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Radio frequency antennas based on Rydberg atom vapor cells can in principle reach sensitivities beyond those of any wire antenna, especially at lower frequencies where long wires are needed to accommodate a growing wavelength. They also have other desirable features such as nonmetallic, lower profile, elements. This paper presents a detailed theoretical investigation of Rydberg antenna sensitivity, elucidating parameter regimes that could cumulatively lead to 2--3 orders of magnitude sensitivity increase beyond that of currently tested configurations. The key insight is to optimally combine the advantages of two well-studied approaches: (i) three laser ``2D star configuration'' setups that, enhanced also with increased laser power, help compensate for atom motion-induced Doppler broadening, and (ii) resonant coupling between a pair of near-degenerate Rydberg levels, tuned via a local oscillator to the incident signal. The advantage of the star setup is subtle because it only restores overall sensitivity to the expected Doppler-limited value, compensating for additional off-resonance reductions where differently moving atom populations destructively interfere with each other in the net signal. The additional unique advantage of the local oscillator tuning is that it leads to vastly narrower line widths, as low as ~10 kHz set by the intrinsic Rydberg state lifetimes, rather than the typical ~10 MHz set by the core state lifetimes. Intuitively, with this setup the two Rydberg states may be tuned to act as an independent high-q cavity, a point of view supported through a study of the frequency-dependence of the antenna resonant response. There are a number of practical experimental advances, especially larger ~1 cm laser beam widths, required to suppress various extrinsic line broadening effects and to fully exploit this cavity response., Comment: 22 pages, 12 figures

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored., Comment: 25 pages, 9 figures

Radio frequency antennas based on Rydberg atoms can in principle reach sensitivities beyond those of any conventional wire antenna, especially at lower frequencies where very long wires are needed to accommodate the growing wavelength. This paper presents a detailed theoretical investigation of Rydberg antenna sensitivity, elucidating parameter regimes that could cumulatively lead to 2--3 orders of magnitude sensitivity increase. Of special interest are three-laser setups proposed to compensate for atom motion-induced Doppler spreading. Such setups are in indeed shown to be advantageous, but only because they restore sensitivity to the \emph{expected} Doppler-limited value, removing significant additional off-resonance reductions., Comment: 5 pages, 6 figures

Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with much broader applicability. Such algorithms are computationally intensive, involving coherent processing of large sensor data sets in order to extract a small number of low profile targets from a cluttered background. Target enhancement is accomplished through accurate statistical characterization of the environment, followed by optimal identification of statistical outliers. The key result of the work is that the environmental covariance matrix estimation and manipulation at the heart of the statistical analysis actually enables a highly efficient quantum implementation. The algorithm is inspired by recent approaches to quantum machine learning, but requires significant extensions, including previously overlooked `quantum analog--digital' conversion steps (which are found to substantially increase the required number of qubits), `quantum statistical' generalization of the classic phase estimation and Grover search algorithms, and careful consideration of projected measurement operations. Application regimes where quantum efficiencies could enable significant overall algorithm speedup are identified. Key possible bottlenecks, such as data loading and conversion, are identified as well., Comment: 31 pages, 3 figures

A model of quantum measurement, illustrated using the spin--boson model, is formulated in terms of a cascading pair of quantum phase transitions. The first produces the desired superposition of macroscopic responses to the microscopic state under investigation, while the second provides a mechanism for subsequent "wavefunction collapse," suppressing superpositions of distinct macroscopic states, producing instead a density matrix that implements the expected classical observation outcome via the Born probability rule. Motivated by numerous carefully designed measurements that may occur during the course of a quantum computation, effects of entanglement are investigated when the measurement is performed on only a subset of the microscopic degrees of freedom., Comment: 5 pages, plus 10 page supplementary material

A model of single photon detection, illustrated by a photon-absorbing superfluid or superconducting microvolume, is formulated as a cascading pair of quantum phase transitions. In the first, the microvolume transitions to the normal state upon photon absorption, resulting in a superposition of macrostates depending on whether the photon is absorbed or not. The second enables subsequent "wavefunction collapse," producing a density matrix implementing the Born probability rule. Next, EPR-type measurements on space-like separated entangled photon pairs are considered. It is argued that macro-entangled superposition indeed survives until such time as the component states come into causal contact, following which the state rapidly collapses to one or the other expected outcome. Apparent superluminal communication effects are entirely avoided., Comment: 5 pages

