Quantum jump method
The quantum jump method, also known as the Monte Carlo wave function (MCWF) method, is a technique in computational physics used for simulating open quantum systems. The quantum jump method was developed by Dalibard, Castin and Mølmer, with a very similar method also developed by Carmichael in the same time frame. Other contemporaneous works on wave-function-based Monte Carlo approaches to open quantum systems include those of Dum, Zoller and Ritsch and Hegerfeldt and Wilser.
The quantum jump method is an approach which is much like the 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 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.
- A recent review is Plenio, M. B.; Knight, P. L. (1 January 1998). "The quantum-jump approach to dissipative dynamics in quantum optics". Reviews of Modern Physics. 70 (1): 101–144. arXiv:quant-ph/9702007. Bibcode:1998RvMP...70..101P. doi:10.1103/RevModPhys.70.101.
- Mølmer, K.; Castin, Y.; Dalibard, J. (1993). "Monte Carlo wave-function method in quantum optics". Journal of the Optical Society of America B. 10 (3): 524. Bibcode:1993JOSAB..10..524M. doi:10.1364/JOSAB.10.000524.
- The associated primary sources are, respectively:
- Dalibard, Jean; Castin, Yvan; Mølmer, Klaus (February 1992). "Wave-function approach to dissipative processes in quantum optics". Physical Review Letters. 68 (5): 580–583. arXiv:0805.4002. Bibcode:1992PhRvL..68..580D. doi:10.1103/PhysRevLett.68.580. PMID 10045937.
- Carmichael, Howard (1993). An Open Systems Approach to Quantum Optics. Springer-Verlag. ISBN 978-0-387-56634-4.
- Dum, R.; Zoller, P.; Ritsch, H. (1992). "Monte Carlo simulation of the atomic master equation for spontaneous emission". Physical Review A. 45 (7): 4879–4887. Bibcode:1992PhRvA..45.4879D. doi:10.1103/PhysRevA.45.4879. PMID 9907570.
- Hegerfeldt, G. C.; Wilser, T. S. (1992). "Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom". In H.D. Doebner; W. Scherer; F. Schroeck, Jr. (eds.). Classical and Quantum Systems (PDF). Proceedings of the Second International Wigner Symposium. World Scientific. pp. 104–105.
- Quantum Optics Toolbox for Matlab
- mcsolve Quantum jump (monte carlo) solver from QuTiP.
- QuantumOptics.jl the quantum optics toolbox in Julia.
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