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We present a pedagogical review of the swelling thermodynamics and phase transitions of polymer gels. In particular, we discuss how features of the volume phase transition of the gel's osmotic equilibrium is analogous to other transitions described by mean-field models of binary mixtures, and the failure of this analogy at the critical point due to shear rigidity. We then consider the phase transition at fixed volume, a relatively unexplored paradigm for polymer gels that results in a phase-separated equilibrium consisting of coexisting solvent-rich and solvent-poor regions of gel. Again, the gel's shear rigidity is found to have a profound effect on the phase transition, here resulting in macroscopic shape change at constant volume of the sample, exemplified by the tunable buckling of toroidal samples of polymer gel. By drawing analogies with extreme mechanics, where large shape changes are achieved via mechanical instabilities, we formulate the notion of extreme thermodynamics, where large shape changes are achieved via thermodynamic instabilities, i.e. phase transitions., 40 pages, 22 figures, Submitted to Nanotechnology

When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume whilst maintaining its toroidal shape. By contrast, if the gel is heated quickly, an impermeable layer of collapsed polymer forms and traps solvent within the gel, arresting the volume change. The ensuing evolution of the gel then happens at fixed volume, leading to phase-separation and the development of inhomogeneous stress that deforms the toroidal shape. We observe that this stress can cause the torus to buckle out of the plane, via a mechanism analogous to the bending of bimetallic strips upon heating. Our results demonstrate that thermodynamic instabilities, i.e., phase transitions, can be used to actuate mechanical deformation in an extreme thermodynamics of materials., 5 pages, 4 figures. To appear in Physical Review E (2018)

Macroscopic properties of suspensions, such as those composed of globular particles (e.g., colloidal or macromolecular), can be tuned by controlling the equilibrium aggregation of the particles. We examine how aggregation -- and, hence, macroscopic properties -- can be controlled in a system composed of both globular particles and long, flexible polymer chains that reversibly bind to one another. We base this on a minimal statistical mechanical model of a single aggregate in which the polymer chain is treated either as ideal or self-avoiding, and, in addition, the globular particles are taken to interact with one another via excluded volume repulsion. Furthermore, each of the globular particles is taken to have one single site to which at most one polymer segment may bind. Within the context of this model, we examine the statistics of the equilibrium size of an aggregate and, thence, the structure of dilute and semidilute suspensions of these aggregates. We apply the model to biologically relevant aggregates, specifically those composed of macromolecular proteoglycan globules and long hyaluronan polymer chains. These aggregates are especially relevant to the materials properties of cartilage and the structure-function properties of perineuronal nets in brain tissue, as well as the pericellular coats of mammalian cells., 8 pages, 3 figures, Soft Matter (2015)

Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of the fluid can yield insights into experimentally realizable active flows, but this connection is well understood in only a few select cases. We introduce a model of self-propelled particles based on an analogy with the motion of electrons that have strong spin-orbit coupling. We find that, within our model, self-propelled particles are subject to an analog of the Heisenberg uncertainty principle that relates translational and rotational noise. Furthermore, by coarse-graining this microscopic model, we establish expressions for the coefficients of the Toner-Tu equations---the hydrodynamic equations that describe an active fluid composed of these "active spins." The connection between self-propelled particles and quantum spins may help realize exotic phases of matter using active fluids via analogies with systems composed of strongly correlated electrons., 13 pages, 3 figures

Topology has emerged as a crucial and fruitful component of modern physics.Topology has emerged as a crucial and fruitful component of modern physics.

We consider the quantum-control task of obtaining a target unitary operation via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise. We allow for two sources of noise: fluctuations in the control fields and those arising from the environment. We address the issue of error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. We express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity, which characterizes the proximity of the sought-after evolution to ones achievable in the presence of noise. Error mitigation is then accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the `forward' and `backward' branches of the time-contour are inequivalent with respect to the noise. The present approach naturally allows the incorporation of constraints on the control fields; a useful feature in practice, given that they feature in real experiments. We illustrate this MSR-SK approach by considering a system consisting of a single spin $s$ freedom (with $s$ arbitrary), focusing on the case of $1/f$ noise. We discover that optimal error-mitigation is accomplished via a universal control field protocol that is valid for all $s$, from the qubit (i.e., $s=1/2$) case to the classical (i.e., $s \to \infty$) limit. In principle, this MSR-SK approach provides a framework for addressing quantum control in the presence of noise for systems of arbitrary complexity., 25 pages, 4 figures. To be published in Physical Review A

Orbital order is important to many correlated electron phenomena, including colossal magnetoresistance and high-temperature superconductivity. A study of a previously unreported structure transition in KCuF3 suggests that direct interorbital exchange is important to understanding such order.