The macroscale structure and microscale fluctuation statistics of late-time asymptotic steady state flows in cylindrical geometries is studied using the methods of equilibrium statistical mechanics. The axisymmetric assumption permits an effective two-dimensional description in terms of the (toroidal) flow field $\sigma$ about the cylinder axis and the vorticity field $\xi$ that generates mixing within the (poloidal) planes of fixed azimuth. As for a number of other 2D fluid systems, extending the classic 2D Euler equation, the flow is constrained by an infinite number of conservation laws, beyond the usual kinetic energy and angular momentum. All must be accounted for in a consistent equilibrium description. It is shown that the most directly observable impact of the conservation laws is on $\sigma$, which displays interesting large-scale radius-dependent flow structure. However, unlike in some previous treatments, we find that the thermodynamic temperature is always positive. As a consequence, except for an infinitesimal boundary layer that maintains the correct (conserved) value of the overall poloidal circulation, the impact on $\xi$ resides in the statistics of the strongly fluctuating, fine-scale mixing, where it is sensitive to `antiferromagnetic' microscale correlations that help maintain the analogue of local charge neutrality. The poloidal flow is macroscopically featureless, displaying no large scale circulating jet- or eddy-like features (which typically emerge as negative temperature states in analogous Euler and quasigeostrophic equilibria)., Comment: 10 pages, 4 figures

In recent work, Renaud, Venaille, and Bouchet (RVB) revisit the equilibrium statistical mechanics theory of the shallow water equations, within a microcanonical approach, focusing on a more careful treatment of the energy partition between inertial gravity wave and eddy motions in the equilibrium state, and deriving joint probability distributions for the corresponding dynamical degrees of freedom. The authors derive a Liouville theorem that determines the underlying phase space statistical measure, but then, through some physical arguments, actually compute the equilibrium statistics using a measure that \emph{violates} this theorem. Here, using a more convenient, but essentially equivalent, grand canonical approach, the full statistical theory consistent with the Liouville theorem is derived. The results reveal several significant differences from the previous results: (1) The microscale wave motions lead to a strongly fluctuating thermodynamics, including long-ranged correlations, in contrast to the mean-field-like behavior found by RVB. The final effective model is equivalent to that of an elastic membrane with a nonlinear wave-renormalized surface tension. (2) Even when a mean field approximation is made, a rather more complex joint probability distribution is revealed. Alternative physical arguments fully support the consistency of the results. Of course, the true fluid final steady state relies on dissipative processes not included in the shallow water equations, such as wave breaking and viscous effects, but it is argued that the current theory provides a more mathematically consistent starting point for future work aimed at assessing their impacts., Comment: 27 pages, 3 figures

The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged correlations between the magnetic and velocity fields. This is quite different from the results of previous variational treatments, which relied on a local product ansatz for the thermodynamic Gibbs distribution. The equilibria display the same type of coherent structures, such as compact eddies and zonal jets, previously found in pure fluid equilibria. Possible consequences of this for recent simulations of the solar tachocline are discussed., Comment: 4 pages, 1 figure

The work reported here details basic validation of our advanced physics-based EMI forward and inverse models against data collected by the NRL TEMTADS system. The data was collected under laboratory-type conditions using both artificial spheroidal targets and real UXO. The artificial target models are essentially exact, and enable detailed comparison of theory and data in support of measurement platform characterization and target identification. Real UXO targets cannot be treated exactly, but it is demonstrated that quantitative comparisons of the data with the spheroid models nevertheless aids in extracting key target discrimination information, such as target geometry and hollow target shell thickness., Comment: 15 pages, 16 figures

Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries. However, there are a number of new problems in remote sensing and classification of buried compact metallic targets that require a wider class of solutions that, if not exact, at least support rapid numerical evaluation. Here, the exact Chandrasekhar theory of the electrostatics of heterogeneously charged \emph{ellipsoids} is used to develop a "mean field" perturbation theory of low frequency electrodynamics of highly conducting ellipsoidal targets, in insulating or weakly conducting backgrounds. The theory is based formally on an expansion in the parameter $\eta_s = L_s/\delta_s(\omega)$, where $L_s$ is the characteristic linear size of the scatterer and $\delta_s(\omega)$ is the electromagnetic skin depth. The theory is then extended to a numerically efficient description of the intermediate-to-late-time dynamics following an excitation pulse. As verified via comparisons with experimental data taken using artificial spheroidal targets, when combined with a previously developed theory of the high frequency, early-time regime, these results serve to cover the entire dynamic range encountered in typical measurements., Comment: 36 pages, 10 figures

