J. Banerji

Spatial coherence and information entropy in optical vortex fields

We show how a vortex structure manifests itself in the one-dimensional projection of a vortex field. We calculate the extent of spatial coherence and entropy of such projections. We quantify the spatial coherence and discuss the properties of the Wigner functions for the projected field.

Intensity correlation properties of high-order optical vortices passing through a rotating ground-glass plate

We study the intensity correlation properties of optical vortices passing through a rotating ground-glass (RGG) plate and compare them with those of the TEM(00) mode of an He-Ne laser beam passed through the same RGG. We have observed that the intensity correlation curves for optical vortices decrease much faster than the corresponding curve for a TEM(00) mode of the He-Ne laser. The rate of decay of the correlation increases with the increase of order of the vortices. Our experimentally observed results are supported by exact analytical results.

Coherent states for exactly solvable potentials

A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials, e.g., Morse and Poeschl-Teller, is given. The method, a priori, is potential independent and connects with earlier developed ones, including the oscillator-based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum-mechanical potential problems, such as the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.

Higher order optical vortices and formation of speckles

We have experimentally generated higher order optical vortices and scattered them through a ground glass plate that results in speckle formation. Intensity autocorrelation measurements of speckles show that their size decreases with an increase in the order of the vortex. It implies an increase in the angular diameter of the vortices with their order. The characterization of vortices in terms of their annular bright ring also helps us to understand these observations. The results may find applications in stellar intensity interferometry and thermal ghost imaging.

Divergence of optical vortex beams.

We show, both theoretically and experimentally, that the propagation of optical vortices in free space can be analyzed by using the width [w(z)] of the host Gaussian beam and the inner and outer radii of the vortex beam at the source plane (z=0) as defined in [Opt. Lett.39, 4364 (2014)10.1364/OL.39.004364OPLEDP0146-9592]. We also studied the divergence of vortex beams, considered as the rate of change of inner or outer radius with the propagation distance (z), and found that it varies with the order in the same way as that of the inner and outer radii at z=0. These results may be useful in designing optical fibers for orbital angular momentum modes that play a crucial role in quantum communication.

Wigner distribution, nonclassicality and decoherence of generalized and reciprocal binomial states

There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the Q-function. The decoherence of the FSFS is studied by considering the time evolution of its Wigner function in amplitude decay and phase damping channels. As examples, we determine the nonclassicality and decoherence of generalized and reciprocal binomial states.

Propagation of an arbitrary vortex pair through an astigmatic optical system and determination of its topological charge

We embed a pair of vortices with different topological charges in a Gaussian beam and study its evolution through an astigmatic optical system, a tilted lens. The propagation dynamics are explained by a closed-form analytical expression. Furthermore, we show that a careful examination of the intensity distribution at a predicted position past the lens can determine the charge present in the beam. To the best of our knowledge, our method is the first noninterferometric technique to measure the charge of an arbitrary vortex pair. Our theoretical results are well supported by experimental observations.

Reconstruction of SU(1,1) states

We show how group symmetries can be used to reconstruct quantum states. The method we propose is presented in the context of the two-mode SU(1,1) states of the radiation field. In our scheme for SU(1,1) states, the input field passes through a nondegenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode. The density matrix in the Fock basis is retrieved from the measured data by the least-squares method after singular value decomposition of the design matrix followed by Tikhonov regularization. Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered.

A time–frequency analysis of wave packet fractional revivals

We show that the time–frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time-domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time–frequency analysis in the study of wave packet fractional revivals.

The role of ro-vibrational coupling in the revival dynamics of diatomic molecular wave packets

We study the revival and fractional revivals of a diatomic molecular wave packet of circular states whose weighing coefficients are peaked about a vibrational quantum number and a rotational quantum number . Furthermore, we show that the interplay between the rotational and vibrational motion is determined by a parameter , where D is the dissociation energy and C is inversely proportional to the reduced mass of the two nuclei. Using I2 and H2 as examples, we show, both analytically and visually (through animations), that for , the rotational and vibrational time scales are so far apart that the ro-vibrational motion gets decoupled and the revival dynamics depends essentially on one time scale. For , on the other hand, the evolution of the wave packet depends crucially on both the rotational and vibrational time scales of revival. In the latter case, an interesting rotational–vibrational fractional revival is predicted and explained.