We systematically generalize Grover algorithm in a density matrix formalism by exploiting the underlying two dimensional subspace of the problem. Using this, we derive analytic expressions for the success probability and $l_{1}$ norm of coherence measure $(C_{l_{1}} )$ after arbitrary iterations of the generalized Grover operator with two generic phase angles (α, β). We show for the phase matching condition α = −β = 0.268π with three iterations, success probability ≥ 0.8 can be achieved only with knowledge about the lower bound λ = 0.14, where λ is the ratio of marked to total number of states in the database. This result will improve the quantum search algorithm when applied to databases with unknown number of marked states.

The precise control and knowledge over the atomic dynamics is central to the advancement of quantum technology. The different experimental conditions namely, atoms in a vacuum, an antirelaxation coated and a buffer gas filled atomic cell provides complementary platform for such investigations. The extent of changes in optical pumping, velocity changing collision and hyperfine changing collision rates associated with these conditions are discussed. There is a phenomenal change in the optical density by a factor of >25 times in presence of a control field in buffer gas environment. We found confinement induced enhanced optical pumping as the mechanism behind the observed transparency in buffer gas cell. The diffusive velocity of atoms is measured to be ~25±12 m/s and ≤8±4 m/s for antirelaxation coated and buffer gas filled cell respectively. The measurements are carried out for 85Rb atoms in natural isotopic composition using pump-probe spectroscopy. The studies will have useful application in measurements of relaxation rates, quantum memory, quantum repeaters and atomic devices.

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