Quantum jump method: Difference between revisions

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[[File:Master equation unravelings.svg|thumb|An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped [[Rabi oscillation]]s. The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.]]

The quantum jump method is an approach which is much like the [[Lindblad equation|master-equation treatment]] except that it operates on the wave function rather than using a [[density matrix]] approach. The main component of the method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each [[time step]], a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a [[Quantum stochastic calculus#Quantum trajectories|quantum trajectory]], and the desired density matrix as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N². Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.<ref name=MCD1993>{{Cite doijournal | last1 = Mølmer | first1 = K. | last2 = Castin | first2 = Y. | last3 = Dalibard | first3 = J. | doi = 10.1364/JOSAB.10.000524 | title = Monte Carlo wave-function method in quantum optics | journal = Journal of the Optical Society of America B | volume = 10 | issue = 3 | pages = 524 | year = 1993 | pmid = | pmc = }}</ref>

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