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We explore the concept of negative pressure and its relevance in a variety of physical contexts: the expansion of the universe, mixture theory, cavitation, and the capillary effect in plants. Using thermodynamic arguments, we discuss the intricate connection between negative pressure and negative thermal expansion. We highlight the fact that metastable states and competing phases are often associated with the emergence of negative pressure. We also propose a new link between the effective Gr\"uneisen parameter and nucleation theory., Comment: 15 pages, 5 figs, comments are welcome

In condensed matter Physics, massive longitudinal Higgs modes emerge from fluctuations of the order parameter. A few years ago, the Higgs mode was \emph{caught} experimentally in the vicinity of an insulator-to-superconductor quantum phase transition [Nat. Phys. $\textbf{11}$, 188 (2015)]. Here, we propose, in analogy to the Higgs mode, the concept of Higgs-like stiffness (HLS), which emerges close to both classical and quantum phase transitions as a universal manifestation of matter. We build up a Landau free energy for the dielectric response function to demonstrate that \emph{any} complex physical quantity can be used to infer the presence of the HLS. Our analysis is corroborated by experimental results of the quasi-static dielectric constant for the (TMTTF)$_2$SbF$_6$ Fabre salt. Yet, we discuss the appearance of fractons in connection with the locking of particular molecular rotational degrees of freedom., Comment: 8 pages, 2 figures. Comments are welcome

Protein compartmentalization in the frame of a liquid-liquid phase separation is a key mechanism to optimize spatiotemporal control of biological systems. Such a compartmentalization process reduces the intrinsic noise in protein concentration due to stochasticity in gene expression. Employing Flory-Huggins solution theory, Avramov/Casalini's model, and the Gr\"uneisen parameter, we unprecedentedly propose a cellular Griffiths-like phase (CGLP), which can impact its functionality and self-organization. The here-proposed CGLP is key ranging from the understanding of primary organisms' evolution to the treatment of diseases. Our findings pave the way for an alternative Biophysics approach to investigate coacervation processes., Comment: 13 pages, 2 figures, suppl. material upon request

For a perfect fluid, pressure $p$ and energy density $\rho$ are related via the equation of state (EOS) $\omega = p/\rho$, where $\omega$ is the EOS parameter, being its interpretation usually constrained to a numerical value for each universe era. Here, based on the Mie-Gr\"uneisen EOS, we show that $\omega$ is recognized as the effective Gr\"uneisen parameter $\Gamma_{eff}$, whose singular contribution, the so-called Gr\"uneisen ratio $\Gamma$, quantifies the barocaloric effect. Our analysis suggests that the negative $p$ associated with dark-energy implies a metastable state and that in the dark-energy-dominated era $\omega$ is time-dependent, which reinforces recent proposals of a time-dependent cosmological constant. Furthermore, we demonstrate that $\Gamma_{eff}$ is embodied in the energy-momentum stress tensor in the Einstein field equations, enabling us to analyse, in the frame of an imperfect fluid picture, anisotropic effects of the universe expansion. We propose that upon going from decelerated- to accelerated-expansion, a phase transition-like behavior can be inferred. Yet, our analysis in terms of entropy, $\Gamma$, and a by us adapted version of Avramov/Casalini's model to Cosmology unveil hidden aspects related to the expansion of the universe. Our findings pave the way to interpret cosmological phenomena in connection with concepts of condensed matter Physics via $\Gamma_{eff}$., Comment: 11 pages, 1 figure, comments are welcome

The Gr\"uneisen ratio $\Gamma$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic $\Gamma$ cannot be employed. We propose a quantum analogue to $\Gamma$ that computes entanglement as a function of a tuning parameter $\lambda$ and show that QPTs take place only for systems in which the ground-state energy depends on $\lambda$ non-linearly. Furthermore, we demonstrate the breakdown of the Hellmann-Feynman theorem in the thermodynamic limit at any QCP. We showcase our approach using the quantum 1D Ising model with transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the "creation of mass" close to any QCP/QPT is also discussed., Comment: 5 pages, 3 figures, comments are wellcome!

We investigate the physics of planar annular Josephson tunnel junctions quenched through their transition temperature in the presence of an external magnetic field. Experiments carried out with long Nb/Al-AlOx/Nb annular junctions showed that the magnetic flux trapped in the high-quality doubly-connected superconducting electrodes forming the junction generates a persistent current whose associated magnetic field affects the both the static and dynamics properties of the junctions. More specifically, the field trapped in the hole of one electrode combined with a d.c. bias current induces a viscous flow of dense trains of Josephson vortices which manifests itself through the sequential appearance of displaced linear slopes, Fiske step staircases and Eck steps in the junction's current-voltage characteristic. Furthermore, a field shift is observed in the first lobe of the magnetic diffraction pattern. The effects of the persistent current can be mitigated or even canceled by an external magnetic field perpendicular to the junction plane. The radial field associated with the persistent current can be accurately modeled with the classical phenomenological sine-Gordon model for extended one-dimensional Josephson junctions. Extensive numerical simulations were carried out to disclose the basic flux-flow mechanism responsible for the appearance of the magnetically induced steps and to elucidate the role of geometrical parameters. It was found that the imprint of the field cooling is enhanced in confocal annular junctions which are the natural generalization of the well studied circular annular junctions., Comment: 26 pages, 10 figures. Supercond. Sci. Technol (2020)

We investigate Josephson flux-flow in annular Josephson tunnel junctions (AJTJs) under the application of magnetic fields generating finite-voltage steps in their current-voltage characteristics. Experimental data are presented for confocal AJTJs which are the natural generalization of the well studied circular AJTJs for which flux flow effects have never been reported. Displaced linear slopes, Fiske step staircases and Eck steps were sequentially recorded at $4.2\,K$ with high-quality Nb/Al-AlOx/Nb confocal AJTJs when increasing the strength of a uniform magnetic field applied in the plane of the junction. Their amplitude was found to strongly depend not only on the strength, but also on the orientation, of the external field. Extensive numerical simulations based on a phenomenological sine-Gordon model developed for confocal AJTJs were carried out to disclose the basic flux-flow mechanism responsible for the appearance of magnetically induced steps and to elucidate the role of several critical parameters, namely, the field orientation, the system loss and the annulus eccentricity. It was found that in a topologically closed system, such as the AJTJ, where the number of trapped fluxons is conserved and new fluxons can be created only in the form of fluxon-antifluxon pairs, the existence of a steady viscous flow of Josephson vortices only relies on the capability of the fluxons and antifluxons to be generated and to annihilate each other inside the junction. This also implies that flux-flow effects are not observable in circular AJTJs., Comment: 26 pages, 8 figures

It is well known that long Josephson tunnel junctions (JTJs) act as active transmission lines for the slow-mode propagation of magnetic flux-quanta (in the form of solitary waves) that is at the base of many superconducting circuits. At the same time, they support the propagation of quasi-TEM dispersive waves with which the magnetic flux non-linearly interact. In this work, we study the properties of the electromagnetic resonances, under different conditions of practical interest, in annular JTJs (AJTJs), in which the wavelengths are limited to the length of the circumference divided by an integer. Our analysis is based on perturbed sine-Gordon equations the (1+1)-dimensional space with periodic boundary conditions. We discuss the discrete modes of the travelling EM waves in circular annular JTJs in the presence of an in-plane magnetic field, as well as in the recently introduced confocal annular JTJs (in the absence of magnetic field). In both cases, a variable-separation method leads to quantitatively different Mathieu equations characterized by even and odd spatially periodic solutions with different eigen-frequencies. It implicates that a single mode circulating wave is given by the superposition of two standing waves with the same wavelengths but different frequencies, and so has a periodically inverting direction of propagation. The control parameters of this frequency splitting are the in-plane magnetic field amplitude for the circular AJTJ and the aspect ratio for the confocal AJTJs. In the appropriate limits, the previously known solutions are recovered., Comment: 27 pages, 5 figures

Confocal Annular Josephson Tunnel Junctions (CAJTJs) which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise., Comment: arXiv admin note: text overlap with arXiv:1707.01672

We report theoretical and experimental work on the development of a Josephson vortex qubit based on a confocal annular Josephson tunnel junction (CAJTJ). The key ingredient of this geometrical configuration is a periodically variable width that generates a spatial vortex potential with bistable states. This intrinsic vortex potential can be tuned by an externally applied magnetic field and tilted by a bias current. The two-state system is accurately modeled by a one-dimensional sine-Gordon like equation by means of which one can numerically calculate both the magnetic field needed to set the vortex in a given state as well as the vortex depinning currents. Experimental data taken at 4.2K on high-quality Nb/Al-AlOx/Nb CAJTJs with an individual trapped fluxon advocate the presence of a robust and finely tunable double-well potential for which reliable manipulation of the vortex state has been classically demonstrated. The vortex is prepared in a given potential by means of an externally applied magnetic field, while the state readout is accomplished by measuring the vortex-depinning current in a small magnetic field. Our proof of principle experiment convincingly demonstrates that the proposed vortex qubit based on CAJTJs is robust and workable., Comment: 20 pages, 11 figures

The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study is made of their magnetic patterns with emphasis on the rate of decay of the sidelobes amplitudes for large field amplitudes., Comment: 16 pages, 3 figures

The physics of Josephson tunnel junctions drastically depends on their geometrical configurations. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. We focus on a wide ensemble of junctions whose shape is invariant under point reflection. We analyze the implications of this type of isometry and derive the threshold curves of junctions whose shape is the union or the relative complement of two point symmetric plane figures., Comment: 4 pages, 2 figures

Long Josephson tunnel junction are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system., Comment: 18 pages, 9 figures

The physics of Josephson tunnel junctions drastically depends on their geometrical configurations and here we show that also tiny geometrical details play a determinant role. More specifically, we develop the theory of short and long confocal annular Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. The behavior of a circular annular Josephson tunnel junction is then seen to be simply a special case of the above result. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with trapped Josephson vortices. For longer junctions a numerical analysis is carried out after the derivation of the appropriate motion equation for the Josephson phase. We found that the system is modeled by a modified and perturbed sine-Gordon equation with a space dependent effective Josephson penetration length inversely proportional to the local junction width. Both the fluxon statics and dynamics are deeply affected by the non-uniform annulus width. Static zero-field multiple-fluxon solutions exist even in presence of a large bias current. The tangential velocity of a traveling fluxon is not determined by the balance between the driving and drag forces due to the dissipative losses. Furthermore, the fluxon motion is characterized by a strong radial inward acceleration which causes electromagnetic radiation concentrated at the ellipse equatorial points., Comment: 21 pages, 5 figures

We analyze the dynamics of a magnetic flux quantum (current vortex) trapped in a current-biased long planar elliptic annular Josephson tunnel junction. The system is modeled by a perturbed sine-Gordon equation that determines the spatial and temporal behavior of the phase difference across the tunnel barrier separating the two superconducting electrodes. In the absence of an external magnetic field the fluxon dynamics in an elliptic annulus does not differ from that of a circular annulus where the stationary fluxon speed merely is determined by the system losses. The interaction between the vortex magnetic moment and a spatially homogeneous in-plane magnetic field gives rise to a tunable periodic non-sinusoidal potential which is strongly dependent on the annulus aspect ratio. We study the escape of the vortex from a well in the tilted potential when the bias current exceeds the depinning current. The smallest depinning current as well as the lowest sensitivity of the annulus to the external field is achieved when the eccentricity is equal to -1. The presented extensive numerical results are in good agreement with the findings of the perturbative approach. We also probe the rectifying properties of an asymmetric potential implemented with an egg-shaped annulus formed by two semi-elliptic arcs., Comment: 17 pages, 9 figures

We have investigated the static properties of one-dimensional planar Josephson tunnel junctions in the most general case of elliptic annuli. We have analyzed the dependence of the critical current in the presence of an external magnetic field applied either in the junction plane or in the perpendicular direction. We report a detailed study of both short and long elliptic annular junctions having different eccentricities. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with one trapped Josephson vortex. For longer junctions a numerical analysis is carried out after the derivation of the appropriate Perturbed sine-Gordon Equation. For a given applied field we find that a number of different phase profiles exist which differ according to the number of fluxon-antifluxon pairs. We demonstrate that in samples made by specularly symmetric electrodes a transverse magnetic field is equivalent to an in-plane field applied in the direction of the current flow. Varying the ellipse eccentricity we reproduce all known results for linear and ring-shaped Josephson tunnel junctions. Experimental data on high-quality Nb/Al-AlOx/Nb elliptic annular junctions support the theoretical analysis provided self-field effects are taken into account., Comment: 30 pages, 13 figures

A superconducting magnetometers based on the magnetic field dependence of the Eck step voltage in long Josephson tunnel junctions (LJTJs) is demonstrated. The field to be measured is applied perpendicular to a continuous superconducting pickup loop. Wherever the loop has a narrow constriction, the density of the flux-restoring circulating currents will become relatively high and will locally create a magnetic field large enough to bring a biased LJTJ in the flux-flow state, i.e., at a finite voltage proportional to the field strength. This method allows the realization of a novel family of robust and general-purpose superconducting devices which, despite their simplicity, function as ultra-low-noise, wide-band and high-dynamics magnetometers. The performances of low-T$_c$ sensor prototypes, among which a highly linear voltage responsivity and a magnetic spectral density $S_B^{1/2}< 3\,fT/Hz^{1/2}$, promise to be competitive with those of the best superconducting quantum interference devices., Comment: 12 pages, 2 figures

The properties of Josephson devices are strongly affected by geometrical effects such as those associated with the magnetic field induced by the bias current. The generally adopted analysis of Owen and Scalapino [{\it Phys. Rev.}{\bf 164}, 538 (1967)] for the critical current, $I_c$, of an in-line Josephson tunnel junction in presence of an in-plane external magnetic field, $H_e$, is revisited and extended to junctions whose electrodes can be thin and of different materials. We demonstrate that the asymmetry of the magnetic diffraction pattern, $I_c(H_e)$, is ascribed to the different electrode inductances for which we provide empirical expressions. We also generalize the modeling to the window-type junctions used nowadays and discuss how to take advantage of the asymmetric behavior in the realization of some superconducting devices. Further we report a systematic investigation of the diffraction patterns of in-line window-type junctions having a number of diverse geometrical configurations and made of dissimilar materials. The experimental results are found in agreement with the predictions and clearly demonstrate that the pattern asymmetry increases with the difference in the electrode inductances., Comment: 13 pages, 8 figures, regular paper

The properties of Josephson devices are strongly affected by geometrical effects. A loop-shaped superconducting electrode tightly couples a long Josephson tunnel junction with the surrounding electromagnetic field. Due to the fluxoid conservation, any change of the magnetic flux linked to the loop results in a variation of the shielding current circulating around the loop, which, in turn, affects the critical current of the Josephson junction. This method allows the realization of a novel family of robust superconducting devices (not based on the quantum interference) which can function as a general-purpose magnetic sensors. The best performance is accomplished without compromising the noise performance by employing an in-line-type junction few times longer than its Josephson penetration length. The linear (rather than periodic) response to magnetic flux changes over a wide range is just one of its several advantages compared to the most sensitive magnetic detectors currently available, namely the Superconducting Quantum Interference Devices (SQUID). We will also comment on the drawbacks of the proposed system and speculate on its noise properties., Comment: 13 pages, 4 figures

In order to mimic the phase changes in the primordial Big Bang, several "cosmological" solid-state experiments have been conceived, during the last decade, to investigate the spontaneous symmetry breaking in superconductors and superfluids cooled through their transition temperature. In one of such experiments the number of magnetic flux quanta spontaneously trapped in a superconducting loop was measured by means of a long Josephson tunnel junction built on top of the loop itself. We have analyzed this system and found a number of interesting features not occurring in the conventional case with simply connected electrodes. In particular, the fluxoid quantization results in a frustration of the Josephson phase, which, in turn, reduces the junction critical current. Further, the possible stable states of the system are obtained by a self-consistent application of the principle of minimum energy., Comment: 34 pages, 9 figures, Phys. Rev. B April 2012

It has long been recognized that a control current $I_a$ injected into the section of a two-junction superconducting quantum interference device (SQUID) is able to produce a change of its critical current $I_c$, so that a current gain $g=|dI_c/dI_a|$ can be identified. We investigate the circumstances under which large gains can be achieved by using vertical Josephson interferometers which are characterized by small loop inductances. We discuss the theory of operation of such a novel device, its performances and its advantages with respect to planar interferometers used in the previous works. Two potential applications are addressed., Comment: 18 pages, 6 figures

We measured the magnetic field dependence of the critical current of high quality Nb-based planar Josephson tunnel junctions in the presence of a controllable non-uniform field distribution. We found skewed and slowly changing magnetic diffraction patterns quite dissimilar from the Fraunhofer-like ones typical of a homogeneous field. Our findings can be well interpreted in terms of recent theoretical predictions [R. Monaco, J. Appl. Phys. vol.108, 033906 (2010)] for a uniform magnetic field gradient leading to Fresnel-like magnetic diffraction patterns. We also show that Fiske resonances can be suppressed by an asymmetric magnetic field profile., Comment: 8 pages, 4 figures

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss our experiment for measuring the Zurek-Kibble scaling exponent sigma for the production of fluxons in annular symmetric Josephson Tunnel Junctions. The predicted exponent is sigma = 0.25, and we find sigma = 0.27 +/- 0.05. Further, there is agreement with the ZK prediction for the overall normalisation.

Zurek has provided simple causal bounds for the onset of phase transitions in condensed matter, that mirror those proposed by Kibble for relativistic quantum field theory. In this paper we show how earlier experiments with annular Josephson tunnel Junctions are consistent with this scenario, and suggest how further experiments might confirm it., Comment: 15 pages, to be published in Journal of Low Temperature Physics (June/July 2001) as part of the refereed proceedings of the ULTI meeting, Finland, Jan 2001