Quantum jump method explained

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]

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.^[2]

Further reading

• A recent review is Plenio. M. B.. Knight, P. L. . The quantum-jump approach to dissipative dynamics in quantum optics. Reviews of Modern Physics. 1 January 1998. 70. 1. 101–144. 10.1103/RevModPhys.70.101. 1998RvMP...70..101P. quant-ph/9702007 . 14721909 .

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

Notes and References

1. The associated primary sources are, respectively:
   • Dalibard. Jean. Castin, Yvan . Mølmer, Klaus . Wave-function approach to dissipative processes in quantum optics. Physical Review Letters. February 1992. 68. 5. 580–583. 10.1103/PhysRevLett.68.580. 10045937. 1992PhRvL..68..580D . 0805.4002.
   • Book: Carmichael, Howard . An Open Systems Approach to Quantum Optics . 1993 . Springer-Verlag . 978-0-387-56634-4.
   • Dum. R.. Zoller, P. . Ritsch, H. . Monte Carlo simulation of the atomic master equation for spontaneous emission. Physical Review A. 1992. 45. 7. 4879–4887. 10.1103/PhysRevA.45.4879. 9907570. 1992PhRvA..45.4879D .
   • Book: Hegerfeldt . G. C. . Wilser . T. S. . 1992 . Classical and Quantum Systems . Proceedings of the Second International Wigner Symposium . World Scientific. 104–105. Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom. H.D. Doebner. W. Scherer. F. Schroeck, Jr..
2. Mølmer . K. . Castin . Y. . Dalibard . J. . 10.1364/JOSAB.10.000524 . Monte Carlo wave-function method in quantum optics . Journal of the Optical Society of America B . 10 . 3 . 524 . 1993 . 1993JOSAB..10..524M .