## Posterior quantum dynamics for a continuous diffusion observation of a coherent channel |

JOSA B, Vol. 29, Issue 11, pp. 3072-3077 (2012)

http://dx.doi.org/10.1364/JOSAB.29.003072

Enhanced HTML Acrobat PDF (251 KB)

### Abstract

We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time development of a squeezed coherent state is studied and compared with the previous results obtained for the measuring apparatus prepared initially in the vacuum state.

© 2012 Optical Society of America

**OCIS Codes**

(000.5490) General : Probability theory, stochastic processes, and statistics

(270.0270) Quantum optics : Quantum optics

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(270.5290) Quantum optics : Photon statistics

(270.6570) Quantum optics : Squeezed states

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 17, 2012

Revised Manuscript: September 20, 2012

Manuscript Accepted: September 20, 2012

Published: October 18, 2012

**Citation**

Anita Dąbrowska and Przemysław Staszewski, "Posterior quantum dynamics for a continuous diffusion observation of a coherent channel," J. Opt. Soc. Am. B **29**, 3072-3077 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-11-3072

Sort: Year | Journal | Reset

### References

- R. L. Hudson and K. R. Parthasarathy, “Quantum Ito’s formula and stochastic evolutions,” Commun. Math. Phys. 93, 301–323 (1984). [CrossRef]
- K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992).
- V. P. Belavkin, “A posterior Schrödinger equation for continuous nondemolition measurement,” J. Math. Phys. 31, 2930–2934 (1990). [CrossRef]
- A. Barchielli and V. Belavkin, “Measurement continuous in time and a posteriori states in quantum mechanics,” J. Phys. A: Math. Gen. 24, 1495–1514 (1991). [CrossRef]
- V. P. Belavkin, “Measurement, filtering and control in quantum open dynamical systems,” Rep. Math. Phys. 43, A405–A425 (1999). [CrossRef]
- V. P. Belavkin, “Quantum causality, decoherence, trajectories and information,” Rep. Prog. Phys. 65, 353–420 (2002). [CrossRef]
- A. Barchielli and A. M. Paganoni, “Detection theory in quantum optics: stochastic representation,” Quantum Opt. 8, 133–156 (1996). [CrossRef]
- J. E. Gough and C. Köstler, “Quantum filtering in coherent states,” Commun. Stoch. Anal. 4, 505–521 (2010).
- A. Da¸browska and P. Staszewski, “Filtering equation for measurement of a coherent channel,” J. Opt. Soc. Am. B 28, 1238–1244 (2011). [CrossRef]
- Ch. Gerry and P. Knight, Introductory Quantum Optics(Cambridge University, 2005).
- A. Da¸browska and P. Staszewski, “Squeezed coherent state undergoing a continuous nondemolition observation,” Phys. Lett. A 375, 3950–3955 (2011). [CrossRef]
- H. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, 1993).
- A. C. Doherty and H. Mabuchi, “Atoms in microcavities: quantum electrodynamics, quantum statistical mechanics, and quantum information science,” in Optical Microcavities, K. Vahala, ed. (World Scientific Press, 2004), pp. 367–414.
- H. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University, 2010).
- T. Brun, “A single model of quantum trajectories,” Am. J. Phys. 70, 719–737 (2002). [CrossRef]
- R. van Handel, J. K. Stockton, and H. Mabuchi, “Modelling and feedback control design for quantum state preparation,” J. Opt. B: Quantum Semiclass. Opt. 7, S179–S197 (2005). [CrossRef]
- K. Jacobs and D. Steck, “A straightforward introduction to continuous quantum measurement,” Contemp. Phys. 47, 279–303 (2006). [CrossRef]
- L. Bouten, R. van Handel, and M. James, “An introduction to quantum filtering,” SIAM J. Control Optim. 46, 2199–2241 (2007). [CrossRef]
- A. Barchielli, “Continual measurements in quantum mechanics and quantum stochastic calculus,” in Open Quantum Systems III. Recent Developments, S. Attal, A. Joye, and C.-A. Pillet, eds. (Springer, 2006), pp. 207–288.
- V. P. Belavkin and M. Guţă, eds. Quantum Stochastics and Information (World Scientific, 2006).
- A. Barchielli and M. Gregoratti, Quantum Trajectories and Measurement in Continuous Time: The Diffusive Case(Springer-Verlag, 2009).
- C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, 2010).
- H. Mabuchi, J. Ye, and H. J. Kimble, “Full observation of single-atom dynamics in cavity QED,” Appl. Phys. B 68, 1095–1108 (1999). [CrossRef]
- M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Adaptive homodyne measurement of optical phase,” Phys. Rev. Lett. 89, 133602 (2002). [CrossRef]
- J. M. Geremia, J. K. Stockton, A. C. Doherty, and H. Mabuchi, “Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry,” Phys. Rev. Lett. 91, 250801 (2003). [CrossRef]
- J. M. Geremia, J. K. Stockton, and H. Mabuchi, “Tensor polarizability and dispersive quantum measurement of multilevel atoms,” Phys. Rev. A 73, 042112 (2006). [CrossRef]
- P. Goetsch and R. Graham, “Linear stochastic wave equation for continuously measured quantum system,” Phys. Rev. A 50, 5242–5255 (1994). [CrossRef]
- M. J. Collet and C. W. Gardiner, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985). [CrossRef]
- A. Barchielli, “Direct and heterodyne detection and other applications of quantum stochastic calculus to quantum optics,” Quantum Opt. 2, 423–441 (1990). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.