Transient Cherenkov radiation from an inhomogeneous string excited by an ultrashort laser pulse at superluminal velocity

An optical response of one-dimensional string made of dipoles with a periodically varying density excited by a spot of light moving along the string at the superluminal (sub-luminal) velocity is theoretically studied. The Cherenkov radiation in such system is rather unusual, possessing both transient and resonant character. We show that under certain conditions, in addition to the resonant Cherenkov peak another Doppler-like frequency appears in the radiation spectrum. Both linear (small-signal) and nonlinear regimes as well as different string topologies are considered.Comment: accepted to Phys. Rev.

Generation of unipolar half-cycle pulse via unusual reflection of a single-cycle pulse from an optically thin metallic or dielectric layer

We present a significantly different reflection process from an optically thin flat metallic or dielectric layer and propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse. Unipolar pulses in reflection arise due to specifics of effectively one-dimensional pulse propagation. Namely, we show that in considered system the field emitted by a flat medium layer is proportional to the velocity of oscillating medium charges instead of their acceleration as it is usually the case. When the single-cycle pulse interacts with linear optical medium, the oscillation velocity of medium charges can be then forced to keep constant sign throughout the pulse duration. Our results essentially differ from the direct mirror reflection and suggest a possibility of unusual transformations of the few-cycle light pulses in linear optical systems

Super Tonks-Girardeau state in an attractive one-dimensional dipolar gas

The ground state of a one-dimensional (1D) quantum gas of dipoles oriented perpendicular to the longitudinal axis, with a strong 1/x^3 repulsive potential, is studied at low 1D densities $n$. Near contact the dependence of the many-body wave function on the separation x_{jl} of two particles reduces to a two-body wave function \Psi_{rel}(x_{jl}). Immediately after a sudden rotation of the dipoles so that they are parallel to the longitudinal axis, this wave function will still be that of the repulsive potential, but since the potential is now that of the attractive potential, it will not be stationary. It is shown that as nd^2 -> 0 the rate of change of this wave function approaches zero. It follows that for small values of nd^2, this state is metastable and is an analog of the super Tonks-Girardeau state of bosons with a strong zero-range attraction. The dipolar system is equivalent to a spinor Fermi gas with spin $z$ components \sigma_{\uparrow}=\perp (perpendicular to the longitudinal axis) and \sigma_{\downarrow}=|| (parallel to the longitudinal axis). A Fermi-Fermi mapping from spinor to spinless Fermi gas followed by the standard 1960 Fermi-Bose mapping reduces the Fermi system to a Bose gas. Potential experiments realizing the sudden spin rotation with ultracold dipolar gases are discussed, and a few salient properties of these states are accurately evaluated by a Monte Carlo method.Comment: 5 pages, 2 figures, revtex4. Published versio

Modules over the small quantum group and semi-infinite flag manifold

We develop a theory of perverse sheaves on the semi-infinite flag manifold $G((t))/N((t))\cdot T[[t]]$, and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of representations of the small quantum group at an even root of unity

Fifty years of the Glauber diffraction theory

In this minireview a historical excursus in theoretical studies related to the Glauber diffraction theory has been presented with an accent on the recent developments in this subject.Comment: 22 pages, 4 figures, in russian;v2: an atempt to improve hyphenatio

Population density gratings creation and control in resonant medium by half-cycle terahertz pulses

Electromagnetically induced gratings (EIG) are created by standing-wave laser field in resonant media. Such gratings can be also created by few-cycle electromagnetic pulses counter-propagating in the medium via coherent Rabi oscillations of atomic inversion. In this case, instantaneous cross-section of the pulses in the medium is not necessary for grating formation. In this paper, we revise our recent results in study of such grating formation and their control by few-cycle pulses coherently propagating in a resonant medium. We demonstrate the grating formation and their control in three-level medium excited by three subcycle THz pulses