Methods of solution of differential equations in general relativity and related potential problems

Imperial Users onl

A Lorentz Invariant Pairing Mechanism: Relativistic Cooper Pairs

We study a Lorentz invariant pairing mechanism that arises when two relativistic spin-1/2 fermions are subjected to a Dirac string coupling. In the weak coupling regime, we find remarkable analogies between this relativistic bound system and the well known superconducting Cooper pair. As the coupling strength is raised, quenched phonons become unfrozen and dynamically contribute to the gluing mechanism, which translates into novel features of this relativistic superconducting pair.Comment: Revtex4 file, color figures with less resolution to comply with arxiv restriction

Multiphoton Bloch-Siegert shifts and level-splittings in a three-level system

In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.Comment: 29 pages, 13 figure

Role of electromagnetically induced transparency in resonant four-wave-mixing schemes.

Published versio

Ground state laser cooling using electromagnetically induced transparency

A laser cooling method for trapped atoms is described which achieves ground state cooling by exploiting quantum interference in a driven Lambda-shaped arrangement of atomic levels. The scheme is technically simpler than existing methods of sideband cooling, yet it can be significantly more efficient, in particular when several motional modes are involved, and it does not impose restrictions on the transition linewidth. We study the full quantum mechanical model of the cooling process for one motional degree of freedom and show that a rate equation provides a good approximation.Comment: 4 pages, 3 figures; v2: minor modifications to abstract, text and figure captions; v3: few references added and rearranged; v4: One part significantly changed, 1 figure removed, new equations; v5: typos corrected, to appear in PR

Driving atoms into decoherence-free states

Published versio

Bound mode of an atom laser

We use a Fano diagonalization technique to find the eigenmodes of an atom laser consisting of a single-mode atomic cavity that is coherently coupled to the continuum of free space modes. Under very general conditions the system exhibits a single, stationary bound mode. We discuss the properties of this bound mode depending on the system parameters and investigate its effect on the output beam of the atom laser