Nonclassical Properties of Para-Bose Superposition States

Abstract

It is well known that the nonclassical states of the light field play an important role in quantum optics. In the last decade, the nonclassical states which arise as the coherent superposition of two quantum states has attracted much attention [1–3]. In Ref. [1] Wodkiewicz et al. introduce a new kind of superposition states which exhibit squeezing fluctuations and open new possibilities of generating squeezed states. In recent years, simulated by recent experimental observation of fractional quantum Hall effect [4, 5] in two-dimensional electron gas, much attention has been focused on various nontraditional statistics: fractional statistics [6–8] and parastatistics [9–11]. Parastatistics was first introduced by Green [9] as a generalization of the Bose and Fermi statistics. This generalization introduced trilinear relations in place of the bilinear relations that describe the Bose and Fermi systems. Recently, Greenberg and Mishra [11] have shown that the parastatistics can be quantized by using path integrals. In this letter, we present two kinds of generalized para-Bose superposition states and investigate its nonclassical properties. It is shown that these para-Bose superposition states exhibit stronger squeezing and antibunching. The amplitude-squared squeezing for these states is also examined.