Магистрант
  1. Классическая механика  1.1. Продвинутая кинематика  1.1.1. Обобщенные системы координат  1.1.2. Параметрические уравнения движения  1.1.3. Неинерциальные системы и фиктивные силы  1.1.4. Ковариантная формулировка импульса  1.1.5. Action-angle variable  1.2. Лагранжева и гамильтонова механика  1.2.1. Принцип минимального действия  1.2.2. Уравнения Эйлера-Лагранжа  1.2.3. Теорема Нётер и законы сохранения  1.2.4. Нормализованная скорость  1.2.5. Каноническое преобразование  1.2.6. Скобка Пуассона и теория Гамильтона–Якоби  1.2.7. Гамильтонова хаоса и интегрируемость  1.3. Мобильность жесткого тела  1.3.1. Euler's equations of motion  1.3.2. Principal moments of inertia  1.3.3. Гироскопическое движение и прецессия  1.3.4. Тензор инерции  1.3.5. Стабильность скорости вращения  1.4. Нелинейная динамика и хаос  1.4.1. Phase space and stability analysis  1.4.2. Секции Пуанкаре и теория бифуркации  1.4.3. Странные аттракторы и фракталы  1.4.4. Показатель Ляпунова  1.4.5. Теорема КАМ и квазипериодическое движение
  2. Электромагнетизм  2.1. Advanced Electrodynamics  2.1.1. Функция Грина и теория потенциала  2.1.2. Multipole expansion  2.1.3. Метод заряда изображения  2.1.4. Граничные условия и теорема о единственности  2.2. Распространение электромагнитных волн  2.2.1. Plane waves in dielectrics and conductors  2.2.2. Волноводы и резонаторы  2.2.3. Давление излучения и оптические пинцеты  2.2.4. Поляризация и теорема Джонса  2.3. Релятивистская электродинамика  2.3.1. Covariant formulation of electrodynamics  2.3.2. Потенциалы Лиенара-Вихерта  2.3.3. Синхротронное излучение и тормозное излучение  2.3.4. Тензор электромагнитного поля и преобразования Лоренца  2.4. Физика плазмы  2.4.1. Magnetohydrodynamics  2.4.2. Экранирование Дебая и плазменные колебания  2.4.3. Волны Альфвена и удержание в токамаке  2.4.4. Нестабильности и турбулентность в плазме
  3. Статистическая механика и термодинамика  3.1. Продвинутая термодинамика  3.1.1. Преобразования Лежандра и термодинамические потенциалы  3.1.2. Теорема флуктуаций-диссипации  3.1.3. Онсагерские взаимные отношения  3.1.4. Critical events and phase transitions  3.2. Квантовая статистическая механика  3.2.1. Density Matrix and Ensemble Theory  3.2.2. Конденсаты Бозе – Эйнштейна  3.2.3. Квантовый фазовый переход  3.2.4. Статистика Ферми–Дирака и Бозе–Эйнштейна  3.2.5. Функции распределения и большие канонические ансамбли
  4. Квантовая механика  4.1. Углубленная механика волн  4.1.1. Приближение ВКБ  4.1.2. Формулировка с использованием интегралов по путям  4.1.3. Quantum harmonic oscillator and coherent states  4.2. Угловой момент и спин  4.2.1. Сферические Гармоники  4.2.2. Клебш–Гордан коэффициент  4.2.3. Теорема Вигнера–Экарта  4.2.4. Спин-орбитальное взаимодействие  4.3. Теория квантового рассеяния  4.3.1. Приближение Борна  4.3.2. Анализ частичных волн  4.3.3. Оптическая теорема  4.3.4. Теория S-матрицы  4.4. Quantum field theory  4.4.1. Вторая квантование  4.4.2. Диаграммы Фейнмана и пропагаторы  4.4.3. Теория перенормировки  4.4.4. Gauge theory and Yang–Mills fields  4.4.5. Спонтанное нарушение симметрии и механизм Хиггса
  5. Общая теория относительности и космология  5.1. Тензорное исчисление и дифференциальная геометрия  5.1.1. Уравнения Эйнштейна  5.1.2. Метрики Шварцшильда и Керра  5.1.3. Геодезия и символы Христоффеля  5.2. Космология и Вселенная  5.2.1. Метрика Фридмана-Леметра-Робертсона-Уокера и космическая инфляция  5.2.2. Темная энергия и образование структур  5.2.3. Космическое микроволновое фоновое излучение
  6. Физика конденсированного состояния  6.1. Структура зон и теория переноса  6.1.1. Теорема Блоха и модель Кронига-Пенни  6.1.2. Топология поверхности Ферми  6.1.3. Квантовый эффект Холла  6.2. Superconductivity  6.2.1. BCS theory and Cooper pairs  6.2.2. Эффект Мейснера и квантизация потока  6.2.3. The Josephson Effect and SQUIDs  6.3. Топологические фазы вещества  6.3.1. Топологические изоляторы  6.3.2. Фермионы Майораны в топологических фазах материи
  7. Nuclear and Particle Physics  7.1. Квантовая хромодинамика (КХД)  7.1.1. Кварк-глюонная плазма  7.1.2. Асимптотическая свобода  7.1.3. Конфайнмент и адронизация  7.2. За пределами Стандартной модели  7.2.1. Великие объединённые теории  7.2.2. Суперсимметрия и дополнительные измерения  7.2.3. Neutrino oscillations

Магистрант → Физика конденсированного состояния → Superconductivity ↓


The Josephson Effect and SQUIDs


The study of superconductivity is a fascinating field in condensed matter physics that highlights the fascinating properties of materials that exhibit zero electrical resistance below a specific temperature. Two fascinating phenomena within this domain are the Josephson effect and superconducting quantum interference devices (SQUIDs). This text discusses these topics in depth, exploring the underlying principles and applications while keeping the language as accessible as possible.

