SQUID Magnetometer Demonstration | Superconducting Quantum Interference Device

For a wave function to be single-valued when transported around a closed loop C, the total phase change must be an integer multiple of 2π: Δφ = 2πn, where n is an integer. Applying Stokes' theorem to convert the line integral of the vector potential to a surface integral of the magnetic field, we find that the magnetic flux through any surface bounded by the loop must satisfy Φ_B = ∫B·dS = (hc/e)n. This demonstrates that magnetic flux is quantized in units of hc/e, known as the flux quantum. This quantization arises from the requirement that wave functions remain single-valued under closed loops around magnetic singularities.

The quantization of magnetic flux in superconductors can be derived from the requirement that the superconducting wave function must be single-valued. For a superconducting ring in a magnetic field, the current density J = (ħ/M)(∇θ - (Q/ħ)A) must be zero deep inside the superconductor. Taking the line integral around a closed contour and applying Stokes' theorem gives (Q/ħ)Φ = ∮∇θ·dl. Since the wave function must be single-valued, the phase change around a closed loop must be an integer multiple of 2π. This leads to the quantization condition: Φ = n(2πħ/Q) = nΦ₀, where Q = 2e (charge of Cooper pair), so Φ₀ = h/(2e) is the flux quantum.

Superconductors can trap magnetic fields in a completely impermeable loop. The magnetic flux through such a loop is quantized in discrete units (flux quanta). This phenomenon, discovered by Hertz 100 years earlier, is analogous to the quantum oscillatory circuits of the 2025 laureates.

Quantum flux quantization is a microscopic quantum phenomenon where the magnetic flux through a superconductor can only take on integer values of the flux quantum (Φ₀ = h/2e), providing experimental confirmation of the microscopic theory of superconductivity which describes superconducting current as arising from the motion of Cooper electron pairs.

Magnetic flux in superconductors is quantized in discrete units called magnetic flux quanta, Φ₀ = h/(2e). This quantization means magnetic flux cannot take arbitrary values—it must be integer multiples of Φ₀. Some literature uses the reduced magnetic flux quantum Φ₀/2, which differs by a factor of 2. Understanding this distinction is crucial when reading research papers or textbooks, as different conventions may use either definition depending on context.

The Josephson effect is a macroscopic quantum phenomenon where a supercurrent flows indefinitely without voltage across a Josephson junction—a device consisting of two superconductors coupled by a weak link (such as an insulating barrier, nonsuperconducting metal, or physical constriction). Predicted by Brian David Josephson in 1962 and for which he received the Nobel Prize in Physics in 1973, this effect enables three main phenomena: the DC Josephson effect (direct current without external electromagnetic field), the AC Josephson effect (AC current with frequency proportional to applied voltage), and the inverse AC Josephson effect (DC current from AC voltage). Key applications include SQUIDs (superconducting quantum interference devices) for sensitive magnetometry, precision metrology standards for voltage calibration, superconducting single-electron transistors, RSFQ digital electronics, superconducting quantum computing qubits, and advanced radiation detection.

The Josephson effect, predicted in 1962 and observed in 1963, occurs when a voltage is applied across a narrow junction between two superconductors. A time-dependent oscillating current flows with frequency ν satisfying hν = 2eV, where V is the applied voltage. This relationship is exact and defines the volt in SI units. The precision of this effect is extraordinary—frequencies agree to better than one part in 10¹⁷ between different junctions.

In 1962, while studying superconductivity theory at Cambridge, Brian Josephson became fascinated by the concept of 'broken symmetry' and wondered if the theoretical phase property of superconductors could be observed experimentally. He proposed a hypothetical setup of two superconductors separated by an insulating barrier, predicting that electron pairs could tunnel through this barrier—a phenomenon impossible according to classical physics. His calculations predicted two effects: a supercurrent flowing without voltage, and oscillating current at frequencies proportional to applied voltage. When he published his findings in Physics Letters, John Bardeen, co-inventor of the transistor and leading authority on superconductivity, dismissed the idea as impossible. At a conference in September 1962, Josephson publicly interrupted Bardeen to defend his calculations. Two months later, Philip Anderson and John Rowell at Bell Labs confirmed the effect experimentally. This discovery led to SQUIDs, advanced metrology, and earned Josephson the Nobel Prize at age 33, proving that being an outsider does not mean being incorrect.

