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arXiv:1407.7642 · Communications in Theoretical Physics

Nonlinear Quantum Optical Springs and Their Nonclassical Properties

Mohammad Javad Faghihi, Mohammad Kazem Tavassoly

Published Aug 1, 2011• 12 citations
arXivHTMLPDF

Abstract

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ω to the mentioned idea can be established. In the present paper, we generalize the approach of quantum optical spring with particular attention to the dependence of frequency to the intensity of radiation field that naturally observes in the nonlinear coherent states, from which we arrive at a physical system has been called by us as nonlinear quantum optical spring. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters, as particular quantum features, will be revealed.

DOI
10.1088/0253-6102/56/2/24

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The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ω to the mentioned idea can be established. In the present paper, we generalize the approach of quantum optical spring with particular attention to the dependence of frequency to the intensity of radiation field that naturally observes in the nonlinear coherent states, from which we arrive at a physical system has been called by us as nonlinear quantum optical spring. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters, as particular quantum features, will be revealed.
The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of ωωω to ω1+μa†aω\sqrt{1+μa^\dagger a}ω1+μa†a​ the mentioned idea can be established. In the present paper we generalize the approach of quantum optical spring (has been called by us as nonlinear quantum optical spring) with attention to the {\it dependence of frequency to the intensity of radiation field} that {\it naturally} observed in nonlinear coherent states. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters as particular quantum features will be revealed.
Statistical properties of light generated in nonlinear optical couplers are discussed. Methods suitable for the description of non-classical properties of light are mentioned; special attention is paid to generalized superposition of coherent fields and noise. Regimes suitable for non-classical light generation in various types of nonlinear couplers based on second-harmonic and second- subharmonic generation, optical parametric processes, Kerr effect as well as Raman and Brillouin processes are analyzed. Special attention is devoted to the generation of light with sub-Poissonian statistics, squeezed light, and light in purely quantum states. Role of real effects like damping of optical fields and phase mismatches is also discussed.
Abstract Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times n ˆ M on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.
We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.
Abstract Generation of nonclassical states is a necessary requirement for all quantum science and technology protocols. In this regard, Schrödinger cat states, as quantum superpositions of mocroscopically distinguishable coherent states with equal amplitude and opposite phases, have been of great importance in recent years. In this paper, using some appropriate nonlinear optical media, a theoretical scheme is employed to generate various classes of cat-like states with the help of the connection between quantum and nonlinear optics. In fact, we have exploited a single simple method to produce even, odd and also Yurke-Stoler cat-like states by considering different input states such as coherent squeezed, squeezed coherent, photon-added coherent, pair coherent and trio coherent states. To achieve the purpose, we extensively use cross-Kerr interaction and its further generalizations to higher-orders. Projective measurement is the original conception behind the represented approach by which distinct types of nonclassical states are obtained. At last, we pay our attention to the unavoidable effect of field dissipation and show that in most of the above-studied states we may still achieve the cat-like states, however, with attenuated amplitudes.
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency ω, coupled by means of springs. Such systems have been studied before, and appear in various models. In this paper, we approach the system as a Wigner quantum system, not imposing the canonical commutation relations, but using instead weaker relations following from the compatibility of Hamilton’s equations and the Heisenberg equations. In such a setting, the quantum system allows solutions in a finite-dimensional Hilbert space, with a discrete spectrum for all physical operators. We show that a class of solutions can be obtained using generators of the Lie superalgebra gl(1∣M). Then we study – from a mathematical point of view – the properties and spectra of the physical operators in a class of unitary representations of gl(1∣M). These properties are both interesting and intriguing. In particular, we can give a complete analysis of the eigenvalues of the Hamiltonian and of the position and momentum operators (including multiplicities). We also study probability distributions of position operators when the quantum system is in a stationary state, and the effect of the position of one oscillator on the positions of the remaining oscillators in the chain.