What is the Josephson effect?

The Josephson effect is a quantum mechanical phenomenon observed in superconductors. It describes the flow of supercurrent — a current that flows indefinitely without any voltage applied — between two pieces of superconducting material separated by a very thin insulating layer. This configuration is known as a Josephson junction.

A fundamental feature of the Josephson effect is that it arises from quantum tunneling. The supercurrent is carried by Cooper pairs, which are pairs of electrons bound together at low temperatures in a correlated quantum state. Tunneling occurs due to the overlap of the wave functions of these Cooper pairs across an insulating barrier.

Superconductor A Superconductor B insulator

Josephson Junction and Current

The behavior of a Josephson junction can be described by two equations:

I = I_c * sin(φ)
V = (h/2e) * (dφ/dt)

Here, I is the overcurrent, I_c is the critical current (the maximum overcurrent that can flow without resistance), φ is the phase difference of the superconducting wave functions at the junction, V is the voltage at the junction, h is the Planck constant, and e is the electron charge.

The first equation shows that the supercurrent is a function of the sine of the phase difference. In the absence of any voltage (i.e., for zero applied voltage), a direct current known as the Josephson current flows across the junction with a magnitude up to I_c.

The second equation relates the rate of change of the phase difference with the voltage at the junction. The applied voltage results in an oscillatory supercurrent, leading to high frequency applications.

Applications of the Josephson Effect

The Josephson effect is used in many technological fields. One of its major uses is in the development of sensitive magnetometers called SQUIDs (superconducting quantum interference devices), which can detect extremely small magnetic fields. SQUIDs are important in fields such as medical imaging and geophysical exploration.

Another important application is in quantum computers. Josephson junctions serve as the basic elements of superconducting qubits, which are the building blocks of quantum computers. These qubits can exist in a superposition of states, providing the basis for quantum computation.

What are SQUIDs?

Superconducting quantum interference devices, or SQUIDs, are highly sensitive magnetometers used to measure small magnetic fields. The operation of SQUIDs relies on the principles of the Josephson effect and quantum interference, making them extremely powerful tools in a variety of scientific and applied fields.

Fundamentals of SQUIDs

At the core of a SQUID is a superconducting loop containing one or more Josephson junctions. There are two key concepts involved in understanding how a SQUID works: flux quantization and the Josephson effect.

  • Flux quantization: In a superconducting loop, the magnetic flux is quantized. This means that it can only take discrete values that are integral multiples of the magnetic flux quantum Φ₀, which is approximately 2.067833848 × 10^(-15) webers.
  • Josephson Effect: As mentioned earlier, this effect results in the generation of overcurrent which can be controlled by external magnetic fields affecting the phase difference between the two sides of the Josephson junction.
Josephson Junction Superconducting Loop

Types of SQUIDs

There are two main types of SQUIDs:

  1. DC SQUID: It consists of a superconducting loop with two Josephson junctions. It operates by maintaining a constant current through the loop. The voltage across the device is measured and varies periodically with the applied magnetic flux.
  2. RF SQUID: It consists of a single Josephson junction in a loop. It works with radio frequencies to detect changes in the magnetic field, using a resonant tank circuit.

DC SQUIDs are more sensitive than RF SQUIDs due to their design, making them the preferred choice for accurate measurements.

Function of SQUID

The basic working principle of SQUID involves detecting changes in magnetic flux. As magnetic fields pass through the superconducting loop, they alter the phase difference across the junctions. This change in phase leads to a variation in the supercurrent due to the Josephson effect, causing voltage fluctuations that can be measured with high precision.

Magnetic Field

When a magnetic signal is detected, the supercurrent shifts, and the interference pattern of waves in the superconducting loop changes. This change is converted into an electrical signal that is read by an external circuit.

Applications of SQUIDs

Because of their exceptional sensitivity, SQUIDs have a diverse range of applications:

  • Medical imaging: SQUIDs are used in techniques such as magnetoencephalography (MEG), which maps brain activity by detecting magnetic fields generated by neural activity.
  • Geophysical exploration: They help identify mineral deposits by mapping subtle variations in the Earth's magnetic field.
  • Fundamental physics research: SQUIDs are integral to experiments requiring magnetic field measurements at quantum precision, such as in the study of superconducting materials and fundamental particles.
  • Non-destructive evaluation: These are used to inspect structural integrity and detect defects in critical components such as aircraft parts.

Theoretical background and quantum mechanics

The Josephson effect and SQUIDs are deeply rooted in the principles of quantum mechanics. The concept of quantum tunneling, where particles pass through potential barriers, challenges classical mechanics and forms the basis of the Josephson effect.

The quantum state of superconducting materials, described by a complex wave function, reflects the macroscopic quantum coherence that makes these phenomena possible. The phase of this wave function interacts with magnetic fields, leading to observable effects such as Josephson junction current modulation.

Conclusion

The Josephson effect and SQUIDs represent important scientific advances in the fields of superconductivity and condensed matter physics. These phenomena demonstrate how quantum mechanics, when applied to macroscopic materials, leads to practical technologies that push the boundaries of modern science and engineering.

From cutting-edge medical diagnostics to exploring the fundamental laws of physics, the applications of the Josephson effect and SQUIDs continue to grow, providing deeper insights into the quantum world and its impact on our daily lives.


Магистрант → 6.2.3


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Топологические фазы вещества

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The Josephson Effect and SQUIDs

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