A measure of the interaction energy between two quantum systems, here in the megahertz range.Coupling strength is a measure of the interaction energy between two quantum systems, such as two qubits, an atom and a photon, or a mechanical resonator and a superconducting circuit. It quantifies how strongly one system influences the other, and it is typically expressed in units of frequency (e.g., megahertz or gigahertz) via Planck's relation E = hν. In quantum technology, the coupling strength determines how fast quantum operations can be performed and how well quantum information can be transferred between systems. A strong coupling (much larger than the decoherence rate) is essential for building reliable quantum gates and for observing coherent quantum phenomena.
The concept of coupling strength has roots in early quantum mechanics, particularly in the Jaynes–Cummings model (1963) describing atom-photon interactions. The modern engineering of strong coupling in solid-state systems emerged in the 2000s with the development of circuit QED by Alexandre Blais and colleagues.
When two quantum systems interact, their combined energy levels shift by an amount proportional to the coupling strength. This shift can be measured spectroscopically, for example by observing the splitting of resonance frequencies. In circuit QED, a superconducting qubit coupled to a microwave cavity exhibits a vacuum Rabi splitting of magnitude 2g, where g is the coupling strength. The coupling strength also determines the rate of coherent energy exchange between the systems: a stronger coupling leads to faster oscillations (Rabi oscillations) between the states. In practice, coupling is engineered by controlling the physical distance, the overlap of wavefunctions, or the mediating fields between the systems.
Coupling strength is a key parameter in designing quantum processors, quantum memories, and quantum transducers. It is also crucial for quantum sensing, where stronger coupling to a target signal improves sensitivity, and for quantum batteries, where it controls charging speed.
In circuit QED, coupling strengths can reach values of several hundred megahertz, which is orders of magnitude larger than the decoherence rates, enabling thousands of coherent quantum operations before information is lost.
| g | variable | coupling strength between the two modes — coupling strength radian per second |
| κ₁ | variable | decay rate of the first mode — decay rate radian per second |
| κ₂ | variable | decay rate of the second mode — decay rate radian per second |











