# Collapse Operators

**Collapse operators** are synonymous with [[qutip-lindblad-operators|Lindblad operators]]—they're the quantum jumps that model irreversible evolution. The name comes from the Monte Carlo trajectory interpretation: each collapse operator represents a possible "jump" (measurement outcome or dissipative event) the system can undergo.

In [[qutip-mcsolve|Monte Carlo simulation]], collapse operators are applied stochastically. The system evolves unitarily until a random time, when a collapse operator "jumps" the state, then unitary evolution resumes. Running many trajectories gives the ensemble average, which matches the master equation result.

## Choosing Collapse Operators

Collapse operators depend on the physical system:

**Superconducting qubits**:
- Energy decay: $\sigma_- = \frac{1}{\sqrt{2}}(s_x + is_y)$ (relaxation)
- Dephasing: $\sigma_z$ (pure dephasing)

**Cavity QED**:
- Photon loss: $\sqrt{\kappa} a$ (cavity decay, $a$ is annihilation)
- Atomic decay: $\sqrt{\gamma} \sigma_-$ (spontaneous emission)

**Trapped ions**:
- Spontaneous emission: $\sqrt{\gamma} \sigma_-$
- Heating: $\sqrt{\dot{n}} a^\dagger$ (vibrational mode heating)

Collapse operators are phenomenological—they capture environment effects without explicitly simulating the environment. Well-chosen operators match experimental measurements of decoherence rates (T1, T2, linewidths, etc.).