We provide an algebraic procedure to find the eigenstates of two-charged particles in an oscillator potential, known as {\it{Hooke's}} atom. For the planar Hooke's atom, the exact eigenstates and single particle densities for arbitrary azimuthal quantum number, are obtained analytically. Information entropies associated with the wave functions for the relative motion are then studied systematically, since the same incorporates the effect of the Coulomb interaction. The {\it{quantum pottery}} of the information entropy density reveals a number of intricate structures, which differ significantly for the attractive and repulsive cases. We indicate the procedure to obtain the approximate eigen states. Making use of the relationship of this dynamical system with the quasi-exactly solvable systems, one can also develop a suitable perturbation theory, involving the Coulomb coupling $Z$, for the approximate wave functions.
The Pauli Exclusion Operator (PEO) which ensures proper symmetry of the eigenstates of multi-electron systems with respect to exchange of each pair of electrons is introduced. Once PEO is added to the Hamiltonian, no additional constraints on multi-electron wave function due to the Pauli exclusion principle are needed. For two-electron states in two dimensions ($2D$) the PEO can be expressed in a closed form in terms of momentum operators, while in the position representation PEO is a non-local operator. Generalizations of PEO for multi-electron systems is introduced. Several approximations to…
Dynamics of entropy and nonclassical properties of the state of a $Λ$-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium
We have computed the global quantum discord and von Neumann entropy of multipartite two-level atomic systems interacting with a single-mode Fock field. We use Tavis-Cumming model. We have explored how quantum correlations and quantum entanglement evolve with time in such systems. The quantum system is prepared initially in a mixed state and different parameters are varied to see how they affect the information processing in the system. The dynamical character of the global quantum discord and von Neumann entropy show an interplay between classical and non-classical correlations. Photons in thi…
We show for a general pure entangled state of two two-level atoms, the von Neumann entropy of the partial traces can be directly measured from the magnitude of the mean spin vector of a single atom of the pair. We emphasize the fact that the von Neumann entropy of the partial traces for such a system can be obtained without knowing the exact form of the quantum state of the two atoms, if we have the value of the magnitude of the mean spin vector of a single atom of the pair. Mean spin vector, used in the context of spin squeezing and spectroscopic squeezing in population spectroscopy, is exper…
Dynamics of entropy and nonclassicality features of the interaction between a $\diamondsuit$-type four-level atom and a single-mode field in the presence of intensity-dependent coupling and Kerr nonlinearity
We study the von Neumann entropy of the partial trace of a system of two two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single mode electromagnetic field in the cavity. We make a contrast of this entanglement entropy with the spin squeezing property of the system. We find a close relationship between this von Neumann entropy and the spin squeezing of the system. We observe that this entanglement entropy attains its maximum value when the spin squeezing in the system goes to its maximum and is zero when the spin squeezing in the system vanish…
Shell confined atom can serve as a generalized model to explain both \emph{free} and \emph{confined} condition. In this scenario, an atom is trapped inside two concentric spheres of inner $(R_{a})$ and outer $(R_{b})$ radius. The choice of $R_{a}, R_{b}$ renders four different quantum mechanical systems. In hydrogenic atom, they are termed as (a) free hydrogen atom (FHA) (b) confined hydrogen atom (CHA) (c) shell-confined hydrogen atom (SCHA) (d) left-confined hydrogen atom (LCHA). By placing $R_{a}, R_{b}$ at the location of radial nodes of respective \emph{free} $n,\ell$ states, a new kind o…
The entanglement witness and the entropy uncertainty are investigated by using the pseudomode theory for the open two-atom system under the quantum Zeno effect. The results show that, only when the two spectrums satisfy strong coupling with the atom, the time of entanglement witness can be prolonged and the lower bound of the entropic uncertainty can be reduced, and the entanglement can be witnessed many times. We also gave the corresponding physical explanation by the non-Markovianity. The Zeno effect not only can very effectively prolong the time of entanglement witness and reduce the lower …
In this paper, we are interested in studying entropy and dynamics entanglement between a single time dependent three-level atom interacting with one-mode cavity field when the atomic motion is taken into account. An exact analytical solution for the wave function is given by using Schrödinger equation for a specific initial condition. The field entropy of this system is investigated in the non-resonant case. The influences of the detuning parameters and atomic motion on the entanglement degree are examined. We show that both of the detuning parameters and atomic motion play important roles in …
In this work, we have investigated the phenomenon of acceleration radiation exhibited by an atom falling into a quantum corrected Schwarzschild black hole. We observe that the excitation-probability of the atom with simultaneous emission of a photon satisfies the equivalence principle when we compare it to the excitation probability of a mirror accelerating with respect to an atom. We also demonstrate the validity of the equivalence principle for a generic black hole geometry. Then we calculate the horizon brightened acceleration radiation (HBAR) entropy for this quantum corrected black hole g…
The statistical properties of physical systems in thermal equilibrium are blatantly different from their far-from-equilibrium counterparts. In the latter, fluctuations often dominate the dynamics and might cluster in ordered patterns in the form of dissipative coherent structures. Here, we study the transition of a cold atomic cloud, driven close to a sharp electronic resonance, from a stable to a turbulent phase. From the atomic density distribution -- measured using a spatially-resolved pump-probe technique -- we have computed the Shannon entropy on two different basis sets. Information comp…