Andreev reflection-where an electron in a normal metal backscatters off a superconductor into a hole-forms the basis of low energy transport through superconducting junctions. Andreev reflection in confined regions gives rise to discrete Andreev bound states (ABS), which can carry a supercurrent and have recently been proposed as the basis of qubits [1-3]. Although signatures of Andreev reflection and bound states in conductance have been widely reported [4], it has been difficult to directly probe individual ABS. Here, we report transport measurements of sharp, gate-tunable ABS formed in a superconductor-quantum dot (QD)-normal system, which incorporates graphene. The QD exists in the graphene under the superconducting contact, due to a work-function mismatch [5, 6]. The ABS form when the discrete QD levels are proximity coupled to the superconducting contact. Due to the low density of states of graphene and the sensitivity of the QD levels to an applied gate voltage, the ABS spectra are narrow, can be tuned to zero energy via gate voltage, and show a striking pattern in transport measurements., Comment: 25 Pages, included SOM

We propose that condensed-matter phenomena involving the spontaneous emergence and dynamics of crystal lattices can be realized using Bose–Einstein condensates coupled to multimode optical cavities. It is known that, in the case of a transversely pumped single-mode cavity, the atoms crystallize at either the even or the odd antinodes of the cavity mode at sufficient pump laser intensity, thus spontaneously breaking a discrete translational symmetry. Here we demonstrate that, in multimode cavities, crystallization involves the spontaneous breaking of a continuous translational symmetry, through a variant of Brazovskii’s transition, thus paving the way for realizations of compliant lattices and associated phenomena, such as dislocations, frustration, glassiness and even supersolidity, in ultracold atomic settings, where quantum effects have a dominant role. We apply a functional-integral formalism to explore the role of fluctuations in this correlated many-body system, to calculate their effect on the threshold for ordering, and to determine their imprint on the correlations of the light emitted from the cavity. Optical lattices, generated by interfering laser beams, provide a platform for observing condensed-matter phenomena in ultracold-atom systems. By extending the lattice idea to a multimode cavity, it should be possible to observe even more complex effects, such as frustration, crystallization, glass phases and supersolidity.

Measurements of the distribution of stochastic switching currents in homogeneous, ultra-narrow superconducting nanowires provide strong evidence that the low-temperature current-switching in such systems occurs through quantum phase slips—topological quantum fluctuations of the superconducting order parameter via which tunnelling occurs between current-carrying states.

The dc Josephson effect refers to the dissipationless electrical current -- the supercurrent -- that can be sustained across a weak link connecting two bulk superconductors. This effect is a probe of the fundamental nature of the superconducting state. Here, we analyze the case of two superconducting thin films connected by a point contact. Remarkably, the Josephson effect is absent at nonzero temperature, and the resistance across the contact is nonzero. Moreover, the point contact resistance is found to vary with temperature in a nearly activated fashion, with a UNIVERSAL energy barrier determined only by the superfluid stiffness characterizing the films, an angle characterizing the geometry, and whether or not the Coulomb interaction between Cooper pairs is screened. This behavior reflects the subtle nature of the superconductivity in two-dimensional thin films, and should be testable in detail by future experiments., Comment: 16 + 8 pages. 1 figure, 1 table

Louis Kaplow and Stven Shavell have shown that liability rules tend to efficiently harness the defendant’s private information when courts are imperfectly informed as to litigants’ valuations. But they claim that liability rules cannot harness private information when the disputants’ valuations are correlated. This article rejects the correlated‐value claim. While correlated valuations create real problems of implementation, Kaplow and Shavell’s own harnessing result can be extended to redeem the usefulness of liability rules. When values are correlated, enlightened courts can enlarge the damages that takers expect to pay so as to induce efficient takings. The relative efficiency of property and liability rules turns out to be independent of whether the disputants’ values are correlated.

