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## From repeated to continuous quantum interactions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.24%

We consider the general physical situation of a quantum system $\H_0$
interacting with a chain of exterior systems $\bigotimes_\N \H$, one after the
other, during a small interval of time $h$ and following some Hamiltonian $H$
on $\H_0 \otimes \H$. We discuss the passage to the limit to continuous
interactions ($h \to 0$) in a setup which allows to compute the limit of this
Hamiltonian evolution in a single state space: a continuous field of exterior
systems $\otimes_{\R} \H$. Surprisingly, the passage to the limit shows the
necessity for 3 different time scales in $H$. The limit evolution equation is
shown to spontaneously produce quantum noises terms: we obtain a quantum
Langevin equation as limit of the Hamiltonian evolution. For the very first
time, these quantum Langevin equations are obtained as the effective limit from
repeated to continuous interactions and not only as a model. These results
justify the usual quantum Langevin equations considered in continual quantum
measurement or in quantum optics. We show that the three time scales correspond
to the normal regime, the weak coupling limit and the low density limit. Our
approach allows to consider these two physical limits altogether for the first
time. Their combination produces an effective Hamiltonian on the small system...

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## Einstein-Langevin Equations from Running Coupling Constants

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/09/1996

Relevância na Pesquisa

56.09%

The Einstein-Langevin equations take into account the backreaction of quantum
matter fields on the background geometry. We present a derivation of these
equations to lowest order in a covariant expansion in powers of the curvature.
For massless fields, the equations are completely determined by the running
coupling constants of the theory.; Comment: 10 pages, RevTex file, no figures

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## Entanglement of remote quantum systems by environmental modes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.08%

We investigate the generation of quantum mechanical entanglement of two
remote oscillators that are locally coupled to a common bosonic bath. Starting
with a Lagrangian formulation of a suitable model, we derive two coupled
Quantum Langevin Equations that exactly describe the time evolution of the two
local oscillators in presence of the coupling to the bosonic bath. Numerically
obtained solutions of the Langevin Equations allow us to study the entanglement
generation between the oscillators in terms of the time evolution of the
logarithmic negativity. Our results confirm and extend our previously obtained
findings, namely that significant entanglement between oscillators embedded in
a free bosonic bath can only be achieved if the system are within a microscopic
distance. We also consider the case where the bosonic spectral density is
substantially modified by imposing boundary conditions on the bath modes. For
boundary conditions corresponding to a wave-guide like geometry of the bath we
find significantly enlarged entanglement generation. This phenomenon is
additionally illustrated within an approximative model that allows for an
analytical treatment.

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## A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

66%

In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom.

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## Quantum Langevin theory of excess noise

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/04/1999

Relevância na Pesquisa

66.01%

In an earlier work [P. J. Bardroff and S. Stenholm], we have derived a fully
quantum mechanical description of excess noise in strongly damped lasers. This
theory is used here to derive the corresponding quantum Langevin equations.
Taking the semi-classical limit of these we are able to regain the starting
point of Siegman's treatment of excess noise [Phys. Rev. A 39, 1253 (1989)].
Our results essentially constitute a quantum derivation of his theory and allow
some generalizations.; Comment: 9 pages, 0 figures, revtex

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## Nonclassical statistics of intracavity coupled $\chi^{(2)}$ waveguides: the quantum optical dimer

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.19%

A model is proposed where two $\chi^{(2)}$ nonlinear waveguides are contained
in a cavity suited for second-harmonic generation. The evanescent wave coupling
between the waveguides is considered as weak, and the interplay between this
coupling and the nonlinear interaction within the waveguides gives rise to
quantum violations of the classical limit. These violations are particularly
strong when two instabilities are competing, where twin-beam behavior is found
as almost complete noise suppression in the difference of the fundamental
intensities. Moreover, close to bistable transitions perfect twin-beam
correlations are seen in the sum of the fundamental intensities, and also the
self-pulsing instability as well as the transition from symmetric to asymmetric
states display nonclassical twin-beam correlations of both fundamental and
second-harmonic intensities. The results are based on the full quantum Langevin
equations derived from the Hamiltonian and including cavity damping effects.
The intensity correlations of the output fields are calculated
semi-analytically using a linearized version of the Langevin equations derived
through the positive-P representation. Confirmation of the analytical results
are obtained by numerical simulations of the nonlinear Langevin equations
derived using the truncated Wigner representation.; Comment: 15 pages...