A number of new problems in remote sensing and identification of buried compact metallic targets motivate the search for new models that, if not exact, at least enable extremely rapid numerical predictions of electromagnetic scattering/induction data. Here the elegant Chandrasekhar theory of the electrostatics of charged ellipsoids is used to develop an essentially exact, extremely efficient description of low- to intermediate frequency (or late- to intermediate-time) responses of ellipsoidal targets. Comparisons with experimental data demonstrate that, together with a previously developed theory of the high frequency (or early time) regime, the results serve to cover the entire dynamic range encountered in typical measurements., Comment: 4 pages, 3 figures

We propose a new mechanism for the generation of zonal flows in magnetically confined plasmas, complementing previous theories based on a modulational instability. We derive a new conservation law that operates in the regime of weakly nonlinear dynamics, and show that it serves to focus the inverse cascade of turbulent drift wave energy into zonal flows. This mechanism continues to operate in the absence of the separation of dynamical scales typically assumed in instability calculations., Comment: 4 pages, 1 figure

We show that rotating shallow water dynamics possesses an approximate (adiabatic-type) positive quadratic invariant, which exists not only at mid-latitudes (where its analogue in the quasigeostrophic equation has been previously investigated), but near the equator as well (where the quasigeostrophic equation is inapplicable). Deriving the extra invariant, we find "small denominators" of two kinds: (1) due to the triad resonances (as in the case of the quasigeostrophic equation) and (2) due to the equatorial limit, when the Rossby radius of deformation becomes infinite. We show that the "small denominators" of both kinds can be canceled. The presence of the extra invariant can lead to the generation of zonal jets. We find that this tendency should be especially pronounced near the equator. Similar invariant occurs in magnetically confined fusion plasmas and can lead to the emergence of zonal flows., Comment: 29 pages, 4 figures

A concise, somewhat personal, review of the problem of superfluidity and quantum criticality in regular and disordered interacting Bose systems is given, concentrating on general features and important symmetries that are exhibited in different parts of the phase diagram, and that govern the different possible types of critical behavior. A number of exact results for various insulating phase boundaries, which may be used to constrain the results of numerical simulations, can be derived using large rare region type arguments. The nature of the insulator-superfluid transition is explored through general scaling arguments, exact model calculations in one dimension, numerical results in two dimensions, and approximate renormalization group results in higher dimensions. Experiments on He-4 adsorbed in porous Vycor glass, on thin film superconductors, and magnetically trapped atomic vapors in a periodic optical potential, are used to illustrate many of the concepts., Comment: 26 pages, 9 figures, submitted to Modern Physics Letters B (Brief Reviews)

We study the role of particle-hole symmetry on the universality class of various quantum phase transitions corresponding to the onset of superfluidity at zero temperature of bosons in a quenched random medium. The functional integral formulation of this problem in d spatial dimensions yields a (d+1)-dimensional classical XY-model with extended disorder--the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero site energies. We may distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero, vanishing on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the non-superfluid Mott insulating and Bose glass phases. We find that the Bose glass compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the relevance of type (ii) particle-hole symmetry breaking perturbations to the random rod critical behavior. We argue that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. To study higher dimensions we attempt, with partial success, to generalize the Dorogovtsev-Cardy-Boyanovsky double epsilon expansion technique to this problem. The qualitative renormalization group flow picture this technique provides is quite compelling., Comment: 43 pages, 14 figures, submitted to Phys. Rev. B

The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid phases, with the latter distinguished by the absence of atomic off-diagonal long-range order, gapped atomic excitations, and deconfined atomic pi-vortices. The properties of the molecular superfluid are explored, and it is shown that across a Feshbach resonance it undergoes a quantum Ising transition to the atomic superfluid, where both atoms and molecules are condensed. In addition to its distinct thermodynamic signatures and deconfined half-vortices, in a trap a molecular superfluid should be identifiable by the absence of an atomic condensate peak and the presence of a molecular one., Comment: 55 pages, 18 eps figures, submitted to Annals of Physics