We study a liquid of zigzagging two-dimensional directed polymers with bending rigidity, i.e., polymers whose conformations follow checkerboard paths. In the continuum limit the statistics of such polymers obey the Dirac equation for particles of imaginary mass. We exploit this observation to investigate a liquid of these polymers via a quantum many-fermion analogy. A self-consistent approximation predicts a phase of tilted order, in which the polymers may develop a preference to zig rather than zag. We compute the phase diagram and key response functions for the polymer liquid, and comment on the role played by fluctuations., 5 pages, 4 figures

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state., 7 pages, 1 figure

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond., Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop, International Centre for Theoretical Physics, Trieste, Italy (September 15-18, 1999)

Low-energy quasiparticle states, arising from scattering by single-particle potentials in d-wave superconductors, are addressed. Via a natural extension of the Andreev approximation, the idea that sign-variations in the superconducting pair-potential lead to such states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials, such as those due to impurities. The index-theoretic origin of these states is exhibited via a simple connection with Witten's supersymmetric quantum-mechanical model., Comment: 5 pages

Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even if the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal /superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximity-like effects, including the local enhancement (suppression) of superconducting fluctuations on the quasi-normal (quasi-superconducting) side of the step, significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire., Comment: 5 pages, 2 figures (eps)

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure $\pi$ of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension $\phi$, we can determine $\phi$ from $\pi$, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using $\phi$, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluid-like, irrespective of volume fraction. By calculating the dependence on $\phi$ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid coexistence., Comment: 5 pages, 3 figures

It is shown, within the framework of the Ginzburg-Landau theory for a superconductor with d_{x^2-y^2} symmetry, that the passing of a supercurrent through the sample results, in general, in the induction of order-parameter components of distinct symmetry. The induction of s-wave and d_{xy(x^2-y^2)-wave components are considered in detail. It is shown that in both cases the order parameter remains gapless; however, the structure of the lines of nodes and the lobes of the order parameter are modified in distinct ways, and the magnitudes of these modifications differ in their dependence on the (a-b plane) current direction. The magnitude of the induced s-wave component is estimated using the results of the calculations of Ren et al. [Phys. Rev. Lett. 74, 3680 (1995)], which are based on a microscopic approach., 15 pages, includes 2 figures. To appear in Phys. Rev. B

The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is predicated on the well-known equivalence between the classical equilibrium statistical mechanics of directed polymers in two spatial dimensions and the imaginary-time quantum dynamics of particles in one spatial dimension, originally exploited by P.-G. de Gennes [P.-G. de Gennes, J. Chem. Phys. 48, 2257 (1968)]. Known results concerning two exactly solvable microscopic models of quantum particles moving in one spatial dimension---the Lieb-Liniger model of contact interactions and the Calogero-Sutherland model of long-range interactions---are used to shed light on the behavior of the corresponding polymeric systems. In addition, the technique of bosonization is used to reveal how generic polymer interactions give rise to an emergent polymer fluid that has universal collective excitations. Additionally, the response of the system to topological constraints such as pins though which polymers cannot pass is explored. Immediately on the compressed side of a pin there is a divergent pile-up in polymer density, while on the other side there is a gap of finite area in which polymer density is negligible. Comparison of this response to that of a system of simply noncrossing (i.e., noncrossing but otherwise noninteracting) directed polymers, explored in a companion paper, reveals that generic interactions leave the structure quantitatively unchanged on the line transverse to the pin, and leave it qualitatively unchanged throughout the two dimensions of the system's extent. Furthermore, the free-energy cost associated with a pin that partitions a system having generic interactions is found to be proportional to the pin-partitioning cost for a system of simply noncrossing polymers.

We address the statistical mechanics of randomly and permanently crosslinked networks. We develop a theoretical framework (vulcanization theory) which can be used to systematically analyze the correlation between the statistical properties of random networks and their histories of formation. Generalizing the original idea of Deam and Edwards, we consider an instantaneous crosslinking process, where all crosslinkers (modeled as Gaussian springs) are introduced randomly at once in an equilibrium liquid state, referred to as the preparation state. The probability that two functional sites are crosslinked by a spring exponentially decreases with their distance squared. After formally averaging over network connectivity, we obtained an effective theory with all degrees of freedom replicated 1 + n times. Two thermodynamic ensembles, the preparation ensemble and the measurement ensemble, naturally appear in this theory. The former describes the thermodynamic fluctuations in the state of preparation, while the latter describes the thermodynamic fluctuations in the state of measurement. We classify various correlation functions and discuss their physical significances. In particular, the memory correlation functions characterize how the properties of networks depend on their history of formation, and are the hallmark properties of all randomly crosslinked materials. We clarify the essential difference between our approach and that of Deam-Edwards, discuss the saddle-point order parameters and its physical significance. Finally we also discuss the connection between saddle-point approximation of vulcanization theory, and the classical theory of rubber elasticity as well as the neo-classical theory of nematic elastomers., 18 pages, 3 pdf figures

