).
Intermodal entanglement is reported between a) pump mode and anti-Stokes mode,
b) pump mode and vibration (phonon) mode c) Stokes mode and vibration phonon
mode, d) Stokes mode and anti-stokes mode in the stimulated Raman processes for
the variation of the phase angle of complex eigenvalue of pump
mode . Some incidents of intermodal entanglement in the spontaneous and the
partially spontaneous Raman processes are also reported. Further it is shown
that the specific choice of coupling constants may produce genuine entanglement
among Stokes mode, anti-Stokes mode and vibration-phonon mode. It is also shown
that the two mode entanglement not identified by Duan's criterion may be
identified by Hillery-Zubairy criteria. It is further shown that intermodal
entanglement, intermodal antibunching and intermodal squeezing are independent
phenomena.Comment: 11 pages, 4 figure
Quantum Zeno and anti-Zeno effects in the dynamics of non-degenerate hyper-Raman processes coupled to two linear waveguides
The effect of the presence of two probe waveguides on the dynamics of
hyper-Raman processes is studied in terms of quantum Zeno and anti-Zeno
effects. Specifically, the enhancement (diminution) of the evolution of the
hyper-Raman processes due to interaction with the probe waveguides via
evanescent waves is viewed as quantum Zeno (anti-Zeno) effect. We considered
the two probe waveguides interacting with only one of the optical modes at a
time. For instance, as a specific scenario, it is considered that the two
non-degenerate pump modes interact with each probe waveguide linearly while
Stokes and anti-Stokes modes do not interact with the probes. Similarly, in
another scenario, we assumed both the probe waveguides interact with Stokes
(anti-Stokes) mode simultaneously. The present results show that quantum Zeno
(anti-Zeno) effect is associated with phase-matching (mismatching). However, we
did not find any relation between the presence of the quantum Zeno effect and
antibunching in the bosonic modes present in the hyper-Raman processes.Comment: Dynamics of hyper-Raman processes is studied in terms of quantum Zeno
and anti-Zeno effect
Transformers can optimally learn regression mixture models
Mixture models arise in many regression problems, but most methods have seen
limited adoption partly due to these algorithms' highly-tailored and
model-specific nature. On the other hand, transformers are flexible, neural
sequence models that present the intriguing possibility of providing
general-purpose prediction methods, even in this mixture setting. In this work,
we investigate the hypothesis that transformers can learn an optimal predictor
for mixtures of regressions. We construct a generative process for a mixture of
linear regressions for which the decision-theoretic optimal procedure is given
by data-driven exponential weights on a finite set of parameters. We observe
that transformers achieve low mean-squared error on data generated via this
process. By probing the transformer's output at inference time, we also show
that transformers typically make predictions that are close to the optimal
predictor. Our experiments also demonstrate that transformers can learn
mixtures of regressions in a sample-efficient fashion and are somewhat robust
to distribution shifts. We complement our experimental observations by proving
constructively that the decision-theoretic optimal procedure is indeed
implementable by a transformer.Comment: 24 pages, 9 figure
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