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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 2 — Jul. 20, 1998
  • pp: 60–62
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Quantum structures in nonlinear optics and atomic physics: a background overview

Luigi A. Lugiato and Gian-Luca Oppo  »View Author Affiliations


Optics Express, Vol. 3, Issue 2, pp. 60-62 (1998)
http://dx.doi.org/10.1364/OE.3.000060


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Abstract

A brief overview of quantum effects in spatial structures such as nonlinear optical patterns, chains of trapped ions and atoms in optical lattices is presented. Some of the main results of the contributions to this Focus Issue are also briefly described.

© Optical Society of America

Introduction

Spontaneous formation of spatial structures and patterns is ubiquitous in several branches of science such as, for example, Physics, Chemistry and Biology. Crystals, metals, spotted animal coats, liquid crystals and sand dunes are just few common examples. In nonlinear physics, the combination of nonlinear dynamics with a spatial cross-talk mechanism, e.g. diffusion or diffraction, gives rise to self-organization processes in spatially extended systems. These phenomena, which arise in macroscopic systems, are typically studied on a purely classical basis. This Focus Issue of Optics Express is devoted, however, to two outstanding cases of spatial coherence in which such effects can exhibit relevant quantum aspects.

Quantum Structures in Optical Pattern Formation

This Focus Issue includes four articles on quantum aspects of spatial structures. Santagiustina et al. [5

5. M. Santagiustina, P. Colet, M. SanMiguel, and D. Walgraef, “Growth dynamics of noise-sustained structures in nonlinear optical resonators” Opt. Express 3, 63–70 (1998). http://www.osa.org/oearchive/source/4451.htm [CrossRef] [PubMed]

] show numerical evidence of structures sustained by quantum noise, with an intensity comparable with that of above-threshold patterns. In a series of breathtaking videoclips, they show that in convective instability regions noise-sustained structures can arise in Kerr resonators and optical parametric oscillators in the presence of both diffraction and advection (i.e. pump tilting and walk-off, respectively) [5

5. M. Santagiustina, P. Colet, M. SanMiguel, and D. Walgraef, “Growth dynamics of noise-sustained structures in nonlinear optical resonators” Opt. Express 3, 63–70 (1998). http://www.osa.org/oearchive/source/4451.htm [CrossRef] [PubMed]

]. Marte et al. [6

6. M. Marte, H. Ritsch, K.I. Petsas, A. Gatti, L.A. Lugiato, C. Fabre, and D. Leduc, “Spatial patterns in optical parametric oscillators with spherical mirrors: classical and quantum effects” Opt. Express 3, 71–80 (1998). http://www.osa.org/oearchive/source/4471.htm [CrossRef] [PubMed]

] discuss classical and quantum aspects of spatial patterns in optical parametric oscillators with spherical mirrors. They not only present a colorful videoclip of the formation of a spatial structure above threshold but also determine the dependence of the quantum image below threshold on the width of the input pump, an important feature for future experimental observations [6

6. M. Marte, H. Ritsch, K.I. Petsas, A. Gatti, L.A. Lugiato, C. Fabre, and D. Leduc, “Spatial patterns in optical parametric oscillators with spherical mirrors: classical and quantum effects” Opt. Express 3, 71–80 (1998). http://www.osa.org/oearchive/source/4471.htm [CrossRef] [PubMed]

]. Jost et al. [7

7. B.M. Jost, A.V. Sergienko, A.F. Abouraddy, B.E.A. Saleh, and M.C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera” Opt. Express 3, 81–88 (1998). http://www.osa.org/oearchive/source/4652.htm [CrossRef] [PubMed]

] describe, both theoretically and experimentally, spatial correlations in the quantum process of spontaneous parametric down-conversion. By making use of a single-photon-sensitive intensified charge-coupled-device they simultaneously detect photon-pairs over a broad spatial area to measure quantum spatial correlations [7

7. B.M. Jost, A.V. Sergienko, A.F. Abouraddy, B.E.A. Saleh, and M.C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera” Opt. Express 3, 81–88 (1998). http://www.osa.org/oearchive/source/4652.htm [CrossRef] [PubMed]

]. The information retrieved from the entangled photon measurements can be used to significantly reduce background, detector and quantum noise in optical images.

Quantum Structures in Atomic Physics

In Atomic Physics one can also find fascinating spatial structures. In the late eighties, H. Walther and his group in Garching (Germany) realized microcrystals formed by a small number of ions in a trap and observed via their fluorescent emission. When their kinetic energy is increased, the crystal melts and one observes chaotic motion. They also obtained linear arrangements of ions in storage rings. The groups of H. Walther and of R. Blatt (Innsbruck, Austria) are presently realizing linear configurations of trapped ions tailor–made for applications to quantum computing. In this Focus Issue on Quantum Structures the reader can find an experimental article with fascinating images of an ion chain: Nägerl et al. [8

8. H.C. Nägerl, D. Leibfried, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Coherent excitation of normal modes in a string of Ca+ ions” Opt. Express 3, 89–96 (1998). http://www.osa.org/oearchive/source/4515.htm [CrossRef]

] have prepared crystal structures of up to 15 Calcium ions in a linear Paul trap and observed their normal modes of oscillation via resonant rf-fields. In particular the eigenmodes of the oscillations can be selectively excited in sequence [8

8. H.C. Nägerl, D. Leibfried, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Coherent excitation of normal modes in a string of Ca+ ions” Opt. Express 3, 89–96 (1998). http://www.osa.org/oearchive/source/4515.htm [CrossRef]

]. Experimental observation of the collective motion of the ion string has been done by recording CCD images directly visualized in [8

8. H.C. Nägerl, D. Leibfried, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Coherent excitation of normal modes in a string of Ca+ ions” Opt. Express 3, 89–96 (1998). http://www.osa.org/oearchive/source/4515.htm [CrossRef]

].

Acknowledgments

This work is partially supported by the TMR network QSTRUCT (ERB FMRX-CT96-0077) of the European Union and EPSRC (GR/K70212).

References and links

1.

Special Issue on “Nonlinear Optical Structures, Patterns and Chaos,” edited by L.A. Lugiato, in Chaos, Solitons and Fractals, 4, 1249–1844 (1994).

2.

A. Gatti, H. Wiedemann, L.A. Lugiato, I. Marzoli, G.-L. Oppo, and S.M. Barnett, Phys. Rev. A 56, 877 (1997). [CrossRef]

3.

M.I. Kolobov and I.V. Sokolov, Sov. Phys. JETP 69, 1097 (1989).

4.

A. Gatti and L.A. Lugiato, Phys. Rev. A 52, 1675 (1995). [CrossRef] [PubMed]

5.

M. Santagiustina, P. Colet, M. SanMiguel, and D. Walgraef, “Growth dynamics of noise-sustained structures in nonlinear optical resonators” Opt. Express 3, 63–70 (1998). http://www.osa.org/oearchive/source/4451.htm [CrossRef] [PubMed]

6.

M. Marte, H. Ritsch, K.I. Petsas, A. Gatti, L.A. Lugiato, C. Fabre, and D. Leduc, “Spatial patterns in optical parametric oscillators with spherical mirrors: classical and quantum effects” Opt. Express 3, 71–80 (1998). http://www.osa.org/oearchive/source/4471.htm [CrossRef] [PubMed]

7.

B.M. Jost, A.V. Sergienko, A.F. Abouraddy, B.E.A. Saleh, and M.C. Teich, “Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera” Opt. Express 3, 81–88 (1998). http://www.osa.org/oearchive/source/4652.htm [CrossRef] [PubMed]

8.

H.C. Nägerl, D. Leibfried, F. Schmidt-Kaler, J. Eschner, and R. Blatt, “Coherent excitation of normal modes in a string of Ca+ ions” Opt. Express 3, 89–96 (1998). http://www.osa.org/oearchive/source/4515.htm [CrossRef]

9.

L. Guidoni, C. Trichè, P. Verkerk, and G. Grynberg, Phys. Rev. Lett. 79, 3363 (1997). [CrossRef]

10.

T. Müller-Seydlitz et al., Phys. Rev. Lett. 78, 1038, (1997). [CrossRef]

11.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 764508 (1996). [CrossRef] [PubMed]

12.

S.R. Wilkinson, C.F. Bharucha, K.W. Madison, Q. Niu, and M.G. Raizen, Phys. Rev. Lett. 76, 4512 (1996). [CrossRef] [PubMed]

13.

S. Friebel, J. Waltz, M. Weitz, and T.W. Hänsen, Phys. Rev. A 57, R20 (1998). [CrossRef]

14.

S. Friebel, PhD thesis, Ludwig-Maximilian Universität Munich (1998).

15.

S. Schlipf, H. Katori, L. Perotti, and H. Walther, “Diffusion of a Single-Ion in a One-Dimensional Optical Lattice” Opt. Express 3, 97–103 (1998). http://www.osa.org/oearchive/source/5557.htm [CrossRef] [PubMed]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(190.0190) Nonlinear optics : Nonlinear optics
(270.0270) Quantum optics : Quantum optics

ToC Category:
Focus Issue: Quantum structures in nonlinear optics and atomic physics

History
Original Manuscript: July 16, 1998
Published: July 20, 1998

Citation
Luigi Lugiato and Gian-Luca Oppo, "Quantum structures in nonlinear optics and atomic physics: a background overview," Opt. Express 3, 60-62 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-2-60


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References

  1. Special Issue on "Nonlinear Optical Structures, Patterns and Chaos," edited by L.A. Lugiato,in Chaos, Solitons and Fractals, 4, 1249-1844 (1994).
  2. A. Gatti, H. Wiedemann, L.A. Lugiato, I. Marzoli, G.-L. Oppo, and S.M. Barnett, Phys. Rev. A 56, 877 (1997). [CrossRef]
  3. M.I. Kolobov and I.V. Sokolov, Sov. Phys. JETP 69, 1097 (1989).
  4. A. Gatti and L.A. Lugiato, Phys. Rev. A 52, 1675 (1995). [CrossRef] [PubMed]
  5. M. Santagiustina, P. Colet, M. SanMiguel, and D. Walgraef, "Growth dynamics of noise-sustained structures in nonlinear optical resonators" Opt. Express 3, 63-70 (1998). http://www.osa.org/oearchive/source/4451.htm [CrossRef] [PubMed]
  6. M. Marte, H. Ritsch, K.I. Petsas, A. Gatti, L.A. Lugiato, C. Fabre and D. Leduc, "Spatial patterns in optical parametric oscillators with spherical mirrors: classical and quantum effects" Opt. Express 3, 71-80 (1998). http://www.osa.org/oearchive/source/4471.htm [CrossRef] [PubMed]
  7. B.M. Jost, A.V. Sergienko, A.F. Abouraddy, B.E.A. Saleh, and M.C. Teich, "Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera" Opt. Express 3, 81-88 (1998). http://www.osa.org/oearchive/source/4652.htm [CrossRef] [PubMed]
  8. H.C. Nagerl, D. Leibfried, F. Schmidt-Kaler, J. Eschner, and R. Blatt, "Coherent excitation of normal modes in a string of Ca+ ions" Opt. Express 3, 89-96 (1998). http://www.osa.org/oearchive/source/4515.htm [CrossRef]
  9. L. Guidoni, C. Trich‚, P. Verkerk, and G. Grynberg, Phys. Rev. Lett. 79, 3363 (1997). [CrossRef]
  10. T. Muller-Seydlitz et al., Phys. Rev. Lett. 78, 1038, (1997). [CrossRef]
  11. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76 4508 (1996). [CrossRef] [PubMed]
  12. S.R. Wilkinson, C.F. Bharucha, K.W. Madison, Q. Niu, and M.G. Raizen, Phys. Rev. Lett. 76, 4512 (1996). [CrossRef] [PubMed]
  13. S. Friebel, J. Waltz, M. Weitz, and T.W. Hansch, Phys. Rev. A 57, R20 (1998). [CrossRef]
  14. S. Friebel, PhD thesis, Ludwig-Maximilian Universitat Munich (1998).
  15. S. Schlipf, H. Katori, L. Perotti, and H. Walther, "Diffusion of a single-ion in a one-dimensional optical lattice" Opt. Express 3, 97-103 (1998). http://www.osa.org/oearchive/source/5557.htm [CrossRef] [PubMed]

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