The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in the vicinity of the obstacle, and the associated free-energy cost is found to scale quadratically with the average polymer density. The polymer-polymer interactions are accounted for via a sequence of transformations: from the 3D line liquid to a 2D fluid of Bose particles to a 2D composite fermion fluid and, finally, to a 2D one-component plasma. The results presented here are applicable to a range of systems consisting of noncrossing directed lines., Comment: 5 pages, 2 figures

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition., Comment: Review Article, REVTEX, 58 pages, 3 PostScript figures

Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid-crystalline characteristics of an IGNE, as probed via measurements made at high temperatures. In contrast with the case of uncross-linked LCPs, for IGNEs these characteristics are determined not only by thermal fluctuations but also by the quenched disorder associated with the cross-link constraints. To study IGNEs, we consider a microscopic model of dimer nematogens in which the dimers interact via orientation-dependent excluded volume forces. The dimers are, furthermore, randomly, permanently cross-linked via short Hookean springs, the statistics of which we model by means of a Deam-Edwards type of distribution. We show that at length-scales larger than the size of the nematogens this approach leads to a recently proposed phenomenological Landau theory of IGNEs [Lu et al., Phys. Rev. Lett. 108, 257803 (2012)], and hence predicts a regime of short-ranged oscillatory spatial correlations in the nematic alignment, of both thermal and glassy types. In addition, we consider two alternative microscopic models of IGNEs: (i) a wormlike chain model of IGNEs that are formed via the cross-linking of side-chain LCPs; and (ii) a jointed chain model of IGNEs that are formed via the cross-linking of main-chain LCPs. At large length-scales, both of these models give rise to liquid-crystalline characteristics that are qualitatively in line with those predicted by the dimer-and-springs model., Comment: 33 pages, 6 figures, 6 appendices

A theory of Rydberg atom interactions is used to derive analytical forms for the spin wave pair correlation function in laser-excited cold-atom vapors. This function controls the quantum statistics of light emission from dense, inhomogeneous clouds of cold atoms of various spatial dimensionalities. The results yield distinctive scaling behaviors on the microsecond timescale, including generalized exponential decay. A detailed comparison is presented with a recent experiment on a cigar-shaped atomic ensemble [Y. Dudin and A. Kuzmich, Science 336, 887 (2012)], in which Rb atoms are excited to a set of Rydberg levels., 4 pages, Supplemental Material in Appendix, 4 figures

The presence of Majorana zero-energy modes at vortex cores in a topological superconductor implies that each vortex carries an extra entropy $s_0$, given by $(k_{B}/2)\ln 2$, that is independent of temperature. By utilizing this special property of Majorana modes, the edges of a topological superconductor can be cooled (or heated) by the motion of the vortices across the edges. As vortices flow in the transverse direction with respect to an external imposed supercurrent, due to the Lorentz force, a thermoelectric effect analogous to the Ettingshausen effect is expected to occur between opposing edges. We propose an experiment to observe this thermoelectric effect, which could directly probe the intrinsic entropy of Majorana zero-energy modes., 16 pages, 3 figures

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment.

The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding to particle world-lines. This equivalence motivates the application of techniques originally designed for one-dimensional many-particle quantum systems to the exploration of many-polymer systems, as first recognized and exploited by P.-G. de Gennes [J.\ Chem.\ Phys.\ {\bf 48}, 2257 (1968)]. In this low-dimensional setting interactions give rise to an emergent polymer fluid, and we examine how topological constraints on this polymer fluid (e.g., due to uncrossable pins or barriers) and their geometry give rise to strong, entropy-driven forces. In the limit of large polymer densities, in which a type of mean-field theory is accurate, we find that a point-like pin causes a divergent pile-up of polymer density on the high-density side of the pin and a zero-density region (or gap) of finite area on the low-density. In addition, we find that the force acting on a pin that is only mildly displaced from its equilibrium position is sub-Hookean, growing less than linearly with the displacement, and that the gap created by the pin also grows sublinearly with the displacement. By contrast, the forces acting between multiple pins separated along the direction preferred by the polymers are super-Hookean. These nonlinear responses result from effective long-ranged interactions between polymer segments, which emerge via short-ranged interactions between distant segments of long polymer strands. In the present paper, we focus on the case of an infinitely strong, repulsive contact interaction, which ensures that the polymers completely avoid one another. In a companion paper, we consider the effects of a wider set of inter-polymer interactions., Comment: 17 pages, 10 figures

