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Chinese Physics

q-nonlinear cavity field states generated by the excitations on aq-coherent state

Lian-Fu Wei, Xi Ding-ping

Published Aug 1, 2000• 1 citation
Publisher

Abstract

It is shown that photon-excitation state defined by |α, k ⟩ q = â q † k |α⟩ q ( k =1,2,3...) up to a normalization constant can be produced in nonlinear processes in q -nonlinear cavities. The mathematical and quantum statistical properties of this state are studied in detail. We show that this state, along with the number states absented in it, forms a complete set. We also show by numerical method that this state exhibits quantum-squeezing for some values of |α| and always reveals quantum-antibunching effect.

DOI
10.1088/1009-1963/9/8/007

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It is shown that photon-excitation state defined by |α, k ⟩ q = â q † k |α⟩ q ( k =1,2,3...) up to a normalization constant can be produced in nonlinear processes in q -nonlinear cavities. The mathematical and quantum statistical properties of this state are studied in detail. We show that this state, along with the number states absented in it, forms a complete set. We also show by numerical method that this state exhibits quantum-squeezing for some values of |α| and always reveals quantum-antibunching effect.
We introduce states defined by \ensuremath{\Vert}\ensuremath{\alpha},m〉=${\mathit{a}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathit{m}}$\ensuremath{\Vert}\ensuremath{\alpha}〉 up to a normalization constant, where \ensuremath{\Vert}\ensuremath{\alpha}〉 is a coherent state and m an integer. We study the mathematical and physical properties of such states. We demonstrate phase squeezing and the sub-Poissonian character of the fields in such states. We study in detail the quasiprobability distributions and the distribution of the field quadrature. We also show how such states can be produced in nonlinear processes in cavities.
The photon-added nonlinear coherent states, defined as adaggerm∣alpha,f>{a}^{\\dagger m}|\\alpha, f>adaggerm∣alpha,f> up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N+1)]f(N-m)[1-m/(N+1)]f(N−m)[1−m/(N+1)]. Here % |\\alpha, f> is the nonlinear coherent state with the nonlinear function f(N)f(N)f(N), NNN is the number operator, adaggera^{\\dagger}adagger is the boson creation operator and mmm is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)] obtained from the photon-added nonlinear coherent states with negative values of m.m.m. The nonlinear coherent states corresponding to the positive and negative values of mmm are shown to be the result of nonunitarily deforming the number states ∣m>|m>∣m> and ∣0>|0>∣0>, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of mmm in detail.
The two-mode photon-added state defined by |?, q; m>?=?a+mb+m|?, q> up to a normalization constant is introduced, where |?, q> is a pair coherent state and m an integer. It is shown that the fields in such a state have remarkable quantum features such as sub-Poissonian statistics, violations of Cauch-Schwarz inequalities, correlations in the number fluctuations and squeezing. We examine the influence of photon-adding on the properties of pair coherent state, and propose a method of generating two-mode photon-added states in the context of cavity quantum electrodynamics.
\n\nLight-emitting atoms or material in a cavity are well known to generate thermal or coherent fields depending on, e.g., the quality of the cavity and the strength of the excitation of the emitting material. We investigate the possibilities of generating antibunched photons and nonclassical light by adding nonlinear elements in the cavity and show that it is indeed feasible. In particular, we focus on cavities with emitters formed by macroscopic many-body systems like gas of excitons in semiconductor quantum wells where different nonlinearities in the emitters and absorbers will be shown to lead to bunched, Poissonian, and antibunched photon statistics. We show that, while the single two-state system with suitable coupling parameters can produce antibunched photons, macroscopic systems need an additional nonlinearity to generate antibunching phenomenon. Our results demonstrate that a nonclassical cavity field can be generated by a conventional laser when a suitable nonlinear absorbing element is added to the cavity structure. Thus, the proposed device configuration can be manufactured using standard optoelectronic materials and processing techniques.\n