Nonlinear Coherent Effects

Kōichi Shimoda

Mojgan Momeni-Demneh, Ali Mahdifar, R. Roknizadeh

In this paper, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformed su(2) algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.

Lu Dao

Using the numerical method,the antibunching effects of a new kind of odd and even nonlinear coherent states in a finite-dimensional Hilbert space are studied.The results show that the new kind of odd nonlinear coherent state exhibits antibunching effect and the new kind of even nonlinear coherent state does not exhibits antibunching effect in a finite-dimensional Hilbert space.

H. Kalt, Claus F. Klingshirn

Mohammad Javad Faghihi, Mohammad Haddad, Zahra Mazaheri +1 more

Coherent states and their generalizations are normally appropriate candidates for describing radiation fields. Despite this, the effect of thermal noise on generalized coherent states has not been extensively studied. In fact, thermal effects are unavoidable at finite temperatures, and they should be taken into account to have a better agreement with experimental results. In this regard, we use the concept of thermal coherent states, which are indeed the standard coherent states including thermal effects. So, in this paper, by using a nonlinear coherent states approach, we generalize the thermal coherent states to their nonlinear counterparts. In other words, we find a natural link between the thermal coherent states and the nonlinear coherent states associated with nonlinear oscillator algebra. Afterwards, the nonclassicality features of the obtained states are numerically investigated to explore the roles of both nonlinearity and thermal noise in physical properties. The results show that the thermal effects lead to the transition from nonclassical states to classical ones. Moreover, it is seen that the operator-valued intensity-dependent function plays a leading role in controlling the depth as well as the domain of nonclassicality aspects.