Flux Quantization in Type II Superconductors

We examine from first principles one of the basic assumptions of modern quantum theories of structure formation in the early universe, i.e., the conditions upon which fluctuations of a quantum field may transmute into classical stochastic perturbations, which grew into galaxies. Our earlier works have discussed the quantum origin of noise in stochastic inflation and quantum fluctuations as measured by particle creation in semiclassical gravity. Here we focus on decoherence and the relation of quantum and classical fluctuations. Instead of using the rather ad hoc splitting of a quantum field into long and short wavelength parts, the latter providing the noise which decoheres the former, we treat a nonlinear theory and examine the decoherence of a quantum mean field by its own quantum fluctuations, or that of other fields it interacts with. This is an example of `dynamical decoherence' where an effective open quantum system decoheres through its own dynamics. The model we use to discuss fluctuation generation has the inflation field coupled to the graviton field. We show that when the quantum to classical transition is properly treated, with due consideration of the relation of decoherence, noise, fluctuation and dissipation, the amplitude of density contrast predicted falls in the acceptable range without requiring a fine tuning of the coupling constant of the inflation field ($\lambda$). The conventional treatment which requires an unnaturally small $\lambda \approx 10^{-12}$ stems from a basic flaw in naively identifying classical perturbations with quantum fluctuations.

In this work we axe interested in dephasing or decoherence in the zero-temperature limit. The only source of decoherence are then provided by vacuum (zero-point) fluctuations. Concern with vacuum fluctuations has a long history [1] starting with theories of black-body radiation and the Planck spectrum and important effects like the Lamb shift, the Casimir effect and the Debye-Waller factor. More recently, the role of vacuum fluctuations was discussed in theories of macroscopic quantum tunneling and even more closely related to our subject in theories of macroscopic quantum coherence [2, 3]. In mesoscopic physics, we deal with systems that are so small and are cooled to such low temperatures that the wave nature of electrons becomes important and interference effects become measurable. Dephasing processes are therefore also of central importance in mesoscopic physics. Ultimately in the zero-temperature limit only vacuum fluctuations remain and it is clearly very interesting and fascinating to inquire about a possible role of such fluctuations.

We study the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength. To do so, we derive a description similar to the stochastic Gross–Pitaevskii equation (SGPE) but keeping a fully quantum description of the low-energy fields using the positive-P representation. This allows us to treat both the quantum and thermal fluctuations together in an integrated way. A plain SGPE only allows for thermal fluctuations. The approach is applicable to such situations as finite temperature quantum quenches, but not equilibrium calculations due to the time limitations inherent in positive-P descriptions of interacting gases. One sees the appearance of antibunching, the generation of counter-propagating atom pairs, and increased phase fluctuations. We show that the behavior can be estimated by adding the T = 0 quantum fluctuation contribution to the thermal fluctuations described by the plain SGPE.

The uncertainty principle guarantees a non-zero value for the positional uncertainty, ⟨ Δ x 2 ⟩ > 0 , even without thermal fluctuations. This implies that quantum fluctuations inherently enhance positional uncertainty at zero temperature. A natural question then arises: what happens at finite temperatures, where the interplay between quantum and thermal fluctuations may give rise to complex and intriguing behaviors? To address this question, we systematically investigate the positional uncertainty, ⟨ Δ x 2 ⟩ , of a particle in equilibrium confined within a nonlinear potential of the form V ( x ) ∝ x n , where n = 2 , 4 , 6 , … represents an even exponent. Using path integral Monte Carlo simulations, we calculate ⟨ Δ x 2 ⟩ in equilibrium as a function of the thermal de Broglie wavelength Λ. Interestingly, for large values of n, ⟨ Δ x 2 ⟩ exhibits a non-monotonic dependence on Λ: it initially decreases with increasing Λ at small Λ but increases at larger Λ. To further understand this behavior, we employ a semiclassical approximation, which reveals that quantum fluctuations can reduce positional uncertainty for small Λ when the nonlinearity of the potential is sufficiently strong. Finally, we discuss the potential implications of this result for many-body phenomena driven by strong nonlinear interactions, such as glass transitions, where the transition densities exhibit a similar non-monotonic dependence on Λ.

We demonstrate the presence of an extended critical phase in the transverse\nfield Ising magnet on the triangular lattice, in a regime where both thermal\nand quantum fluctuations are important. We map out a complete phase diagram by\nmeans of quantum Monte Carlo simulations, and find that the critical phase is\nthe result of thermal fluctuations destabilising an order established by the\nquantum fluctuations. It is separated by two Kosterlitz-Thouless transitions\nfrom the paramagnet on one hand and the quantum-fluctuation driven\nthree-sublattice ordered phase on the other. Our work provides further evidence\nthat the zero temperature quantum phase transition is in the 3d XY universality\nclass.\n

The quantum scenario concerning Hawking radiation, gives us a precious clue that a black hole has its temperature directly connected to its area gravity and that its entropy is proportional to the horizon area. These results have shown that there exist a deep association between thermodynamics and gravity. The recently introduced Barrow formulation of back holes entropy, influenced by the spacetime geometry, shows the quantum fluctuations effects through Barrow exponent, Δ, where Δ=0 represents the usual spacetime and its maximum value, Δ=1, characterizes a fractal spacetime. The quantum fluctuations are responsible for such fractality. Loop quantum gravity approach provided the logarithmic corrections to the entropy. This correction arises from quantum and thermal equilibrium fluctuations. In this paper we have analyzed the nonextensive thermodynamical effects of the quantum fluctuations upon the geometry of a Barrow black hole. We discussed the Tsallis' formulation of this logarithmically corrected Barrow entropy to construct the equipartition law. Besides, we obtained a master equation that provides the equipartition law for any value of the Tsallis q-parameter and we analyzed several different scenarios. After that, the heat capacity were calculated and the thermal stability analysis was carried out as a function of the main parameters, namely, one of the so-called pre-factors, q and Δ.

We report the effects of quantum and thermal fluctuations on the stability of phase-locking in one-dimensional long Josephson junction (LJJ) devices, involving high temperature superconductors. Accounting for both the magnetic induction effect and the charging effect, we determine the zero temperature (T = 0) stability phase diagram using renormalization group (RG) analysis. This phase diagram shows that the in-phase mode is stable but some out-of-phase modes are unstable against quantum fluctuations. At finite T, all stable phase-locked modes (at T = 0) are unstable, but its stability is maintained within the decoherence length which decreases inversely with T.

We study an information-theoretic measure of uncertainty for quantum systems. It is the Shannon information I of the phase-space probability distribution 〈z\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}z〉, where \ensuremath{\Vert}z〉 are coherent states and \ensuremath{\rho} is the density matrix. As shown by Lieb I\ensuremath{\ge}1, and this bound represents a strengthened version of the uncertainty principle. For a harmonic oscillator in a thermal state, I coincides with von Neumann entropy, -Tr(\ensuremath{\rho}ln\ensuremath{\rho}), in the high-temperature regime, but unlike entropy, it is nonzero (and equal to the Lieb bound) at zero temperature. It therefore supplies a nontrivial measure of uncertainty due to both quantum and thermal fluctuations. We study I as a function of time for a class of nonequilibrium quantum systems consisting of a distinguished system coupled to a heat bath. We derive an evolution equation for I. For the harmonic oscillator, in the Fokker-Planck regime, we show that I increases monotonically, if the width of the coherent states is chosen to be the same as the width of the harmonic oscillator ground state. For other choices of the width, and for more general Hamiltonians, I settles down to a monotonic increase in the long run, but may suffer an initial decrease for certain initial states that undergo ``reassembly'' (the opposite of quantum spreading). Our main result is to prove, for linear systems, that I at each moment of time has a lower bound ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$, over all possible initial states.This bound is a generalization of the uncertainty principle to include thermal fluctuations in nonequilibrium systems, and represents the least amount of uncertainty the system must suffer after evolution in the presence of an environment for time t. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ is an envelope, equal for each time t, to the time evolution of I for a certain initial state, which we calculate to be a nonminimal Gaussian. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ coincides with the Lieb bound in the absence of an environment, and is related to von Neumann entropy in the long-time limit. The form of ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ indicates that the thermal fluctuations become comparable with the quantum fluctuations on a time scale equal to the decoherence time scale, in agreement with earlier work of Hu and Zhang. Our results are also related to those of Zurek, Habib, and Paz, who looked for the set of initial states generating the least amount of von Neumann entropy after a fixed period of nonunitary evolution.

Bose-Einstein condensates of atoms with non-zero spin are known to constitute an ideal system to investigate fundamental properties of magnetic superfluids. More recently it was realized that they also provide the fascinating opportunity to investigate the macroscopic amplification of quantum and classical fluctuations. This is strikingly manifested in a sample initially prepared in the m F = 0 state, where spin-changing collisions triggered by quantum fluctuations may lead to the creation of correlated pairs in m F = ±1. We show that the pair creation efficiency is strongly influenced by the interplay between the external trapping potential and the Zeeman effect. It thus reflects the confinement-induced magnetic field dependence of elementary spin excitations of the condensate. Remarkably, pair production in our experiments is therefore characterized by a multi-resonant dependence on the magnetic field. Pair creation at these resonances acts as strong parametric matter-wave amplifier. Depending on the resonance condition, this amplification can be extremely sensitive or insensitive to the presence of seed atoms. We show that pair creation at a resonance which is insensitive to the presence of seed atoms is triggered purely by quantum fluctuations and thus the system acts as a matter-wave amplifier for the vacuum state.

The Heisenberg triangular antiferromagnet is a model widely studied by analytic low-temperature expansion and Monte Carlo simulation. The classical version of the model is characterized by infinitely many minimum energy configurations even if an in-plane external magnetic field is turned on. This degeneracy is lifted by thermal fluctuations and the same effect is found when quantum fluctuations are accounted for. We find an analogous scenario in the 3D hexagonal model where the intrachain coupling is ferromagnetic and the interchain one is antiferromagnetic. Such a model is suitable to describe some hexagonal ABX3 compounds. We are interested, in particular, in CsCuCl3, where our theoretical results compare favorably with magnetic resonance experimental data and with magnetization measurements as a function of the external magnetic field. The role of quantum and thermal fluctuations in the selection of a particular spin pattern out of the infinitely many configurations that minimize the classical energy of the model is discussed.

We investigate theories in which classical and quantum-mechanical degrees of freedom interact dynamically. In commonly used semiclassical theories, such as those used to study inflationary-universe models, quantum fluctuations do not affect the dynamics of the classical variables. We construct a new semiclassical theory in which the quantum and classical fluctuations do affect each other; the Wigner probability function turns out to be a special case. Relevance to calculations of perturbations from inflation are discussed.

Motivated by the magnetism of pyrochlore oxides, we consider the effect of quantum fluctuations in the most general symmetry-allowed nearest-neighbor Kramers exchange Hamiltonian on the pyrochlore lattice. At the classical level, this Hamiltonian exhibits a rich landscape of classical spin liquids and a variety of nonconventional magnetic phases. In contrast, much remains unclear for the quantum model, where quantum fluctuations have the potential to alter the classical landscape and stabilize novel magnetic phases. Employing state-of-the-art pseudofermion functional renormalization group calculations for the spin-1/2 model, we determine the quantum phase diagram at relevant cross-sections, where the classical model hosts an algebraic nodal rank-2 spin liquid and a spin nematic order. We find large regions in parameter space where dipolar magnetic order is absent, and, based on known fingerprints in the correlation functions, we suggest that this nonconventional region is composed of an ensemble of distinct phases stabilized by quantum fluctuations. Our results hint at the existence of a spin nematic phase, and we identify the quantum analog of the classical rank-2 spin liquid. Furthermore, we highlight the importance of assessing the subtle interplay of quantum and thermal fluctuations in reconciling the experimental findings on the nature of magnetic order in Yb2Ti2O7.

We report on an optical magnetic flux control in high-Tc superconductive loops and films using a femtosecond (fs) laser. The YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// (YBCO) films are patterned into strips with two rectangular parallel holes, with ordered arrays of antidots, or without any holes. The fs optical pulses are focused onto the strips while biasing the current. After removal of the bias current, the supercurrent density distributions are visualized by terahertz radiation imaging. The images indicate that the flux and anti-flux quanta are optically generated in the strips, and the number of the flux quanta between 15 and 2000 flux quantum is controlled by both the bias current and laser power. We then put forward the system to control the number of the fs pulses to generate the flux. The results reveal that even single shot fs optical pulse can generate the flux quanta in the strips.

We demonstrate that in a correlated 2D systems of electrons in the presence of perpendicular magnetic field the magnetic flux quantum may not achieve its value determined for a single or a noncorrelated electron. Correlations induced by the repulsion of electrons at strong magnetic field presence impose topological-type limits on planar cyclotron orbits which cause specific homotopy of trajectories resulting in constraints of the magnetic field flux quantum value. These restrictions occur at discrete series of magnetic field values corresponding to hierarchy of 2D correlated Hall states observed experimentally in GaAs thin films and in graphene. The similar homotopy property is observed in 2D Chern topological insulators when the magnetic field is substituted by the Berry field.

IF phase coherence of the quantum-mechanical wavefunctions between conventional (BCS) and high-transition-temperature (high-Tc) superconductors were shown to exist, this would place powerful constraints on the as yet unknown mechanism in the latter materials. Here we demonstrate the quantum coherence of the macroscopic superconducting wavefunctions of a conventional and a high-Tc superconductor by the observation of persistent supercurrents and the quantization of magnetic flux in units of h/2e within a composite ring of niobium and YBa2Cu3O7 (YBCO). This shows unambiguously that the macroscopic wavefunctions are coupled at the interface between the two superconductors, regardless of the mechanism and nature of electronic pairing in high-Tc superconductors. The experiment is a variant of an earlier measurement in which the quantization of flux was measured in an YBCO superconductor ring1. In our experiment, an adjustable niobium point was used to bridge the gap in a superconducting circuit of YBCO. In addition to observing persistent supercurrents around the ring with discrete flux states separated by the flux quantum, h/2e, the critical current across the junctions also exhibits the expected flux-quantum periodicity. This provides the first demonstration of a d.c. superconducting quantum interference device (SQUID) formed from a composite high-Tc/BCS superconducting circuit.