One of the most fascinating and fundamentally important properties of superconductivity is its quantum behavior over large distances. Usually quantum mechanical effects are only important at low temperatures and over distances on the atomic scale, that is about 10-9 meters. Superconductors are an exception to this rule. As long ago as the late 1940s, Fritz London, with a great leap of the imagination suggested that for superconductors, the wave-particle duality should be able to be seen in vastly larger objects, even to a mile long superconducting loop.
One of the most fascinating and fundamentally important properties of superconductivity is its quantum behavior over large distances. Usually quantum mechanical effects are only important at low temperatures and over distances on the atomic scale, that is about 10-9 meters. Superconductors are an exception to this rule. As long ago as the late 1940s, Fritz London, with a great leap of the imagination suggested that for superconductors, the wave-particle duality should be able to be seen in vastly larger objects, even to a mile long superconducting loop.
Abstract Superconductivity, superfluidity, and Bose–Einstein condensation (BEC) are among the most fascinating phenomena in nature. Their strange and often surprising properties are direct consequences of quantum mechanics. This is why they only occur at low temperatures, and it is very difficult (but hopefully not impossible!) to find a room temperature superconductor. But, while most other quantum effects only appear in matter on the atomic or subatomic scale, superfluids and superconductors show the effects of quantum mechanics acting on the bulk properties of matter on a large scale. In essence they are macroscopic quantum phenomena.
Abstract ‘Quantum matter’ describes how superconductors and superfluids can have properties like those found in the strange quantum world of atoms, electrons, and photons. In quantum theory, properties such as energy cannot have any possible value, but are quantized. Energy comes in discrete lumps. Particles can act like waves, be in more than one place at the same time, and interfere with themselves. The weirdness of quantum theory is captured in the paradox of Schrödinger’s cat, where quantum effects occur on the macroscopic scale. This is realized in a superconductor, where magnetic flux is quantized. Brian Josephson proposed an electrical circuit that is the basis for a Superconducting Quantum Interference Device (SQUID). These devices are of technological significance as they are used in quantum computing, and to make precise measurements of fundamental physical constants and of magnetic field strengths. SQUIDs are now used in metrology, the science of precise measurements, being the basis for the international standard for the volt, the unit of electrical voltage, and are used in quantum computing.
We have seen in Chapter 3 , that as temperature is increased quantum statistics, both Bose-Einstein or Fermi-Dirac, tend to classical. High temperatures blur out quantum effects in a system, which can be safely described in classical terms. In this chapter, we will consider some systems which manifest quantum properties at macroscopic level, but at very low temperatures. We recall that helium is the only substance which remains liquid at low temperature, down to absolute zero (see Chapter 6 ), a phenomenon related to the quantum behavior of its constituent atoms. Liquid helium was instrumental to the discovery that some metals are able to sustain an electrical current for long periods of time without any driving force. This phenomenon is named superconductivity, and is also a macroscopic manifestation of the quantum behavior of the electrons in metals. Later on it was discovered that liquid helium itself shows a similar property, named superfluidity, consisting in its ability to flow through a capillary without viscosity. Hence, a persistent flow of liquid can be maintained without any driving force. While the quantum agents of superconductivity are electrons, which are spin- 1/2 fermions, those of superfluidity are 4 He atoms, which are spin- 0 bosons. There are other systems able to display similar behavior as liquid 3 He, atomic nuclei and nuclear matter. In fact, superfluidity and superconductivity are new phases of matter related to the bosonic character of 4 He atoms or of pairs of fermions (either electrons, 3 He atoms or nucleons), the same as Bose-Einstein condensation in ultracold atomic gases. The temperatures where these new phases manifest range from 165 K for superconductivity down to a few nano-Kelvin for Bose-Einstein condensation.
New experiments are revealing the power of large-scale quantum devices .
Entanglement is the counterintuitive idea that particles can have an intrinsic connection—a connection that endures no matter the distance between them. The phenomenon remains one of the most bizarre and least understood consequences of quantum mechanics. Measure the quantum properties of one of a pair of entangled particles, and the other changes instantaneously.
Researchers have pioneered ways to demonstrate quantum entanglement in mechanical systems. This artist’s conception of one experiment depicts an interferometer’s light field, which “carries” the entangled state. Image credit: Kavli Institute of Nanoscience, Delft University of Technology/Moritz Forsch.
