Decay of multiply charged vortices at nonzero temperatures

We study the instability of multiply charged vortices in the presence of thermal atoms and find various scenarios of splitting of such vortices. The onset of the decay of a vortex is always preceded by the increase of a number of thermal (uncondensed) atoms in the system and manifests itself by the sudden rise of the amplitude of the oscillations of the quadrupole moment. Our calculations show that the decay time gets shorter when the multiplicity of a vortex becomes higher.Comment: 4 pages, 6 figure

Strong-field approximation for intense-laser atom processes: the choice of gauge

The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schr\"odinger equation.Comment: 5 pages, 3 figures, revtex

Dipolar Relaxation in an ultra-cold Gas of magnetically trapped chromium atoms

We have investigated both theoretically and experimentally dipolar relaxation in a gas of magnetically trapped chromium atoms. We have found that the large magnetic moment of 6 $\mu_B$ results in an event rate coefficient for dipolar relaxation processes of up to $3.2\cdot10^{-11}$ cm$^{3}$s$^{-1}$ at a magnetic field of 44 G. We present a theoretical model based on pure dipolar coupling, which predicts dipolar relaxation rates in agreement with our experimental observations. This very general approach can be applied to a large variety of dipolar gases.Comment: 9 pages, 9 figure

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

Optical signatures of quantum phase transitions in a light-matter system

Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric amplifier. Our findings boost the motivation for exploring exotic quantum phase transition phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.Comment: 4 pages, 4 figure

Fluorescence spectrum of a two-level atom driven by a multiple modulated field

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving held is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mellow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving held. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are 180 degrees out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we shaw that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied