Physics:Quantum jump method: Difference between revisions
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{{Short description|Computational simulation method for open quantum systems}} | |||
{{Quantum book backlink|Quantum dynamics and evolution}} | |||
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The '''quantum jump method''', also known as the '''[[Monte Carlo method|Monte Carlo]] wave function (MCWF)''' is a technique in [[Physics:Computational physics|computational physics]] used for simulating [[Physics:Open quantum system|open quantum system]]s and [[Physics:Quantum dissipation|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard|Dalibard]], Castin and [[Biography:Klaus Mølmer|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael|Carmichael]]. Other contemporaneous works on wave-function-based [[Monte Carlo method|Monte Carlo]] approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller|Zoller]] and [[Biography:Helmut Ritsch|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively: | The '''quantum jump method''', also known as the '''[[Monte Carlo method|Monte Carlo]] wave function (MCWF)''' is a technique in [[Physics:Computational physics|computational physics]] used for simulating [[Physics:Open quantum system|open quantum system]]s and [[Physics:Quantum dissipation|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard|Dalibard]], Castin and [[Biography:Klaus Mølmer|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael|Carmichael]]. Other contemporaneous works on wave-function-based [[Monte Carlo method|Monte Carlo]] approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller|Zoller]] and [[Biography:Helmut Ritsch|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively: | ||
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*{{cite journal|last=Dum|first=R.|author2=Zoller, P. |author3=Ritsch, H. |title=Monte Carlo simulation of the atomic master equation for spontaneous emission|journal=Physical Review A|year=1992|volume=45|issue=7|pages=4879–4887|doi=10.1103/PhysRevA.45.4879|pmid=9907570|bibcode = 1992PhRvA..45.4879D }} | *{{cite journal|last=Dum|first=R.|author2=Zoller, P. |author3=Ritsch, H. |title=Monte Carlo simulation of the atomic master equation for spontaneous emission|journal=Physical Review A|year=1992|volume=45|issue=7|pages=4879–4887|doi=10.1103/PhysRevA.45.4879|pmid=9907570|bibcode = 1992PhRvA..45.4879D }} | ||
*{{cite book |last1=Hegerfeldt |first1=G. C. |last2=Wilser |first2=T. S. |year=1992 |title=Classical and Quantum Systems |series= Proceedings of the Second International Wigner Symposium |publisher=World Scientific|url=http://www.theorie.physik.uni-goettingen.de/~hegerf/collaps_gesamt.pdf|pages=104–105|chapter=Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom|editor1=H.D. Doebner|editor2=W. Scherer|editor3=F. Schroeck, Jr.}}</ref> | *{{cite book |last1=Hegerfeldt |first1=G. C. |last2=Wilser |first2=T. S. |year=1992 |title=Classical and Quantum Systems |series= Proceedings of the Second International Wigner Symposium |publisher=World Scientific|url=http://www.theorie.physik.uni-goettingen.de/~hegerf/collaps_gesamt.pdf|pages=104–105|chapter=Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom|editor1=H.D. Doebner|editor2=W. Scherer|editor3=F. Schroeck, Jr.}}</ref> | ||
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== Method == | == Method == | ||
Revision as of 21:52, 17 May 2026
The quantum jump method, also known as the Monte Carlo wave function (MCWF) is a technique in computational physics used for simulating open quantum systems and quantum dissipation. The quantum jump method was developed by Dalibard, Castin and Mølmer at a similar time to the similar method known as Quantum Trajectory Theory developed by Carmichael. 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 this 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.[1]
References
- ↑ 1.0 1.1 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. doi:10.1364/JOSAB.10.000524. Bibcode: 1993JOSAB..10..524M.
- ↑ 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. doi:10.1103/PhysRevLett.68.580. PMID 10045937. Bibcode: 1992PhRvL..68..580D.
- 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. doi:10.1103/PhysRevA.45.4879. PMID 9907570. Bibcode: 1992PhRvA..45.4879D.
- Hegerfeldt, G. C.; Wilser, T. S. (1992). "Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom". Classical and Quantum Systems. Proceedings of the Second International Wigner Symposium. World Scientific. pp. 104–105. http://www.theorie.physik.uni-goettingen.de/~hegerf/collaps_gesamt.pdf.
Further reading
- 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. doi:10.1103/RevModPhys.70.101. Bibcode: 1998RvMP...70..101P.
External links
- mcsolve Quantum jump (Monte Carlo) solver from QuTiP for Python.
- QuantumOptics.jl the quantum optics toolbox in Julia.
- Quantum Optics Toolbox for Matlab
Source attribution: Quantum jump method