Such strange phenomena typically have been relegated to the subatomic. But recently, physicists have taken entanglement and other quantum effects to new extremes by observing them in large systems including clouds of atoms, quantum drums, wires, and etched silicon chips. Device by device, they are bringing the quantum world into new territory—the macroscopic world.
This work is driving new applications. Some experimental quantum computers use loops of superconducting wire as qubits, storing quantum information. Large quantum objects have already been used to help detect gravitational waves; they could appear in next-generation devices such as ultrasensitive sensors and encryption systems. These innovations, though, reach beyond cutting-edge tech. Building bigger and bigger quantum objects even raises the possibility of exploring some of the most pervasive unsolved mysteries at the intersection between quantum and classical worlds—and between quantum mechanics and gravity.
Ever since Austrian physicist Erwin Schrodinger first described wave–particle duality 90 years ago (1), physicists have been probing the boundary between the observable, predictable macroscopic world and the one where probabilistic quantum rules dominate. In the quantum world, a particle exists as a wave representing the probabilities of its location. Once measured, however, the particle is found at a point …
Good order is the foundation of all good things. E. Burke, Reflections on the Revolution in France , 1790 Josephson effect Superconductivity: A crash course The transition from the theoretical description of hypothetical building blocks of a quantum coherent device to something which can be actually fabricated and controlled is made much easier by the existence of superconductivity . This phenomenon, roughly speaking, allows a macroscopic quantum coherent flow of electrons in a sufficiently cold piece of an appropriate material by establishing a specific long-range order among them. Due to this one can, for example, use macroscopically different states of a superconductor as quantum states of a qubit, with the obvious advantage over “microscopically quantum” systems (like actual atoms) from the point of view of control, measurement and, last but not least, fabrication of structures with the desired parameters and on the desired scale. The phenomenon of superconductivity – the history of its discovery, experimental manifestations, theoretical explanation, open questions, relevance to other branches of physics, and technological applications – requires a thorough treatment, which can be found in any number of books. For our purposes Tinkham (2004) will provide more than sufficient background. We will not wander into the field of exotic/high-temperature superconductors for two simple reasons: the quantum coherent behaviour of the kind we need to realize qubits or other quantum coherent devices has not yet been properly and/or routinely achieved in these systems; and the fabrication of such devices is not yet reliable enough or even feasible.
The importance of topological excitations in physics, mainly in the description of phase transitions, has a long history beginning with the superconductivity phenomenon in the rst years of the last century. However, the ideas behind this new concept has been more accurately described by Kosterlitz and Thouless, about 40 years ago. Conductor-superconductor, uidsuperuid, rough transitions and many others are characterized as being due the appearance of topological excitations in the system. Another concept of great importance is that the universality in phase transitions . Close to a phase transition the correlations of the system become innity, so that, the details of the model become irrelevant. In this situation, systems originaly so dierent as superconductors and ferromagnets, can be described by the same theory. The critical expoents, that caracterize the transition, depend only on the system dimension, the range of the potential and of their symmetries. This work is dedicated to study of the anisotropic Heisenberg model in two dimensions. This model has a non-usual phase transition, with quasi-long range order, characterized by a change in the behavior of the spin-spin correlation function C(r). In low temperature, T < TBKT, C(r) decays as a power law with distance, r. For temperatures greater than TBKT the correlation function falls o exponencially. The free energy has all the continuous derivatives, for this reason the transition is known as innity order transition. The BKT teory assume that the transition is driven by a vortice-antivortice unbiding mechanism in the system. In our study we did extensive numerical simulations with the tecnique known as Replica Exchange Wang-Landau. This method allow us to estimate the density of states g(E) of the model. With g(E) we can calculated the relevant termodynamic functions of the system (energy, magnetization, suceptibility and correlations for instance). Using Finite Size Scaling tecniques we have determinade the transition temperature TBKT and the behavior of the correlation function for a large range of temperatures. The calculations were done for various dilutions of non-magnetic sites, p, with p = 0,0;0,20;0,30 e 0,35, that allowed us to describe with great precision the critical behavior of the model in particular the correlation lentgh