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Nonlinear coherent states for the Susskind-Glogower operators

Roberto de J. León‐Montiel, H. M. Moya-Cessa, Francisco Soto

Published May 1, 2010• 2 citations
OpenAlex

Abstract

In this thesis, we construct nonlinear coherent states for the Susskind-Glogower\noperators by the application of the displacement operator on the vacuum state.\nWe also construct nonlinear coherent states as eigenfunctions of a Hamiltonian\nconstructed with the Susskind-Glogower operators. We generalize the solution\nto the eigenfunction problem to an arbitrary jmi initial condition. To analize\nthe obtained results, we plot the Husimi Q function, the photon number\nprobability distribution and the Mandel Q-parameter. For both cases, we nd\nthat the constructed states exhibit interesting nonclassical features such as\namplitude squeezing and quantum inteferences due to a self-splitting into two\ncoherent-like states. Additionally, we show that nonlinear coherent states may\nbe modelled by propagating light in semi-innite arrays of optical bers.

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In this thesis, we construct nonlinear coherent states for the Susskind-Glogower\noperators by the application of the displacement operator on the vacuum state.\nWe also construct nonlinear coherent states as eigenfunctions of a Hamiltonian\nconstructed with the Susskind-Glogower operators. We generalize the solution\nto the eigenfunction problem to an arbitrary jmi initial condition. To analize\nthe obtained results, we plot the Husimi Q function, the photon number\nprobability distribution and the Mandel Q-parameter. For both cases, we nd\nthat the constructed states exhibit interesting nonclassical features such as\namplitude squeezing and quantum inteferences due to a self-splitting into two\ncoherent-like states. Additionally, we show that nonlinear coherent states may\nbe modelled by propagating light in semi-innite arrays of optical bers.
We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with the Susskind-Glogower operators. We generalize the solution of the eigen- function problem to an arbitrary |mi initial condition. To analyze the obtained results, we plot the Husimi Q function, the photon number probability distribution and the Mandel Q-parameter. For both cases, we find that the constructed states exhibit interesting nonclassical features, such as amplitude squeezing and quantum interferences due to a self-splitting into two coherent-like states. Additionally, we show that non- linear coherent states may be modeled by propagating light in semi-infinite arrays of optical fibers.
We construct a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.