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From repeated to continuous quantum interactions

Attal, S.; Pautrat, Y.
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...

Einstein-Langevin Equations from Running Coupling Constants

Lombardo, Fernando C.; Mazzitelli, Francisco D.
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

Entanglement of remote quantum systems by environmental modes

Queisser, Friedemann; Zell, Thomas; Klesse, Rochus
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.

A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

James, M. R.
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.

Quantum Langevin theory of excess noise

Bardroff, P. J.; Stenholm, S.
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

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

Bache, M.; Gaididei, Yu. B.; Christiansen, P. L.
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...

Quantum noise in optical fibers I: stochastic equations

Drummond, P. D.; Corney, J. F.
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

A quantum Langevin model for non-equilibrium condensation

Chiocchetta, Alessio; Carusotto, Iacopo
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.

Coupled quantum oscillators within independent quantum reservoirs

Dorofeyev, Illarion
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

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

Koide, T.; Maruyama, M.; Takagi, F.
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

Quantum chaotic attractor in a dissipative system

Liu, W. Vincent; Schieve, William C.
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

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

Giovannetti, Vittorio; Vitali, David
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

Quantum Langevin Equations and Stability

Jaekel, Marc-Thierry; Reynaud, Serge
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

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

Fujisaki, Hiroshi; Shimizu, Akira
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...

Quantum Langevin equations for optomechanical systems

Barchielli, Alberto; Vacchini, Bassano
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...

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

Zhou, Zheng-Yang; Chen, Mi; Yu, Ting; You, J. Q.
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

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

Banerjee, Dhruba; Bag, Bidhan Chandra; Banik, Suman Kumar; Ray, Deb Shankar
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

Coherent backscattering in nonlinear atomic media: quantum Langevin approach

Gr{é}maud}, Beno{\^ı}t; Wellens, Thomas; Delande, Dominique; Miniatura, Christian
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...

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

Gallis, Michael R.
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

A quantum Langevin formulation of risk-sensitive optimal control

James, Matthew
Fonte: Institute of Physics Publishing Publicador: Institute of Physics Publishing
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
86.24%
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.