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arXiv:1406.0749 · International Journal of Quantum Information

Engineering nonlinear coherent states as photon-added and photon-subtracted coherent states

I. Ramos-Prieto, B. M. Rodríguez-Lara, H. M. Moya-Cessa

Published Nov 1, 2014• 15 citations
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Abstract

We propose a class of nonlinear coherent states which are experimentally feasible in cavity or ion-trap quantum electrodynamics. These quantum field states arise from a new type of photon addition and subtraction based on London phase operators, also known as Susskind–Glogower operators, that just displaces the mean photon number without scaling the photon distribution.

DOI
10.1142/s0219749915600059

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We propose a class of nonlinear coherent states which are experimentally feasible in cavity or ion-trap quantum electrodynamics. These quantum field states arise from a new type of photon addition and subtraction based on London phase operators, also known as Susskind–Glogower operators, that just displaces the mean photon number without scaling the photon distribution.
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.
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 propose a scheme to add/subtract excitations to/from an arbitrary quantum state or the harmonic oscillator. The method displaces the photon-number distribution and leaves its shape unchanged for a wide range of displacements. Mathematically this is realized by the action of phase operators of the Susskind-Glogower type onto the initial quantum state. Consequently, the shape of the phase distribution is preserved unless the number statistics are modified due to displacing it by subtraction onto the vacuum state. Starting with an initially coherent state one may realize pure quantum states displaying either amplitude or phase squeezing. The implementation of the method is based on interactions of the Jaynes-Cummings type, in the case of subtracting quanta one additionally needs to perform measurements on the electronic quantum state of the atoms. Our approach could be used for adding and subtracting both photons on a cavity field and motional quanta of a trapped ion.