Effective damping in the Raman cooling of trapped ions

We present a method of treating the interaction of a single three-level ion with two laser beams. The idea is to apply a unitary transformation such that the exact transformed Hamiltonian has one of the three levels decoupled for all values of the detunings. When one takes into account damping, the evolution of the system is governed by a master equation usually obtained via adiabatic approximation under the assumption of far-detuned lasers. To go around the drawbacks of this technique, we use the same unitary transformation to get an effective master equation.Comment: 15 pages, 5 figures. To appear in Optics Communication

Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring Z2xZ3. A "peculiar" feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit Pauli operators' space and surmised to be exhibited by any other higher-level quantum system.Comment: 8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'

Effective Hamiltonian Theory and Its Applications in Quantum Information

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.Comment: 5 pages, 3 figures, to be published in Canadian Journal of Physic

Optimal Sizes of Dielectric Microspheres for Cavity QED with Strong Coupling

The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number, n, and critical atom number, N, cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean, (n x N)^(1/2), is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is minimized occurs at a=7.83microns. On an experimental front, we have fabricated fused-silica microspheres with radii a=10microns and consistently observed quality factors Q=0.8x10^(7). These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.Comment: 12 pages, 14 figure

Non-negative Wigner functions in prime dimensions

According to a classical result due to Hudson, the Wigner function of a pure, continuous variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [D. Gross, J. Math. Phys. 47, 122107 (2006)]. For the case of systems of odd prime dimension, a greatly simplified proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods.Comment: 5 pages. Special case of a result proved in quant-ph/0602001. The proof is greatly simplified, making the general case more accessible. To appear in Appl. Phys. B as part of the proceedings of the 2006 DPG Spring Meeting (Quantum Optics and Photonics section

Low Energy Wave Packet Tunneling from a Parabolic Potential Well through a High Potential Barrier

The problem of wave packet tunneling from a parabolic potential well through a barrier represented by a power potential is considered in the case when the barrier height is much greater than the oscillator ground state energy, and the difference between the average energy of the packet and the nearest oscillator eigenvalue is sufficiently small. The universal Poisson distribution of the partial tunneling rates from the oscillator energy levels is discovered. The explicit expressions for the tunneling rates of different types of packets (coherent, squeezed, even/odd, thermal, etc.) are given in terms of the exponential and modified Bessel functions. The tunneling rates turn out very sensitive to the energy distributions in the packets, and they may exceed significantly the tunneling rate from the energy state with the same average number of quanta.Comment: 14 pages, LaTex type, to appear in Physics Letters

Mimicking a Kerrlike medium in the dispersive regime of second-harmonic generation

We find an effective Hamiltonian describing the process of second-harmonic generation in the far-off resonant limit. We show that the dynamics of the fundamental mode is governed by a Kerrlike Hamiltonian. Some dynamical consequences are examined.Comment: 12 pages, 4 figures Submitted to Optics Communication

Asymmetrical two-atom entanglement in a coated microsphere

We study evolution of entanglement of two two-level atoms placed inside a multilayered microsphere. We show that due to inhomogeneity of the field modes this entanglement essentially depends on the atomic positions (asymmetrical entanglement) and also on the detuning between the atomic transitions and field frequencies. The robust and complete entanglement can be achieved even in the resonant case when the atoms have different effective coupling constants, and it can be extended in time if the detuning is large enough. We study analytically the lossless case and estimate numerically the effect of dissipative processes

Quantum phase-space description of light polarization

We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization in the classical spirit by superposing two harmonic oscillators of the same angular frequency along two orthogonal axes. By describing each oscillator by a $s$-parametrized quasidistribution, we derive in a consistent way the final function for the polarization. We compare with previous approaches and discuss how this formalism works in some relevant examples.Comment: 17 pages, 4 eps color figure

Development of an approximate method for quantum optical models and their pseudo-Hermicity

An approximate method is suggested to obtain analytical expressions for the eigenvalues and eigenfunctions of the some quantum optical models. The method is based on the Lie-type transformation of the Hamiltonians. In a particular case it is demonstrated that $E\times \epsilon$ Jahn-Teller Hamiltonian can easily be solved within the framework of the suggested approximation. The method presented here is conceptually simple and can easily be extended to the other quantum optical models. We also show that for a purely imaginary coupling the $E\times \epsilon$ Hamiltonian becomes non-Hermitian but $P\sigma _{0}$-symmetric. Possible generalization of this approach is outlined.Comment: Paper prepared fo the "3rd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics" June 2005 Istanbul. To be published in Czechoslovak Journal of Physic