The Josephson Effect, predicted by Brian Josephson in 1962 at age 22, occurs when two superconductors are separated by a thin insulating barrier just a few atomic layers thick. This produces a supercurrent—a direct current that flows through the insulator without resistance or significant energy loss. Unlike traditional transistor gates that generate heat during switching, Josephson junctions operate with minimal energy dissipation. This effect demonstrates quantum tunneling observable at macroscopic scales and earned Josephson a Nobel Prize.

When two superconductors are separated by a very thin insulating layer, Cooper pairs can tunnel through the insulator via quantum tunneling even when no voltage is applied. This quantum tunneling current was first proposed by Brian Josephson and is now known as the Josephson effect. The device formed by this setup is called a Josephson junction. For this groundbreaking discovery, Brian Josephson was awarded the Nobel Prize in Physics in 1973. Josephson junctions became key components in the experiments that led to the 2025 Nobel Prize.

Cryogenics is the branch of physics that studies phenomena occurring at very low temperatures (below 123 Kelvin or -150°C), utilizing gas compression and expansion cycles to achieve these temperatures; at cryogenic conditions, materials exhibit unique properties such as vanishing specific heat, superconductivity (simultaneous disappearance of electrical resistance and appearance of perfect diamagnetism, first observed in mercury at 4.15K by Kamerlingh Onnes in 1911), ductile-to-brittle transitions in metals, and changes in thermal conductivity, with applications spanning space science, medical preservation, food industry, gas liquefaction, and advanced technologies like magnetic levitation trains and MRI scanning.

Cryogenics is the physics of materials at very low temperatures, with a cryogenics being a specialist in this field. The boundary between refrigeration and cryogenics is not precisely defined, but scientists consider gases cryogenic if they can be liquefied at or below -150°C, while the US NIST defines cryogenics as temperatures below -180°C. High-temperature cryogenics spans from just above liquid nitrogen's boiling point (-195.79°C) to -50°C. The field uses Kelvin or Rankine scales measuring from absolute zero. Key branches include cryobiology (organism preservation), cryosurgery (tissue destruction), cryoelectronics (superconductivity studies), and cryonics (preservation for future revival). Common cryogenic fluids include liquid nitrogen (most widely used, legally purchasable globally) and liquid helium (lowest attainable temperatures). Storage occurs in Dewar flasks—double-walled containers with high vacuum. Cryogenic processing began during WWII when scientists discovered metals frozen to low temperatures showed increased wear resistance. Eadie Bush founded Cryo Tech in 1966, pioneering commercial applications that extended metal tool life by 200-400%. Applications include pharmaceutical production requiring ~-100°C environments, cryogenic food freezing using nitrogen blast or immersion systems, and cryogenic milling for brittle materials.

Cryogenics is the branch of physics dealing with the production and effects of very low temperatures (below -238°F), enabling the efficient storage and handling of atmospheric gases by reducing them to liquefied states that occupy only 1/1800th the volume of their gaseous form; this technology relies on fundamental thermodynamic principles including phase equilibrium, evaporation, condensation, boiling, and flashing, which govern how cryogenic fluids behave under varying pressure and temperature conditions, and is applied across diverse fields such as medical oxygen delivery, food preservation, rocket fuel production, and industrial gas processing.

Cryogenics (crônica) is a technique that allows refrigeration of the body to temperatures of -196 degrees Celsius (nitrogen liquid temperature). This process stops deterioration and aging, enabling the body to be maintained in the same conditions for several years with the hope of future reanimation. When a person is placed in the nitrogen liquid tank, they are not definitively dead because, after death, all body cells collapse, blood coagulates rapidly, and organs and brain stop functioning. Therefore, the person must be induced into a deep coma before being placed in the cryogenic apparatus.

Solid air production requires extreme conditions beyond standard vacuum capabilities. Liquid air's triple point requires pressures 100 times lower than liquid nitrogen, requiring multi-million dollar equipment. Liquid helium achieves -269°C (73°C colder than liquid nitrogen), producing immediate fog from evaporating air. Solid air forms at approximately -220°C. Despite appearing solid, it rapidly melts and immediately vaporizes due to minimal difference between melting and boiling points. Solid air retains magnetic properties from concentrated oxygen, attracting to magnets even as it melts. This demonstrates how extreme cryogenics enables unusual states of matter normally impossible under Earth's conditions.