Quantum jump method
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Quantum jump method
The quantum jump method, also known as the Monte Carlo wave function 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.[1][2]
Method
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. For a Hilbert space of dimension N, the number of wave function components is of the order of N while the number of density matrix components is of the order of N2. For certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.[1]
Further reading
- An early overview of the method provided by Mølmer, Castin and Dalibard.[1]
- A more recent and complete discussion given at Plenio, M. B. (1 January 1998). "The quantum-jump approach to dissipative dynamics in quantum optics". Reviews of Modern Physics. 70 (1): 101–144. doi:10.1103/RevModPhys.70.101.
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References
- ^ a b c Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1364/JOSAB.10.000524, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1364/JOSAB.10.000524instead. - ^ The associated primary sources are, respectively:
- Dalibard, Jean (NaN undefined NaN). "Wave-function approach to dissipative processes in quantum optics". Physical Review Letters. 68 (5): 580–583. doi:10.1103/PhysRevLett.68.580.
{{cite journal}}: Check date values in:|date=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - Carmichael, Howard (1993). An Open Systems Approach to Quantum Optics. Springer-Verlag. ISBN 9780387566344.
- Dum, R. (1992). "Monte Carlo simulation of the atomic master equation for spontaneous emission". Physical Review A. 45 (7): 4879–4887. doi:10.1103/PhysRevA.45.4879.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - Hegerfeldt, G. C.; Wilser, T. S. (1992). "Classical and Quantum Systems". Proceedings of the Second International Wigner Symposium. World Scientific.
- Dalibard, Jean (NaN undefined NaN). "Wave-function approach to dissipative processes in quantum optics". Physical Review Letters. 68 (5): 580–583. doi:10.1103/PhysRevLett.68.580.
Category:Quantum mechanics Category:Computational physics Category:Monte Carlo methods