Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

Interference-induced gain in Autler-Townes doublet of a V-type atom in a cavity

We study the Autler-Townes spectrum of a V-type atom coupled to a single-mode, frequency-tunable cavity field at finite termperature, with a pre-selected polarization in the bad cavity limit, and show that, when the mean number of thermal photons $N\gg 1$ and the excited sublevel splitting is very large (the same order as the cavity linewidth), the probe gain may occur at either sideband of the doublet, depending on the cavity frequency, due to the cavity-induced interference.Comment: Minor changes are mad

Quantum interference in the fluorescence of a molecular system

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. {\bf 77}, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifested in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory which explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. If the excitation process is composed of both a two-step one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.Comment: 11 pages, including 8 figure

Quantum trajectory approach to stochastically-induced quantum interference effects in coherently-driven two-level atoms

Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.Comment: paper accepted for publicatio

Hidden magnetic transitions in thermoelectric layered cobaltite, [Ca2_2CoO3_3]0.62_{0.62}[CoO2_2]

A positive muon spin rotation and relaxation ($\mu^+$SR) experiment on [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], ({\sl i.e.}, Ca$_3$Co$_4$O$_9$, a layered thermoelectric cobaltite) indicates the existence of two magnetic transitions at $\sim$ 100 K and 400 - 600 K; the former is a transition from a paramagnetic state to an incommensurate ({\sf IC}) spin density wave ({\sf SDW}) state. The anisotropic behavior of zero-field $\mu^+$SR spectra at 5 K suggests that the {\sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c-axis; also the {\sf IC-SDW} is found to exist not in the [Ca$_2$CoO$_3$] subsystem but in the [CoO$_2$] subsystem. In addition, it is found that the long-range {\sf IC-SDW} order completes below $\sim$ 30 K, whereas the short-range order appears below 100 K. The latter transition is interpreted as a gradual change in the spin state of Co ions %% at temperatures above 400 K. These two magnetic transitions detected by $\mu^+$SR are found to correlate closely with the transport properties of [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$].Comment: 7 pages, 8 figures. to be appeared in Phys. Rev.

Cavity implementation of quantum interference in a Λ\Lambda-type atom

A scheme for engineering quantum interference in a $\Lambda$-type atom coupled to a frequency-tunable, single-mode cavity field with a pre-selected polarization at finite temperature is proposed. Interference-assisted population trapping, population inversions and probe gain at one sideband of the Autler-Townes spectrum are predicted for certain cavity resonant frequencies.Comment: 2 postscript figures are adde

Quantum interference in a driven two-level atom

We show that a dynamical suppression of spontaneous emission, predicted for a three-level atom [S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996)] can occur in a two-level atom driven by st polychromatic field. We find that the quantum interference, responsible for the cancellation of spontaneous emission, appears between different channels of transitions among the dressed states of the driven atom. We discuss the effect for bichromatic and trichromatic (amplitude-modulated) fields and fmd that these two cases lead to the cancellation of spontaneous emission in different parts of the fluorescence spectrum. Our system has the advantage of being easily accessible by current experiments. [S1050-2947(99)50712-9]