An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped Rabi oscillations. 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.Animation of the Monte Carlo prediction (blue) for the population of a coherently-driven, damped two-level system as more trajectories are added to the ensemble average, compared to the master equation prediction (red).
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]
Referencesedit
^ abMølmer, 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.
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. ISBN978-0-387-56634-4.
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.
Further readingedit
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. S2CID 14721909.
quantum, jump, method, quantum, jump, method, also, known, monte, carlo, wave, function, mcwf, technique, computational, physics, used, simulating, open, quantum, systems, quantum, dissipation, quantum, jump, method, developed, dalibard, castin, mølmer, simila. 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 Molmer 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 Contents 1 Method 2 References 3 Further reading 4 External linksMethod edit nbsp An example of the quantum jump method being used to approximate the density matrix of a two level atom undergoing damped Rabi oscillations 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 nbsp Animation of the Monte Carlo prediction blue for the population of a coherently driven damped two level system as more trajectories are added to the ensemble average compared to the master equation prediction red 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 edit a b Molmer 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 Molmer 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 Further reading editA 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 S2CID 14721909 External links editmcsolve Quantum jump Monte Carlo solver from QuTiP for Python QuantumOptics jl the quantum optics toolbox in Julia Quantum Optics Toolbox for Matlab nbsp This quantum mechanics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Quantum jump method amp oldid 1113911608, wikipedia, wiki, book, books, library,