A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a dispersion minimum on a circle in momentum space; we show that kinematic constraints due to this dispersion cause interactions to renormalize to universal, angle-dependent values that govern the phase structure in the dilute-gas limit. We find that, regardless of microscopic interactions, (a) the ground state involves condensation at two opposite momenta, and is, in finite systems, a fragmented condensate; and (b) there is a nonzero-temperature instability toward the condensation of pairs of bosons. We discuss how our results can be reconciled with the qualitatively different mean-field phase diagram, which is appropriate for dense gases., Comment: 5 pages, 2 figures

We show that the effective spin-spin interaction between three-level atoms confined in a multimode optical cavity is long-ranged and sign-changing, like the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in positional randomness can realize spin systems having disordered and frustrated interactions. We argue that, whenever the atoms couple to sufficiently many cavity modes, the cavity-mediated interactions give rise to a spin glass. In addition, we show that the quantum dynamics of cavity-confined spin systems is that of a Bose-Hubbard model with strongly disordered hopping but no on-site disorder; this model exhibits a random-singlet glass phase, absent in conventional optical-lattice realizations. We briefly discuss experimental signatures of the realizable phases., 5 pages, 2 figures

Spin-triplet superfluids can support exotic objects, such as half-quantum vortices characterized by the nontrivial winding of the spin structure. We present cantilever magnetometry measurements performed on mesoscopic samples of Sr2RuO4, a spin-triplet superconductor. For micron-sized annular-shaped samples, we observe transitions between integer fluxoid states, as well as a regime characterized by "half-integer transitions," i.e., steps in the magnetization with half the height of the ones we observe between integer fluxoid states. These half-height steps are consistent with the existence of half-quantum vortices in superconducting Sr2RuO4., 43 pages, 13 figures, 3 tables

Microwave Fabry-Perot resonators containing nonlinear mesoscopic elements (such as superconducting nanowires) can be used to explore many-body circuit QED. Here, we report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involve MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, are achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent "crater" on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems, from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude-fluctuations. We conclude by giving a brief discussion of how circuit-QED-based systems have the potential to facilitate understanding of quantum phase-slips in superconducting nanowires., Comment: 40 pages, 20 figures

Systems of superconducting islands placed on normal metal films offer tunable realizations of two-dimensional (2D) superconductivity; they can thus elucidate open questions regarding the nature of 2D superconductors and competing states. In particular, island systems have been predicted to exhibit zero-temperature metallic states. Although evidence exists for such metallic states in some 2D systems, their character is not well understood: the conventional theory of metals cannot explain them, and their properties are difficult to tune. Here, we characterize the superconducting transitions in mesoscopic island-array systems as a function of island thickness and spacing. We observe two transitions in the progression to superconductivity; both transition temperatures exhibit unexpectedly strong depression for widely spaced islands. These depressions are consistent with the system approaching zero-temperature metallic states. The nature of the transitions and the state between them is explained using a phenomenological model involving the stabilization of superconductivity on each island via a weak coupling to and feedback from its neighbors., Comment: 15 pages, 5 figures

