Quantum Trajectory Theory

Quantum Trajectory Theory (QTT) is a formulation of quantum mechanics used for simulating open quantum systems, quantum dissipation and single quantum systems.^[1] It was developed by Howard Carmichael in the early 1990s around the same time as the similar formulation, known as the quantum jump method or Monte Carlo wave function (MCWF) method, developed by Dalibard, Castin and Mølmer.^[2] 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.^[3]

QTT is compatible with the standard formulation of quantum theory, as described by the Schrödinger equation, but it offers a more detailed view.^[4]^[1] The Schrödinger equation can be used to compute the probability of finding a quantum system in each of its possible states should a measurement be made. This approach is fundamentally statistical and is useful for predicting average measurements of large ensembles of quantum objects but it does not describe or provide insight into the behaviour of individual particles. QTT fills this gap by offering a way to describe the trajectories of individual quantum particles that obey the probabilities computed from the Schrödinger equation.^[4]^[5] Like the quantum jump method, QTT applies to open quantum systems that interact with their environment.^[1] QTT has become particularly popular since the technology has been developed to efficiently control and monitor individual quantum systems as it can predict how individual quantum objects such as particles will behave when they are observed.^[4]

^ ^a ^b ^c Ball, Phillip (28 March 2020). "Reality in the making". New Scientist: 35–38.
^ 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. S2CID 85457742.
^
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.
^ ^a ^b ^c Ball, Philip. "The Quantum Theory That Peels Away the Mystery of Measurement". Quanta Magazine. Retrieved 2020-08-14.
^ "Collaborating with the world's best to answer century-old mystery in quantum theory" (PDF). 2019 Dodd-Walls Centre Annual Report: 20–21. Archived from the original (PDF) on 2021-01-26. Retrieved 2020-09-09.

[:73-1] Ball, Phillip (28 March 2020). "Reality in the making". New Scientist: 35–38.

[MCD1993-2] 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. S2CID 85457742.

[PrimaryPapers-3] 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.

[4] 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.

[5] Carmichael, Howard (1993). An Open Systems Approach to Quantum Optics. Springer-Verlag. ISBN 978-0-387-56634-4.

[6] 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.

[7] 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.

[:3-4] Ball, Philip. "The Quantum Theory That Peels Away the Mystery of Measurement". Quanta Magazine. Retrieved 2020-08-14.

[:8-5] "Collaborating with the world's best to answer century-old mystery in quantum theory" (PDF). 2019 Dodd-Walls Centre Annual Report: 20–21. Archived from the original (PDF) on 2021-01-26. Retrieved 2020-09-09.

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