PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Condensed matter physics → Superconductivity ↓


Josephson effect


The Josephson effect is an important phenomenon in the field of superconductivity, which refers to the passage of current between two pieces of superconductor separated by a thin insulating barrier. It was first discovered by physicist Brian D. Josephson in 1962, and since then, it has opened up an important avenue of research and applications in quantum mechanics and condensed matter physics.

Original idea

The essence of the Josephson effect lies in the quantum mechanical properties of superconductors. A superconductor is a substance that exhibits zero electrical resistance below a certain temperature. When two superconductors are brought together with a thin insulating layer in between, they form what is known as a Josephson junction.

Superconductors insulator Superconductors

Two types of currents can flow in such a structure:

  1. Supercurrent: A direct current that can flow across a junction without any voltage drop. This is caused by the coherence of the superconducting wave function across the insulator, which allows pairs of electrons (Cooper pairs) to tunnel through the barrier.
  2. Alternating current (AC): When a constant voltage is applied, alternating current is produced, which is a typical behavior of the Josephson effect.

Mathematical description

There are two primary Josephson equations describing this effect:

  1. The first Josephson equation relates the supercurrent I flowing through the junction to the sine of the phase difference φ between the two superconductors: 
    I = Ic sin(φ)
    Here, Ic is the critical current, which is the maximum current that can flow through the junction without producing a voltage across it.
  2. The second Josephson equation connects the rate of change of the phase difference φ with the voltage V at the junction: 
    dφ/dt = (2eV) / h
    Where e is the elementary charge, h is Planck's constant. This equation implies that if there is a voltage across the junction then the phase difference evolves with time.

Applications of the Josephson effect

The Josephson effect has numerous technological and fundamental applications:

  • Superconducting quantum interference devices (SQUID): These are highly sensitive magnetometers that use the Josephson effect to measure subtle changes in magnetic fields. They are used extensively in medical imaging techniques such as magnetoencephalography (MEG).
  • Voltage Standards: Josephson junctions are used to create voltage standards with extreme accuracy. The relationship between frequency and voltage in the Josephson effect is used to redefine the volt in terms of observable quantities.
  • Quantum computing: Josephson junctions are a potential element in the development of qubits for quantum computers. They offer the ability to operate at very high speeds while maintaining quantum coherence.

Josephson junction types

There are several different types of Josephson junctions, depending on the barrier material and structure:

  • Superconductor–insulator–superconductor (SIS): Classical Josephson junction with an insulating barrier.
  • Superconductor-normal metal-superconductor (SNS): The barrier is a normal, non-superconducting metal.
  • Superconductor-Contraction-Superconductor (SCS): The barrier is a narrow, compressed region of the superconductor.

Phase and Cooper pairs

The quantum mechanical nature of superconducting electrons or Cooper pairs leads to unique properties in the Josephson junction. The phase difference φ appearing in Josephson's equations plays an important role in determining the supercurrent. The phase difference can arise due to various reasons such as differences in magnetic fluxes or external electromagnetic fields.

S1 S2 current flows from S1 to S2

In this visual representation, S1 and S2 denote the superconducting regions. The wave functions of the Cooper pairs extend across the barrier, and it is this overlap that gives rise to the Josephson current.

Macroscopic quantum phenomena

The Josephson effect is an obvious manifestation of a macroscopic quantum phenomenon. Unlike most quantum effects which are microscopic in nature, the Josephson effect can be observed on the scale of meters under the right conditions. This duality of microscopic principles affecting macroscopic properties provides profound insight into the quantum nature of reality.

Conclusion

The Josephson effect is a remarkable example of the work of quantum mechanics in the world of superconductivity. Its discovery has not only generated substantial academic interest, but also paved the way for myriad applications in the quantum field. As our understanding of quantum mechanics continues to deepen, the Josephson effect remains at the forefront of technology and physics, continually shaping how we understand and use quantum phenomena.


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Josephson effect

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