The entanglement in quantum XY spin chains of arbitrary length is investigated via the geometric (measure of) entanglement. The emergence of entanglement is explained intuitively from the perspective of perturbations. The model is solved exactly and the energy spectrum is determined and analyzed in particular for the lowest two levels. The entanglement is obtained over the entire phase diagram, and its behavior can be used to delineate the boundaries in the phase diagram. For example, the field-derivative of the entanglement becomes singular along the critical line. The form of the divergence turns out to be dictated by the universality class controlling the quantum phase transition. The entanglement near criticality can be understood via a scaling hypothesis, analogous to that for free energies. The entanglement density vanishes along the so-called disorder line in the phase diagram, the ground space is doubly degenerate and spanned by two product states. The entanglement for the superposition of the lowest two states is also investigated. Even though the exact value of the entanglement depends on the specific form of superposition, in the thermodynamic limit the entanglement density is independent of the superposition, showing that the entanglement density is insensitive to whether the ground state is chosen to be the spontaneously $Z_2$ symmetry broken one or not. The finite-size scaling of entanglement at critical points is also investigated from two different view points: (1) the maximum in the field-derivative of the entanglement density vs. the system size, used to deduce the correlation length exponent for the Ising class by the behavior of entanglement; (2) the correction to the entanglement density vs. the system size, with the coefficient being universal (but with different values for the two lowest states)., Single column, 36 pages, 10 figures, 1 table, expansion of PRA 71, 060305 (R) (2005) with additional results; to appear in QIC

It has been proposed that the superconductivity of Sr${}_{2}$RuO${}_{4}$ is characterized by pairing that is unconventional and, furthermore, spontaneously breaks time-reversal symmetry. However, one of the key expected consequences, viz., that the ground state should exhibit chiral-charge currents localized near the boundaries of the sample, has not been observed, to date. We explore an alternative implication of time-reversal symmetry breaking: the existence of walls between domains of opposing chirality. Via a general phenomenological approach, we derive an effective description of the superconductivity in terms of the relevant topological variables (i.e., domain walls and vortices). Hence, by specializing to the in-plane rotationally invariant limit, we show that a domain wall that is translationally invariant along the $z$ axis and includes an isolated bend through an angle $\ensuremath{\Theta}$ is accompanied by a nonintegral magnetic bend flux of $[(\ensuremath{\Theta}/\ensuremath{\pi})+n]{\ensuremath{\Phi}}_{0}$, with integral $n$, that penetrates the superconductor, localized near the bend. We generalize this result to the situation in which gauge transformations and rotations about the $z$ axis are degenerate transformations of the chiral superconducting order. These results are independent of the magnitude of chiral-charge currents that are predicted to flow along the core of domain walls. On the basis of the specialized result and its generalization, we note that any observation of localized, nonintegral flux penetrating a $z$-axis surface (e.g., via scanned-probe magnetic imaging) could potentially be interpreted in terms of the presence of bent walls between domains of opposing chirality, and hence is suggestive of the existence of time-reversal symmetry breaking superconductivity.

Recent experiments on the conductance of thin, narrow superconducting strips have found periodic fluctuations, as a function of the perpendicular magnetic field, with a period corresponding to approximately two flux quanta per strip area [A. Johansson et al., Phys. Rev. Lett. {\bf 95}, 116805 (2005)]. We argue that the low-energy degrees of freedom responsible for dissipation correspond to vortex motion. Using vortex/charge duality, we show that the superconducting strip behaves as the dual of a quantum dot, with the vortices, magnetic field, and bias current respectively playing the roles of the electrons, gate voltage and source-drain voltage. In the bias-current vs. magnetic-field plane, the strip conductance displays what we term `Weber blockade' diamonds, with vortex conductance maxima (i.e., electrical resistance maxima) that, at small bias-currents, correspond to the fields at which strip states of $N$ and $N+1$ vortices have equal energy., Comment: 4+a bit pages, 3 figures, 1 table

The self-organization of a Bose-Einstein condensate (BEC) in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasicontinuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature and crosses over into a quantum phase transition. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations in the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments., 4 pages, 1 eps figure included, final version as published

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their \emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lam\'e-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus., Comment: 40 pages, 7 figures

Superconducting nanowires fabricated via carbon-nanotube-templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: Can a single phase-slip event occurring somewhere along the wire--during which the order-parameter fluctuates to zero--induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as tool for evaluating and analyzing the mean switching time at a given value of current. The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the counter-intuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way for exploring the physics of nanoscale quantum tunneling of the superconducting order parameter., 21 pages, 15 figures

