<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi></mml:math>-deformed noncommutative cat states and their nonclassical properties

Abstract

We study several classical-like properties of $q$-deformed nonlinear coherent states as well as nonclassical behaviors of $q$-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in $q$-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the $q$-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.