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## Quantum noise in optical fibers I: stochastic equations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.01%

We analyze the quantum dynamics of radiation propagating in a single mode
optical fiber with dispersion, nonlinearity, and Raman coupling to thermal
phonons. We start from a fundamental Hamiltonian that includes the principal
known nonlinear effects and quantum noise sources, including linear gain and
loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are
treated. This allows quantum Langevin equations to be calculated, which have a
classical form except for additional quantum noise terms. In practical
calculations, it is more useful to transform to Wigner or +$P$
quasi-probability operator representations. These result in stochastic
equations that can be analyzed using perturbation theory or exact numerical
techniques. The results have applications to fiber optics communications,
networking, and sensor technology.; Comment: 1 figure

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## A quantum Langevin model for non-equilibrium condensation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

66.02%

We develop a quantum model for non-equilibrium Bose-Einstein condensation of
photons and polaritons in planar microcavity devices. The model builds upon
laser theory and includes the spatial dynamics of the cavity field, a
saturation mechanism and some frequency-dependence of the gain: quantum
Langevin equations are written for a cavity field coupled to a continuous
distribution of externally pumped two-level emitters with a well-defined
frequency. As a an example of application, the method is used to study the
linearised quantum fluctuations around a steady-state condensed state. In the
good-cavity regime, an effective equation for the cavity field only is proposed
in terms of a stochastic Gross-Pitaevskii equation. Perspectives in view of a
full quantum simulation of the non-equilibrium condensation process are finally
sketched.

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## Coupled quantum oscillators within independent quantum reservoirs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/07/2012

Relevância na Pesquisa

55.96%

System of the quantum Langevin equations for two quantum coupling oscillators
within independent heat baths of quantum oscillators are obtained using a model
Hamiltonian and corresponding Heisenberg equations of motion. Expressions for
mean energy of coupled oscillators and their mean energy of interaction are
derived and analyzed. Nonmonotonic dependence of the interaction energy versus
a coupling constant is demonstrated and explained. Nontrivial dependence of the
quantities as a consequence of the difference in temperatures of heat baths is
shown.; Comment: 13 pages, 3 figures

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## Projection Operator Approach to Langevin Equations in $\phi^4$ Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.24%

We apply the projection operator method (POM) to $\phi^4$ theory and derive
both quantum and semiclassical equations of motion for the soft modes. These
equations have no time-convolution integral term, in sharp contrast with other
well-known results obtained using the influence functional method (IFM) and the
closed time path method (CTP). However, except for the fluctuation force field
terms, these equations are similar to the corresponding equations obtained
using IFM with the linear harmonic approximation, which was introduced to
remove the time-convolution integral. The quantum equation of motion in POM can
be regarded as a kind of quantum Langevin equation in which the fluctuation
force field is given in terms of the operators of the hard modes. These
operators are then replaced with c-numbers using a certain procedure to obtain
a semiclassical Langevin equation. It is pointed out that there are significant
differences between the fluctuation force fields introduced in this paper and
those introduced in IFM. The arbitrariness of the definition of the fluctuation
force field in IFM is also discussed.; Comment: 35pages,2figures, Prog. Theor. Phys. Vol. 107 No. 5 in press

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## Quantum chaotic attractor in a dissipative system

