## Decoherence of highly mixed macroscopic quantum superpositions

JOSA B, Vol. 25, Issue 6, pp. 1025-1030 (2008)

http://dx.doi.org/10.1364/JOSAB.25.001025

Enhanced HTML Acrobat PDF (145 KB)

### Abstract

It is known that a macroscopic quantum superposition (MQS), when it is exposed to an environment, decoheres at a rate scaling with the separation of its component states in phase space. This is more or less consistent with the well-known proposition that a more macroscopic quantum state is reduced more quickly to a classical state in general. Effects of initial mixedness, however, on the subsequent decoherence of MQSs have been less known. We study the evolution of a highly mixed MQS interacting with an environment and compare it with that of a pure MQS having the same size as the central distance between its component states. Although the decoherence develops more rapidly for the mixed MQS in short times, its rate can be significantly suppressed after a certain time and becomes smaller than the decoherence rate of its corresponding pure MQS. In an optics experiment to generate a MQS, our result has the practical implication that nonclassicality of a MQS can still be observable in moderate times, even though a large amount of noise is added to the initial state.

© 2008 Optical Society of America

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

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

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 5, 2008

Revised Manuscript: March 30, 2008

Manuscript Accepted: April 16, 2008

Published: May 23, 2008

**Citation**

Hyunseok Jeong, Jinhyoung Lee, and Hyunchul Nha, "Decoherence of highly mixed macroscopic quantum superpositions," J. Opt. Soc. Am. B **25**, 1025-1030 (2008)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-6-1025

Sort: Year | Journal | Reset

### References

- E. Schrödinger, “Die gegenwartige Situation in der Quantenmechanik,” Naturwiss. 23, 807-812, 823-828, 844-849 (1935). [CrossRef]
- M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, and A. Zeilinger, “Wave-particle duality of C60 molecules,” Nature 401, 680-682 (1999). [CrossRef]
- J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565-582 (2001). [CrossRef]
- A. J. Leggett, “Testing the limits of quantum mechanics: motivation, state of play, prospects,” J. Phys.: Condens. Matter 14, R415-R451 (2002). [CrossRef]
- A. J. Leggett, “The quantum measurement problem,” Science 307, 871-872 (2005). [CrossRef] [PubMed]
- J. I. Korsbakken, K. B. Whaley, J. Dubois, and J. I. Cirac, “Measurement-based measure of the size of macroscopic quantum superpositions,” Phys. Rev. A 75, 042106 (2007). [CrossRef]
- W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715-775 (2003), and references therein. [CrossRef]
- M. Brune, E. Hagley, J. Dreyer, X. Matre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, “Observing the progressive decoherence of the 'meter' in a quantum measurement,” Phys. Rev. Lett. 77, 4887-4890 (1996). [CrossRef] [PubMed]
- B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13-16 (1986). [CrossRef] [PubMed]
- W. Schleich, M. Pernigo, and F. L. Kien, “Nonclassical state from two pseudoclassical states,” Phys. Rev. A 44, 2172-2187 (1991). [CrossRef] [PubMed]
- G. W. Gardiner and P. Zoller, Quantum Noise, 3rd ed. (Springer-Verlag, 2004).
- M. S. Kim and V. Bužek, “Schrodinger-cat states at finite temperature: influence of a finite-temperature heat bath on quantum interferences,” Phys. Rev. A 46, 4239-4251 (1992). [CrossRef] [PubMed]
- H. J. Carmichael, “Quantum future,” in Proceedings of the Xth Max Born Symposium, Poland, Ph.Blanchard and A.Jadczyk, eds. (Springer, 1999), pp. 15-36.
- H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000). [CrossRef]
- H. Jeong and T. C. Ralph, “Transfer of nonclassical properties from a microscopic superposition to macroscopic thermal states in the high temperature limit,” Phys. Rev. Lett. 97, 100401 (2006). [CrossRef] [PubMed]
- E. Schrödinger, “The constant crossover of micro- to macro-mechanics,” Naturwiss. 14, 664-666 (1926). [CrossRef]
- A more general form of such a superposition state is ∣α⟩+eiφ∣−α⟩, where the normalization factor is omitted and φ is arbitrary, while we choose φ=π for convenience. However, all the conclusions in this paper remain the same regardless of the choice of φ.
- A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical 'Schrodinger cats' from photon number states,” Nature 448, 784-786 (2007). [CrossRef] [PubMed]
- E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932). [CrossRef]
- D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
- M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121-167 (1984). [CrossRef]
- S. J. D. Phoenix, “Wave-packet evolution in the damped oscillator,” Phys. Rev. A 41, 5132-5138 (1990). [CrossRef] [PubMed]
- S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford U. Press, 1997).
- M. Paternostro, H. Jeong, and M. S. Kim, “Entanglement of mixed macroscopic superpositions: an entangling-power study,” Phys. Rev. A 73, 012338 (2006). [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.