Microwave Spectroscopy

Contains reports on two research projects.United States Army Signal Corps (Contract DA36-039-sc-74895

Effect of Piezo Electric Oscillations on X-Ray Patterns of Quartz

Experiments have been made to determine the amplitude of vibration of the atoms in a quartz lattice due to piezo electric oscillations. A series of Laue X-ray patterns have been made of quartz plates cut at various angles to the electric axes. Very marked intensity differences are apparent between the patterns made with the plates oscillating and not oscillating

Vortices in attractive Bose-Einstein condensates in two dimensions

The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number $m$. An infinite sequence of radially excited stationary states appear for each value of $m$, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.Comment: 4 pages, 3 figure

Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-anti-vortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.Comment: 22 pages, 9 figure

Asymptotically Friedmann self-similar scalar field solutions with potential

We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are two distinct one-parameter families of asymptotic solutions,one is asymptotic to the proper Friedmann universe, while the other is asymptotic to the quasi-Friedmann universe, i.e., the Friedmann universe with anomalous solid angle. The asymptotically proper Friedmann solution is possible only if the universe is accelerated or the potential is negative. If the potential is positive, the density perturbation in the asymptotically proper Friedmann solution rapidly falls off at spatial infinity, while the mass perturbation is compensated. In the asymptotically quasi-Friedmann solution, the density perturbation falls off only in proportion to the inverse square of the areal radius and the relative mass perturbation approaches a nonzero constant at spatial infinity. The present result shows that a necessary condition holds in order that a self-gravitating body grows self-similarly due to the constant accretion of quintessence in an accelerating universe.Comment: accepted for publication in Physical Review D, minor correction, typos correcte

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte

Black Hole Evaporation in an Expanding Universe

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order $10^{-5} (M/10^{6}M_{\odot})^{1/3} (t/14 {Gyr})^{-1/3}$ but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana-Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.Comment: Accepted for publication in Class.Quant.Grav., 18 pages and 3 figure

Sub-picosecond compression by velocity bunching in a photo-injector

We present an experimental evidence of a bunch compression scheme that uses a traveling wave accelerating structure as a compressor. The bunch length issued from a laser-driven radio-frequency electron source was compressed by a factor >3 using an S-band traveling wave structure located immediately downstream from the electron source. Experimental data are found to be in good agreement with particle tracking simulations.Comment: 19 pages, 9 figures, submitted to Phys. Rev. Spec. Topics A&

Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth

The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schrodinger equation with a finite square well potential, which models a Bose-Einstein condensate in a quasi-one-dimensional trap of finite depth, is solved for the complete set of localized and partially localized stationary states, which the former evolve into when the nonlinearity is increased. An immediate application of these different solution types is tunable tunneling. Magnetically tunable Feshbach resonances can change the scattering length of certain Bose-condensed atoms, such as $^{85}$Rb, by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wavefunction. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wavefunction become nonzero at infinity when the nonlinearity increases. The tunneling of the wavefunction into the non-classical regime and thus its localization therefore becomes an external experimentally controllable parameter.Comment: 11 pages, 5 figure

Probing the size of extra dimension with gravitational wave astronomy

In Randall-Sundrum II (RS-II) braneworld model, it has been conjectured according to the AdS/CFT correspondence that brane-localized black hole (BH) larger than the bulk AdS curvature scale $\ell$ cannot be static, and it is dual to a four dimensional BH emitting the Hawking radiation through some quantum fields. In this scenario, the number of the quantum field species is so large that this radiation changes the orbital evolution of a BH binary. We derived the correction to the gravitational waveform phase due to this effect and estimated the upper bounds on $\ell$ by performing Fisher analyses. We found that DECIGO/BBO can put a stronger constraint than the current table-top result by detecting gravitational waves from small mass BH/BH and BH/neutron star (NS) binaries. Furthermore, DECIGO/BBO is expected to detect 10$^5$ BH/NS binaries per year. Taking this advantage, we found that DECIGO/BBO can actually measure $\ell$ down to $\ell=0.33 \mu$m for 5 year observation if we know that binaries are circular a priori. This is about 40 times smaller than the upper bound obtained from the table-top experiment. On the other hand, when we take eccentricities into binary parameters, the detection limit weakens to $\ell=1.5 \mu$m due to strong degeneracies between $\ell$ and eccentricities. We also derived the upper bound on $\ell$ from the expected detection number of extreme mass ratio inspirals (EMRIs) with LISA and BH/NS binaries with DECIGO/BBO, extending the discussion made recently by McWilliams. We found that these less robust constraints are weaker than the ones from phase differences.Comment: 19 pages, 10 figures. Published in PRD, typos corrected, references and footnotes adde