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Quantum superconductivity is the study of superconductivity as a macroscopic quantum phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.

Superconductivity is one of the best-known examples of a macroscopic quantum phenomenon, together with superfluidity, the Josephson effect, the quantum Hall effect, and Bose–Einstein condensates. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.^[1]^[2]

Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields.

Macroscopic quantum state

A superconducting state is described by a macroscopic wave function,

Ψ = Ψ_{0} \exp (i φ)

where $Ψ_{0}$ is the amplitude and $φ$ is the phase. When a quantum state is occupied by a very large number of particles, the wave function describes not only probability but also a macroscopic density and phase-coherent flow.^[3]^[4]

The particle-flow density can be related to the phase of the wave function. For a condensate, the velocity is

{\vec{v}}_{s} = \frac{1}{m} (\frac{h}{2 π} \vec{\nabla} φ - q \vec{A})

where $m$ is the particle mass, $q$ is the charge, and $\vec{A}$ is the magnetic vector potential.^[5]

This equation shows the central idea: a classical observable such as flow velocity is controlled by the phase of a quantum wave function.

Relation to superfluidity

Superconductivity is closely related to superfluidity, but it is not the same phenomenon. Superfluidity is frictionless mass flow, while superconductivity is resistance-free charge flow.

In superfluid helium, the particles are neutral, so $q = 0$ . The velocity of the superfluid is then determined only by the phase gradient:

{\vec{v}}_{s} = \frac{1}{m} \frac{h}{2 π} \vec{\nabla} φ .

Because the wave function must be single-valued, circulation is quantized:

\oint {\vec{v}}_{s} \cdot d \vec{s} = \frac{h}{m} n .

This leads to quantized vortices in rotating superfluids. Superconductors show a closely related phenomenon, but because the condensate is charged, magnetic flux becomes quantized.

For this reason, superconductivity is often described as a charged superfluid.

Cooper pairs

In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairs. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or phonons.

Although electrons are fermions, a Cooper pair behaves as a composite boson. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.

For a Cooper pair,

m = 2 m_{e}

and

q = - 2 e

where $m_{e}$ is the electron mass and $e$ is the elementary charge.^[6]

Flux quantization

Because the superconducting wave function is single-valued, magnetic flux in a superconducting loop is quantized. The basic flux quantum is

Φ_{0} = \frac{h}{2 e} = 2.067833758 \times 1 0^{- 15} W b .

This value is extremely small, yet it is fundamental in superconducting circuits, vortex physics, and precision measurement.

Flux quantization is one of the clearest macroscopic manifestations of quantum mechanics. It shows that a superconducting ring behaves as a single coherent quantum object.

Type-I and Type-II superconductors

Superconductors are commonly divided into two types.

Type-I superconductors expel magnetic fields completely below a critical magnetic field. When the applied field exceeds this critical value, superconductivity is destroyed abruptly.

Type-II superconductors have two critical fields. Between the lower critical field $H_{c 1}$ and the upper critical field $H_{c 2}$ , magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices.

This mixed state was explained by Alexei Abrikosov using Ginzburg–Landau theory. In a type-II superconductor, the vortices can form an ordered triangular lattice, now called the Abrikosov vortex lattice.^[7]^[8]

Josephson effect

The Josephson effect occurs when two superconductors are separated by a thin insulating barrier or weak link. Even without a voltage, a supercurrent can tunnel through the barrier.

The DC Josephson relation is

i_{s} = i_{1} \sin (Δ φ)

where $Δ φ$ is the phase difference between the two superconductors.^[9]

If a voltage is applied, the phase difference changes in time:

V = \frac{1}{2 π} \frac{h}{2 e} \frac{d Δ φ}{d t} .

This gives an alternating supercurrent with frequency

ν = \frac{2 e V}{h} = \frac{V}{Φ_{0}} .

Josephson junctions are essential in superconducting electronics, SQUIDs, voltage standards, and superconducting quantum circuits.

SQUIDs

A SQUID is a superconducting quantum interference device. It usually consists of a superconducting loop interrupted by one or more Josephson junctions. Because the total flux through the loop is quantized, the current through the SQUID depends sensitively on the applied magnetic field.

This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements.

Superconductivity and phonons

In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to BCS theory. The isotope effect, in which the superconducting critical temperature depends on ionic mass, provides evidence for the role of lattice vibrations in conventional superconductivity.

Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms.

Quantum gases and mechanical systems

Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form Bose–Einstein condensates, in which many atoms occupy a single quantum state.^[10]

Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.^[11]^[12]

Importance

Quantum superconductivity is important because it connects microscopic quantum mechanics to directly observable macroscopic effects. It provides examples of phase coherence, flux quantization, quantum tunneling, collective excitations, and topological defects in real materials.

Applications include superconducting magnets, magnetic sensors, quantum interference devices, particle accelerators, MRI systems, and superconducting qubits for quantum computing.

Table of contents (138 articles)

Index

Core theory

Foundations
Conceptual and interpretations
Mathematical structure and systems
Atomic and spectroscopy
Wavefunctions and modes
Quantum dynamics and evolution
Measurement and information
Quantum information and computing

Applications and extensions

Quantum optics and experiments
Open quantum systems
Quantum field theory
Statistical mechanics and kinetic theory
Condensed matter and solid-state physics
Plasma and fusion physics
Timeline
Advanced and frontier topics

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Physics:Quantum Superconductivity

Macroscopic quantum state

Relation to superfluidity

Cooper pairs

Flux quantization

Type-I and Type-II superconductors

Josephson effect

SQUIDs

Superconductivity and phonons

Quantum gases and mechanical systems

Importance

See also

Table of contents (138 articles)

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