A measure of a resonator's sharpness of resonance, indicating energy loss rate.The quality factor, often denoted as Q, is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the energy stored in the resonator to the energy lost per cycle, multiplied by 2π. A high Q factor indicates that the resonator loses energy slowly, meaning it has a sharp resonance peak and a narrow bandwidth. In physics and engineering, Q is crucial for characterizing the performance of systems ranging from mechanical pendulums to optical cavities and superconducting microwave resonators.
The concept of quality factor was introduced by the electrical engineer K. S. Johnson in the 1920s while working on radio frequency coils at Bell Labs. It was later adopted widely in physics and engineering.
The quality factor is mathematically expressed as Q = 2π × (energy stored) / (energy lost per cycle). For a damped harmonic oscillator, Q is inversely proportional to the damping coefficient. In practice, a resonator with high Q will ring for many cycles after being excited, and its frequency response will be sharply peaked at the resonant frequency. Losses can arise from various mechanisms, such as internal friction in materials, electrical resistance, radiation, or coupling to the environment.
High-Q resonators are essential in technologies such as quartz crystal oscillators for precise timekeeping, superconducting cavities for particle accelerators, and optical microcavities for laser and sensor applications.
The quality factor of a superconducting microwave resonator can exceed one billion, meaning it can store energy for millions of cycles before losing it, which is crucial for quantum computing applications.
| S_a^{1/2} | variable | Spectral density of acceleration noise (square root) — acceleration noise spectral density metre per second squared per root hertz |
| T | variable | Temperature — temperature kelvin |
| k | variable | Spring constant of the resonator — spring constant newton per metre |
| m | variable | Mass of the resonator — mass kilogram |
| ω | variable | Angular resonance frequency — angular frequency radian per second |
| Q | variable | Quality factor of the resonator — quality factor |
| k_B | constant | Boltzmann constant, relates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| G | variable | optomechanical gain |
| Q_m | variable | mechanical quality factor — quality factor |
| P | variable | optical power — power watt |
| G_n | variable | optical response function (complex) |
| M | variable | effective mass of mechanical mode — mass kilogram |
| ω_m | variable | mechanical angular frequency — angular frequency radian per second |
| Re | operator | extracts the real component of a complex number — real part |







