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

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Symbolic framework for linear active circuits based on port equivalence using limit variables

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Dynamics of entropy and nonclassical properties of the state of a Λ\Lambda-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium

In this paper, we study the interaction between a three-level atom and a quantized single-mode field with $` `$intensity-dependent coupling$"$ in a $` `$Kerr medium$"$. The three-level atom is considered to be in a $\Lambda$-type configuration. Under particular initial conditions, which may be prepared for the atom and the field, the dynamical state vector of the entire system will be explicitly obtained, for arbitrary nonlinearity function $f(n)$ associated to any physical system. Then, after evaluating the variation of the field entropy against time, we will investigate the quantum statistics as well as some of the nonclassical properties of the introduced state. During our calculations we investigate the effects of intensity-dependent coupling, Kerr medium and detuning parameters on the depth and domain of the nonclassicality features of the atom-field state vector. Finally, we compare our obtained results with those of $V$-type three-level atoms.Comment: 18 pages, 7 Figure

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

Continuously Guided Atomic Interferometry Using a Single-Zone Optical Excitation: Theoretical Analysis

In an atomic interferometer, the phase shift due to rotation is proportional to the area enclosed by the split components of the atom. However, this model is unclear for an atomic interferometer demonstrated recently by Shahriar et al., for which the atom simply passes through a single-zone optical beam, consisting of a pair of bichromatic counter-propagating beams. During the passage, the atomic wave packets in two distinct internal states couple to each other continuously. The two internal states trace out a complicated trajectory, guided by the optical beams, with the amplitude and spread of each wavepacket varying continuously. Yet, at the end of the single-zone excitation, there is an interference with fringe amplitudes that can reach a visibility close to unity. For such a situation, it is not clear how one would define the area of the interferometer, and therefore, what the rotation sensitivity of such an interferometer would be. In this paper we analyze this interferometer in order to determine its rotation sensitivity, and thereby determine its effective area. In many ways, the continuous interferometer (CI) can be thought of as a limiting version of the Borde-Chu Interferometer (BCI). We identify a quality factor that can be used to compare the performance of these interferometers. Under conditions of practical interest, we show that the rotation sensitivity of the CI can be comparable to that of the BCI. The relative simplicity of the CI (e.g., elimination of the task of precise angular alignment of the three zones) then makes it a potentially better candidate for practical atom interferometry for rotation sensing.Comment: 34 page

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

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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

Spontaneous emission and lifetime modification caused by an intense electromagnetic field

We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi "golden rule" still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an "inverse" quantum Zeno effect and can be analyzed in terms of dressed states.Comment: 25 pages, 6 figure

Driving atoms into decoherence-free states

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