We revisit the problem of the critical velocity of a clean one-dimensional superconductor. {\changed At the level of mean-field theory}, we find that the zero-temperature value of the critical velocity--the uniform velocity of the superfluid condensate at which the superconducting state becomes unstable--is a factor of $\sqrt{2}$ smaller than the Landau critical velocity. This is in contrast to a prior finding, which held that the critical velocity is equal to the Landau critical velocity. The smaller value of the critical velocity, which our analysis yields, is the result of a pre-emptive Clogston-Chandrasekhar--like discontinuous phase transition, and is an analog of the threshold value of the uniform exchange-field of a superconductor, previously investigated by Sarma and by Maki and Tsuneto. We also consider the impact of nonzero temperature, study critical currents, and examine metastability and its limits in the temperature versus flow-velocity phase diagram. In addition, we comment on the effects of electron scattering by impurities., Comment: Single column, double space, 24 pages, 10 figures

We discuss how multichannel Kondo physics can arise in the setting of a localized level coupled to several bosonic Tomonaga-Luttinger liquid leads. We propose one physical realization involving ultracold bosonic atoms coupled to an atomic quantum dot, and a second, based on superconducting nanowires coupled to a Cooper-pair box. The corresponding zero-temperature phase diagram is determined via an interplay between Kondo-type phenomena arising from the dot and the consequences of direct inter-lead hopping, which can suppress the Kondo effect. We demonstrate that the multichannel Kondo state is stable over a wide range of parameters. We establish the existence of two nontrivial phase transitions, involving a competition between Kondo screening at the dot and strong correlations either within or between the leads (which respectively promote local number- and phase-pinning). These transitions coalesce at a self-dual multicritical point., Comment: 5 pages, 4 figures

The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of the superfluidity of helium-four in arbitrary dimensions. The vortices may be idealized as objects of co-dimension two, such as one-dimensional loops and two-dimensional closed surfaces, respectively, in the cases of three- and four-dimensional superfluidity. By using the analogy between vorticial superflow and Ampere-Maxwell magnetostatics, the equilibrium superflow containing any specified collection of vortices is constructed. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension four and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape, which enter via the first and second fundamental forms of classical geometry. For hyper-spherical vortices, which generalize the vortex rings of three dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors., 35 pages, 7 figures

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

As a function of the magnetic flux threading the object, the Little-Parks oscillation in the critical temperature of a large-radius, thin-walled superconducting ring or hollow cylinder has a period given by $h/2e$, due to the binding of electrons into Cooper pairs. On the other hand, the single-electron Aharonov-Bohm oscillation in the resistance or persistent current for a clean (i.e., ballistic) normal-state system, having the same topological structure, has a period given by $h/e$. A basic question is whether the Little-Parks oscillation changes its character, as the radius of the superconducting structure becomes smaller, and if it is even comparable to the zero-temperature coherence length. We supplement a physical argument that the $h/e$ oscillations should also be exhibited with a microscopic analysis of this regime, formulated in terms of the Gor'kov approach to BCS theory. We see that, as the radius of the ring is made smaller, an oscillation in the critical temperature of period $h/e$ emerges in addition to the usual Little-Parks $h/2e$-period oscillation. We argue that, in the clean limit, there is a superconductor-normal transition at nonzero flux as the ring radius becomes sufficiently small and that the transition can be either continuous or discontinuous, depending on the radius and the external flux. In the dirty limit, we argue that the transition is rendered continuous, which results in continuous quantum phase transitions tuned by flux and radius.

We have developed a superconducting phase gradiometer consisting of two parallel DNA-templated nanowires connecting two thin-film leads. We have ramped the cross current flowing perpendicular to the nanowires, and observed oscillations in the lead-to-lead resistance due to cross-current-induced phase differences. By using this gradiometer we have measured the temperature and magnetic field dependence of the superfluid density and observed an amplification of phase gradients caused by elastic vortex displacements. We examine our data in light of Miller-Bardeen theory of dirty superconductors and a microscale version of Campbell's model of field penetration., Comment: 5 pages, 6 figures

In response to recent experiments by the Berkeley group, we construct a model of superflow through an array of nanosize apertures that incorporates two basic ingredients: (1) disorder associated with each aperture having its own random critical velocity, and (2) effective interaperture coupling, mediated through the bulk superfluid. As the disorder becomes weak there is a transition from a regime where phase slips are largely independent to a regime where interactions lead to system-wide avalanches of phase slips. We explore the flow dynamics in both regimes, and make connections to the experiments.

The effects of thermal elastic fluctuations in rubber materials are examined. It is shown that, due to an interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation, and shows a good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation., 4 RevTeX pages, 1 figure, submitted to PRL