Analysis of adiabatic transfer in cavity QED

A three-level atom in a $\Lambda$ configuration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. Through control with an appropriate laser, this system allows for efficient storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity. This process presumes an adiabatic transfer through the `dark state', a coherent superposition of the two lower levels of the $\Lambda$ system, by a slow variation of the intensity of the control laser. We study the full quantum mechanics of this transfer process with a view to examine the nonadiabatic effects, as the control laser is varied in time. The nonadiabatic effects arise due to inevitable excitations of the system to states involving the highest level of the $\Lambda$ configuration, which is radiative. We formulate the problem in terms of the instantaneous eigenstates and solve it numerically, allowing for spontaneous decays from the excited level. We present detailed results for both storage and retrieval for a suitable range of variation rates and intensity of the control laser, and examine optimum conditions for the transfer process.Comment: 24 pages, 9 figure

Duality and even number spin-correlation functions in the two dimensional square lattice ising model

The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature $(T>T_{c})$ expressions for these correlation functions are transformed into the low temperature $(T<T_{c})$ expressions under this duality transformations.Comment: 7 pages, no figure

Speeding up SAT solver by exploring CNF symmetries : Revisited

Boolean Satisfiability solvers have gone through dramatic improvements in their performances and scalability over the last few years by considering symmetries. It has been shown that by using graph symmetries and generating symmetry breaking predicates (SBPs) it is possible to break symmetries in Conjunctive Normal Form (CNF). The SBPs cut down the search space to the nonsymmetric regions of the space without affecting the satisfiability of the CNF formula. The symmetry breaking predicates are created by representing the formula as a graph, finding the graph symmetries and using some symmetry extraction mechanism (Crawford et al.). Here in this paper we take one non-trivial CNF and explore its symmetries. Finally, we generate the SBPs and adding it to CNF we show how it helps to prune the search tree, so that SAT solver would take short time. Here we present the pruning procedure of the search tree from scratch, starting from the CNF and its graph representation. As we explore the whole mechanism by a non-trivial example, it would be easily comprehendible. Also we have given a new idea of generating symmetry breaking predicates for breaking symmetry in CNF, not derived from Crawford's conditions. At last we propose a backtrack SAT solver with inbuilt SBP generator.Comment: 12 pages, Forty-First Southeastern International Conference on Combinatorics, Graph Theory, and Computing (USA, 2010

On the low temperature series expansion for the diagonal correlation functions in the two-dimensional Ising model

A previously tested differential equation method for generating low temperature series expansion for diagonal spin-spin correlation functions in the d=2 Ising model is extended to generate the non-universal terms for arbitrary separation of the spins. This extends the earlier calculations of these correlation functions.Comment: 7 pages, no figure

Is There a Problem with Quantum Gravitation?

We argue that Quantum Gravitation forces us to sum over metrics of all signatures.Comment: 3 pages, no figure

A note on the Lee-Yang circle theorem

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.Comment: 3 pages, no figure

Into the fission valley of magic nucleus Polonium

The word "radioactive" was first coined by Marie Curie when she, along with her husband Pierre Curie, discovered the element Polonium. The nucleus 210Po is a testing ground for many theoretical and experimental aspects of nuclear structure as well as nuclear fission dynamics as it is a magic nucleus with neutron number N=126. At Variable Energy Cyclotron Centre, Kolkata the fission of Polonium nuclei is being studied in order to understand the survival of nuclear shell effects that is known to be the key for the stability of super heavy elements (SHE).Comment: Submitted to Current Science, to honour Prof. Sailajananda Bhattacharya on the eve of the completion of his tenure as a Raja Ramanna Fello

Entanglement like properties in Spin-Orbit Coupled Ultra Cold Atom and violation of Bell like Inequality

We show that the general quantum state of synthetically spin-orbit coupled ultra cold bosonic atom whose condensate was experimentally created recently ( Y. J. Lin {\it et al.}, Nature, {\bf 471}, 83, (2011)), shows entanglement between motional degrees of freedom ( momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provides a unique opportunity to verify fundamental principle like quantum non-contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such atom-laser system and how that influneces quantities like entanglement entropy, violation of Bell like Inequality etc. We also discuss the implication of our result in testing the quantum non-contextuality and Bell's Inequality vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra cold atoms.Comment: Latex file with 4 pdf figure

Spin Relaxation in Silicon Nanowires

We simulate spin polarized transport of electrons along a silicon nanowire and along a silicon two dimensional channel. Spin density matrix calculations are used along with the semi-classical Monte Carlo approach to model spin evolution along the channel. Spin dephasing in silicon is caused due to Rashba Spin Orbit Interaction (structural inversion asymmetry) which gives rise to D'yakonov-Perel' relaxation. Spin relaxation length in a nanowire is found to be an order of magnitude higher than that in a 2-D channel. The effect of driving electric field on spin relaxation is also investigated. These results obtained are essential for design of spintronics based devices.Comment: 12 pages, 8 figure

Dynamics of Spatial Heterogeneity in Landfill - A Stochastic Analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density. In a marked departure from previous predictions, our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure relates to plant production times of approximately 20-30 years instead of the previous (incorrect) deterministic model predictions of 50 years and above.Comment: To be published in Applied Mathematical Modelling; 8 pages, 5 figure