It is shown that previous arguments leading to the equality $z=d$ ($d$ being the spatial dimensionality) for the dynamical exponent describing the Bose glass to superfluid transition may break down, as apparently seen in recent simulations (Ref. \cite{Baranger}). The key observation is that the major contribution to the compressibility, which remains finite through the transition and was predicted to scale as $\kappa \sim |\delta|^{(d-z)\nu}$ (where $\delta$ is the deviation from criticality and $\nu$ is the correlation length exponent) comes from the analytic part, not the singular part of the free energy, and therefore is not restricted by any conventional scaling hypothesis., Comment: 4 pages, no figures, submitted to Phys. Rev. Lett

An experiment is proposed to test a previously developed theory of the hydrodynamics of a nonequilibrium heat current-induced superfluid-normal interface. It is shown that the interfacial ``trapped'' second sound mode predicted by the theory leads to a sharp resonant dip in the reflected signal from an external second sound pulse propagated towards the interface when its horizontal phase speed matches that of the interface mode. The influence of the interface on thermal fluctuations in the bulk superfluid is shown to lead to slow power dependence of the order parameter, and other quantities, on distance from it., Comment: 4 pages, 3 figures

The problem of coherent vortex and zonal jet formation in a system of nonlinear Rossby waves is considered from the point of view of the late time steady state achieved by free decay of a given initial state. Statistical equilibrium equations respecting all conservation laws are constructed, generalizing those derived previously for 2D inviscid Euler flow. Jet-like solutions are ubiquitous, with large coherent vortices existing only when there is uniform background flow with the precise velocity to cancel the beta effect., Comment: 4 pages, 2 figures

It was recently demonstrated [P. B. Weichman, Phys. Rev. Lett. {\bf 91}, 143908 (2003)] that the scattered electric field from highly conducting targets following a rapidly terminated electromagnetic pulse displays a universal $t^{-1/2}$ power law divergence at early time. It is now shown that for strongly permeable targets, $\mu_c/\mu_b \gg 1$, where $\mu_b$ is the background magnetic permeability, the early time regime separates into two distinct power law regimes, with the early-early time $t^{-1/2}$ behavior crossing over to $t^{-3/2}$ at late-early time, reflecting a spectrum of magnetic surface modes. The latter is confirmed by data from ferrous targets where $\mu_c/\mu_b = {\cal O}(10^2)$, and for which the early-early time regime is invisibly narrow., Comment: 4 pages, 3 figures

The time-domain response of highly conducting targets following a rapidly terminated electromagnetic pulse displays three distinct regimes: early, intermediate and late time. The intermediate and late times are characterized by a superposition of exponentially decaying eigenmodes. At early time an ever increasing number of rapidly decaying modes contribute, with the result that the scattered electric field displays a universal $t^{-1/2}$ power law which emerges from the diffusive decay of a pattern of surface currents induced by the pulse. The power law amplitude reflects the surface geometry of the target, a property that may prove useful in buried target classification in geophysical remote sensing applications., Comment: 4 pages, no figures

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrain the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations., Comment: 4 pages, no figures. Submitted to Physical Review Letters

We review a striking array of recent experiments, and their theoretical interpretations, on the superfluid transition in $^4$He in the presence of a heat flux, $Q$. We define and evaluate a new set of critical point exponents. The statics and dynamics of the superfluid-normal interface are discussed, with special attention to the role of gravity. If $Q$ is in the same direction as gravity, a self-organized state can arise, in which the entire sample has a uniform reduced temperature, on either the normal or superfluid side of the transition. Finally, we review recent theory and experiment regarding the heat capacity at constant $Q$. The excitement that surrounds this field arises from the fact that advanced thermometry and the future availability of a microgravity experimental platform aboard the International Space Station will soon open to experimental exploration decades of reduced temperature that were previously inaccessible., Comment: 16 pages, 9 figures, plus harvard.sty style file for references Accepted for publication in Colloquia section of Reviews of Modern Physics

We study passive scalar transport by a stochastic travelling wave field in the physically relevant limit were typical fluid velocities, are much smaller than the typical group velocity, of the waves.

The fractal and marginal fractal regimes in surface geometry are studied. The basic notions of fractal geometry are applied to a small surface patch in a developed sea, corresponding to the equilibrium wave number spectrum. Topothesy, outer and inner boundaries of the fractal range, and a cascade pattern in surface geometry are discussed. Theoretical predictions of whitecap and foam coverage are presented. A fractal decomposition for a surface patch is developed based on the Karhunen-Loeve expansion. The resulting series formalizes the cascade process of constructing realization of a Gaussian random patch. The implications of the research for microwave remote sensing signatures are considered.