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/03/1997

Relevância na Pesquisa

55.96%

A dissipative quantum system is treated here by coupling it with a heat bath
of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's
theorem, we establish explicitly the quantum Duffing equations with a
double-well potential chosen. A quantum noise term appears the only driving
force in dynamics. Numerical studies show that the chaotic attractor exists in
this system while chaos is certainly forbidden in the classical counterpart.; Comment: 5 pages, revtex, all figures included, accepted by Phys. Rev. Lett

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## Phase noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.01%

We study the dynamics of an optical mode in a cavity with a movable mirror
subject to quantum Brownian motion. We study the phase noise power spectrum of
the output light, and we describe the mirror Brownian motion, which is
responsible for the thermal noise contribution, using the quantum Langevin
approach. We show that the standard quantum Langevin equations, supplemented
with the appropriate non-Markovian correlation functions, provide an adequate
description of Brownian motion.; Comment: 11 pages, 2 figures. Changes in the introduction. In press on Phys.
Rev. A

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## Quantum Langevin Equations and Stability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/01/1998

Relevância na Pesquisa

76.06%

Different quantum Langevin equations obtained by coupling a particle to a
field are examined. Instabilities or violations of causality affect the motion
of a point charge linearly coupled to the electromagnetic field. In contrast,
coupling a scatterer with a reflection cut-off to radiation pressure leads to
stable and causal motions. The radiative reaction force exerted on a scatterer,
and hence its quasistatic mass, depend on the field state. Explicit expressions
for a particle scattering a thermal field in a two dimensional space-time are
given.; Comment: 12 pages

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## Quantum Langevin equations for semiconductor light-emitting devices and the photon statistics at a low-injection level

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/04/1998

Relevância na Pesquisa

76.09%

From the microscopic quantum Langevin equations (QLEs) we derive the
effective semiconductor QLEs and the associated noise correlations which are
valid at a low-injection level and in real devices. Applying the semiconductor
QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula
for the Fano factor of photons which gives the photon-number statistics as a
function of the pump statistics and several parameters of LEDs. Key ingredients
are non-radiative processes, carrier-number dependence of the radiative and
non-radiative lifetimes, and multimodeness of LEDs. The formula is applicable
to the actual cases where the quantum efficiency $\eta$ differs from the
differential quantum efficiency $\eta_{d}$, whereas previous theories
implicitly assumed $\eta = \eta_{d}$. It is also applicable to the cases when
photons in each mode of the cavity are emitted and/or detected inhomogeneously.
When $\eta_{d} < \eta$ at a running point, in particular, our formula predicts
that even a Poissonian pump can produce sub-Poissonian light. This mechanism
for generation of sub-Poissonian light is completely different from those of
previous theories, which assumed sub-Poissonian statistics for the current
injected into the active layers of LEDs. Our results agree with recent
experiments. We also discuss frequency dependence of the photon statistics.; Comment: 10 pages...

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## Quantum Langevin equations for optomechanical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

66.18%

We provide a fully quantum description of a mechanical oscillator in the
presence of thermal environmental noise by means of a quantum Langevin
formulation based on quantum stochastic calculus. The system dynamics is
determined by symmetry requirements and equipartition at equilibrium, while the
environment is described by quantum Bose fields in a suitable non-Fock
representation which allows for the introduction of temperature. A generic
spectral density of the environment can be described by introducing its state
trough a suitable P-representation. Including interaction of the mechanical
oscillator with a cavity mode via radiation pressure we obtain a description of
a simple optomechanical system in which, besides the Langevin equations for the
system, one has the exact input-output relations for the quantum noises. The
whole theory is valid at arbitrarily low temperature. This allows the exact
calculation of the stationary value of the mean energy of the mechanical
oscillator, as well as both homodyne and heterodyne spectra. The present
analysis allows in particular to study possible cooling scenarios and to obtain
the exact connection between observed spectra and fluctuation spectra of the
position of the mechanical oscillator.; Comment: 37 pages...

