We have studied the effect of environment induced pure decoherence on the generalized Jaynes-Cummings model (JCM). This generalized JCM is introduced to take into account both atom-field interaction and a class of spin-orbit interactions in the same framework. For generalized JCM with atom-field interaction, it is shown that along with the suppression of the oscillatory behaviour of the atomic and field variables, in the steady state, atomic energy is transferred to the field or vice versa through the dressed state coherence depending on the initial condition of the atom-field system and the model under consideration. It is also shown that initial Poissonian field acquires a sub-Poissonian character in the steady state and thus all the nonclassical properties are not erased by the decoherence in JCM. An interesting effect of this decoherence mechanism is that it affects the population and coherence properties of the individual subsystem in a different way. As an example of generalized JCM with spin-orbit interaction, the dynamics of spin of the hydrogen atom in a magnetic field is studied to show the effect of decoherence.

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time-dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field is spoiled on quantization of the field mode. To reveal this non-classical effect, a Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes-Cummings model (JCM). Possible modification of such an effect on the collapse and revival phenomenon is also discussed by taking the quantized field in a coherent state

We have exactly solved a model of equidistant cascade four-level system interacting with a single-mode radiation field both semiclassically and quantum mechanically by exploiting its similarity with Jaynes-Cummings model. For the classical field, it is shown that the Rabi oscillation of the system initially in the first level (second level) is similar to that of the system when it is initially in the fourth level (third level). We then proceed to solve the quantized version of the model where the dressed state is constructed using a six-parameter four-dimensional matrix and show that the symmetry exhibited in the Rabi oscillation of the system for the semiclassical model is completely destroyed on the quantization of the cavity field. Finally, we have studied the collapse and revival of the system for the cavity field-mode in a coherent state to discuss the restoration of symmetry and its implication is discussed.

We develop a scheme to construct the Hamiltonians of the lambda-, vee- and cascade-type three-level configurations using the generators of $SU(3)$ group. It turns out that this approach provides a well-defined selection rule to give different Hamiltonians for each configuration. The lambda- and vee-type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields. For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models by introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when both field modes are in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.

The upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies andpath lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial toaddress some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations.We describe the simulation framework, the neutrino interactions in the detector, and the expected responseof the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Itscharge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles.