Abstract

We theoretically study evolution of quantum noise of ultrashort pulsed light that propagates a semiconductor waveguide where nonlinear optical interaction occurs. Optical quantum noise is simulated by statistical (pseudo-)random distribution of phasors in a phase space with Gaussian probability weight, and each phasor evolution is governed by beam propagation method. It is shown that Kerr effects squeeze quantum noise of coherent light in a phase space such that photon-number noise is unchanged while phase noise increasing with uncertainty area invariant. However, two-photon absorption alters the photon-number statistics of light unlike Kerr effects.

© 2008 Optical Society of America

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  1. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
    [CrossRef] [PubMed]
  2. W. Hai, X. Changde, P. Qing, X. Chenyang, Z. Yun, and P. Kunchi, "Optical measurement of weak absorption beyond shot-noise limit," Laser Spectroscopy XIII Proc. 13th Int. Conf. on Laser Spectroscopy, Hangzhou, (1997).
  3. E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
    [CrossRef]
  4. M. Hillery, "Quantum cryptography with squeezed states," Phys. Rev. A 61, 022309-022316 (2000).
    [CrossRef]
  5. H.- A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).
  6. H. -A. Bachor, "Quantum noise, quantum measurement, and squeezing," J. Opt. B: Quantum Semiclassical Opt. 6, S626-S633 (2004).
    [CrossRef]
  7. M. B. Ward, G. M. Schucan, K. Turner, T. GoodsonIII, K. J. Donovan, J. S. Aitchison, C. N. Ironside, A. M. Fox and J. F. Ryan, "Photon-number squeezed light generation by multi-photon absorption," CLEO/QELS Technical Digest QWE4, (1999).
  8. R. G. Ispasoiu and T. GoodsonIII, "Photon-number squeezing by two-photon absorption in an organic polymer," Opt. Commun. 178, 371-376 (2000).
    [CrossRef]
  9. H. Cao, W. S. Warren, A. Dogariu, and L. J. Wang, "Reduction of optical intensity noise by means of two-photon absorption," J. Opt. Soc. Am. B 20, 560-563 (2003).
    [CrossRef]
  10. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
    [CrossRef] [PubMed]
  11. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
    [CrossRef]
  12. L. Giles and P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A 48, 1582-1593 (1993).
    [CrossRef]

2004 (1)

H. -A. Bachor, "Quantum noise, quantum measurement, and squeezing," J. Opt. B: Quantum Semiclassical Opt. 6, S626-S633 (2004).
[CrossRef]

2003 (1)

2000 (2)

M. Hillery, "Quantum cryptography with squeezed states," Phys. Rev. A 61, 022309-022316 (2000).
[CrossRef]

R. G. Ispasoiu and T. GoodsonIII, "Photon-number squeezing by two-photon absorption in an organic polymer," Opt. Commun. 178, 371-376 (2000).
[CrossRef]

1993 (1)

L. Giles and P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A 48, 1582-1593 (1993).
[CrossRef]

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
[CrossRef]

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Bachor, H. -A.

H. -A. Bachor, "Quantum noise, quantum measurement, and squeezing," J. Opt. B: Quantum Semiclassical Opt. 6, S626-S633 (2004).
[CrossRef]

Cao, H.

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
[CrossRef]

Dogariu, A.

Giles, L.

L. Giles and P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A 48, 1582-1593 (1993).
[CrossRef]

Goodson, T.

R. G. Ispasoiu and T. GoodsonIII, "Photon-number squeezing by two-photon absorption in an organic polymer," Opt. Commun. 178, 371-376 (2000).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Hillery, M.

M. Hillery, "Quantum cryptography with squeezed states," Phys. Rev. A 61, 022309-022316 (2000).
[CrossRef]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

Ispasoiu, R. G.

R. G. Ispasoiu and T. GoodsonIII, "Photon-number squeezing by two-photon absorption in an organic polymer," Opt. Commun. 178, 371-376 (2000).
[CrossRef]

Kimble, H. J.

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
[CrossRef]

Knight, P. L.

L. Giles and P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A 48, 1582-1593 (1993).
[CrossRef]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Polzik, E. S.

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

Van Styland, E. W.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Wang, L. J.

Warren, W. S.

Yurke, B.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

Appl. Phys. B (1)

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacumm-state limit," Appl. Phys. B B55, 279-290 (1992).
[CrossRef]

IEEE J. Quantum. Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum. Electron. 27, 1296-1309 (1991).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

H. -A. Bachor, "Quantum noise, quantum measurement, and squeezing," J. Opt. B: Quantum Semiclassical Opt. 6, S626-S633 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

R. G. Ispasoiu and T. GoodsonIII, "Photon-number squeezing by two-photon absorption in an organic polymer," Opt. Commun. 178, 371-376 (2000).
[CrossRef]

Phys. Rev. A (2)

M. Hillery, "Quantum cryptography with squeezed states," Phys. Rev. A 61, 022309-022316 (2000).
[CrossRef]

L. Giles and P. L. Knight, "Two-photon absorption and nonclassical states of light," Phys. Rev. A 48, 1582-1593 (1993).
[CrossRef]

Phys. Rev. Lett. (2)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985).
[CrossRef] [PubMed]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Styland. "Dispersion and Band-gap scaling of the electronic Kerr effect in solids assoicated with two-photon absorption," Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Other (3)

M. B. Ward, G. M. Schucan, K. Turner, T. GoodsonIII, K. J. Donovan, J. S. Aitchison, C. N. Ironside, A. M. Fox and J. F. Ryan, "Photon-number squeezed light generation by multi-photon absorption," CLEO/QELS Technical Digest QWE4, (1999).

W. Hai, X. Changde, P. Qing, X. Chenyang, Z. Yun, and P. Kunchi, "Optical measurement of weak absorption beyond shot-noise limit," Laser Spectroscopy XIII Proc. 13th Int. Conf. on Laser Spectroscopy, Hangzhou, (1997).

H.- A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

Quantum noise evolution in a complex phase space

Fig. 2.
Fig. 2.

Quantum noise distribution (blue dots) of an envelop A(L,tc ) with respect to the reference distribution (red dots) for a 1.32 pJ pulse energy (A) and 13.2 pJ pulse energy (B). F≃1.00 for (A) and (B). The uncertainty area ratio (R) between blue and red is R ≃1.00 for (A) and R≃1.01 for (B). Phase uncertainty ratio (ΔΦ)2/(ΔΦ c )2=1.00 for (A) and (ΔΦ)2/(ΔΦ c )2=1.19 for (B).

Fig. 3.
Fig. 3.

Quantum noise distribution (blue dots) of an envelop A(L,tc ) with respect to the reference distribution (red dots) for a 39.5 pJ pulse energy (A) and 52.6 pJ pulse energy (B). F≃1.02 for (A) and F≃0.99 for (B). The uncertainty area ratio (R) between blue and red is R≃0.99 for (A) and R=1.00 for (B). Phase uncertainty ratio (ΔΦ)2/(ΔΦ c )2=2.55 for (A) and (ΔΦ)2/(ΔΦ c )2=3.54 for (B).

Fig. 4.
Fig. 4.

(A) Quantum noise distribution of an envelop A(L,tc ) for a 65.8 pJ pulse energy. F≃1.01, the uncertainty area ratio (R) between blue and red is R≃0.99, and Phase uncertainty ratio (ΔΦ)2/(ΔΦ c )2=5.11. (B) Optical power transmittance under TPA as well as Kerr effects.

Equations (2)

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A ( z , t ) z = i γ A ( z , t ) 2 A ( z , t ) ,
n ( I ) = n 0 + n 2 I .

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