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## Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/09/2015

Relevância na Pesquisa

56.19%

One long-standing difficult problem in quantum dissipative dynamics is to
solve the spin-boson model in a non-Markovian regime where a tractable
systematic master equation does not exist. The spin-boson model is particularly
important due to its crucial applications in quantum noise control and
manipulation as well as its central role in developing quantum theories of open
systems. Here we solve this important model by developing a non-Markovian
quantum Langevin approach. By projecting the quantum Langevin equation onto the
coherent states of the bath, we can derivie a set of non-Markovian quantum
Bloch equations containing no explicit noise variables. This special feature
offers a tremendous advantage over the existing stochastic Schr\"odinger
equations in numerical simulations. The physical significance and generality of
our approach are briefly discussed.; Comment: 5 pages, 1 figure

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## A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/03/2003

Relevância na Pesquisa

56.04%

Based on a coherent state representation of noise operator and an ensemble
averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109
(2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to
derive the equations for time evolution of {\it true} probability distribution
functions in $c$-number phase space. We extend the treatment to develop a
numerical method for generation of $c$-number noise with arbitrary correlation
and strength at any temperature, along with the solution of the associated
generalized quantum Langevin equation. The method is illustrated with the help
of a calculation of quantum mean first passage time in a cubic potential to
demonstrate quantum Kramers turnover and quantum Arrhenius plot.; Comment: RevTex4, 13 pages, 4 figures

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## Coherent backscattering in nonlinear atomic media: quantum Langevin approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/06/2005

Relevância na Pesquisa

56%

In this theoretical paper, we investigate coherence properties of the
near-resonant light scattered by two atoms exposed to a strong monochromatic
field. To properly incorporate saturation effects, we use a quantum Langevin
approach. In contrast to the standard optical Bloch equations, this method
naturally provides the inelastic spectrum of the radiated light induced by the
quantum electromagnetic vacuum fluctuations. However, to get the right spectral
properties of the scattered light, it is essential to correctly describe the
statistical properties of these vacuum fluctuations. Because of the presence of
the two atoms, these statistical properties are not Gaussian : (i) the spatial
two-points correlation function displays a speckle-like behavior and (ii) the
three-points correlation function does not vanish. We also explain how to
incorporate in a simple way propagation with a frequency-dependent scattering
mean-free path, meaning that the two atoms are embedded in an average
scattering dispersive medium. Finally we show that saturation-induced
nonlinearities strongly modify the atomic scattering properties and, as a
consequence, provide a source of decoherence in multiple scattering. This is
exemplified by considering the coherent backscattering configuration where
interference effects are blurred by this decoherence mechanism. This leads to a
decrease of the so-called coherent backscattering enhancement factor.; Comment: 19 pages...

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## Decoherence and Dissipation for a Quantum System Coupled to a Local Environment

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/10/1993

Relevância na Pesquisa

55.98%

Decoherence and dissipation in quantum systems has been studied extensively
in the context of Quantum Brownian Motion. Effective decoherence in coarse
grained quantum systems has been a central issue in recent efforts by Zurek and
by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although
these models can yield very general classical phenomenology, they are incapable
of reproducing relevant characteristics expected of a local environment on a
quantum system, such as the characteristic dependence of decoherence on
environment spatial correlations. I discuss the characteristics of Quantum
Brownian Motion in a local environment by examining aspects of first
principle calculations and by the construction of phenomenological models.
Effective quantum Langevin equations and master equations are presented in a
variety of representations. Comparisons are made with standard results such as
the Caldeira-Leggett master equation.; Comment: 6 Pages (LaTeX), to appear in the Proceedings of the Third
International Workshop on Squeezed States and Uncertainty Relations

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## A quantum Langevin formulation of risk-sensitive optimal control

Fonte: Institute of Physics Publishing
Publicador: Institute of Physics Publishing

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

86.24%

#Keywords: Control equipment#Dynamic programming#Feedback control#Filtration#Quantum optics#Optimal control#Quantum filtering#Quantum Langevin equations#Quantum stochastic calculus#Optimal control systems Optimal control#Quantum filtering

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom.

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