## Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser

Optics Express, Vol. 17, Issue 15, pp. 13059-13069 (2009)

http://dx.doi.org/10.1364/OE.17.013059

Acrobat PDF (1790 KB)

### Abstract

Coherence properties of the photon pair generated via spontaneous parametric down-conversion pumped by a multi-mode cw diode laser are studied with a Mach-Zehnder interferometer. Each photon of the pair enters a different input port of the interferometer and the biphoton coherence properties are studied with a two-photon detector placed at one output port. When the photon pair simultaneously enters the interferometer, periodic recurrence of the biphoton de Broglie wave packet is observed, closely resembling the coherence properties of the pump diode laser. With non-zero delays between the photons at the input ports, biphoton interference exhibits the same periodic recurrence but the wave packet shapes are shown to be dependent on both the input delay as well as the interferometer delay. These properties could be useful for building engineered entangled photon sources based on diode laser-pumped spontaneous parametric down-conversion.

© 2009 Optical Society of America

## 1. Introduction

1. J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum
revolution,” Phil. Trans. R. Soc. Lond. A **361**, 1655–1674
(2003). [CrossRef]

2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum
cryptography,” Rev. Mod. Phys. **74**, 145–195
(2002). [CrossRef]

3. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with
photonic qubits,” Rev. Mod. Phys. **79**, 135–174
(2007). [CrossRef]

*χ*

^{(2)}nonlinear interactions, offers the most versatile and efficient method of generating entangled two-photon states. For example, entanglement in a variety of degrees of freedom (polarization, position-momentum, phase-momentum, energy-time, etc.) has been demonstrated with SPDC photons [4

4. Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm
Experiment Using Pairs of Light Quants Produced by Optical Parametric Down
Conversion,” Phys. Rev. Lett. **61**, 2921–2924
(1988). [CrossRef] [PubMed]

5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of
Polarization-Entangled Photon Pairs,” Phys. Rev.
Lett. **75**, 4337–4341
(1995). [CrossRef] [PubMed]

6. Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and
universal Bell-state synthesizer,” Phys. Rev.
A **67**, 010301(R) (2003). [CrossRef]

7. J. G. Rarity and P. R. Tapster, “Experimental Violation of Bell’s
Inequality Based on Phase and Momentum,” Phys.
Rev. Lett. **64**, 2495–2498
(1990). [CrossRef] [PubMed]

8. D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time
entanglement,” Phys. Rev. A **54**, R1–R4 (1996).
[CrossRef] [PubMed]

*χ*

^{(2)}medium, and the pumping conditions [9

9. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Elimanating frequency and space-tie
corelations in multiphoton states,” Phys. Rev.
A **64**, 063815 (2001). [CrossRef]

10. Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled
two-photon state via temporal and spectral engineering,”
J. Mod. Opt. **49**, 2309–2323
(2002). [CrossRef]

11. A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled
Photons,” Phys. Rev. Lett. **99**, 243601 (2007). [CrossRef]

12. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded Generation of Ultrafast Single
Photons in Pure Quantum States,” Phys. Rev.
Lett. **100**, 133601 (2008). [CrossRef] [PubMed]

*χ*

^{(2)}medium choices include bulk nonlinear crystals, wave-guide type crystals, periodically-poled crystals, and a nonlinear crystal in a cavity. Finally, the SPDC process may be pumped with a continuous wave (cw) laser or a (ultrafast) pulsed laser.

4. Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm
Experiment Using Pairs of Light Quants Produced by Optical Parametric Down
Conversion,” Phys. Rev. Lett. **61**, 2921–2924
(1988). [CrossRef] [PubMed]

5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of
Polarization-Entangled Photon Pairs,” Phys. Rev.
Lett. **75**, 4337–4341
(1995). [CrossRef] [PubMed]

6. Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and
universal Bell-state synthesizer,” Phys. Rev.
A **67**, 010301(R) (2003). [CrossRef]

13. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled
photons,” Phys. Rev. A **60**, R773–R776
(1999). [CrossRef]

14. Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using
femtosecond-pulse-pumped spontaneous parametric
down-conversion,” Phys. Rev. A **63**, 062301 (2001). [CrossRef]

15. Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of
the two-photon state generated via type II spontaneous parametric
downconversion,” Opt. Lett. **30**, 908–910
(2005). [CrossRef] [PubMed]

16. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P Kulik, “Biphoton interference with a multimode
pump,” Phys. Rev. A **63**, 053801 (2001). [CrossRef]

16. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P Kulik, “Biphoton interference with a multimode
pump,” Phys. Rev. A **63**, 053801 (2001). [CrossRef]

## 2. Coherence properties of the multimode diode laser

*a*and monitor the output mode

*f*as a function of

*x*

_{2}. Note that the input mode

*b*is not used in this measurement.

*x*

_{2}=0, a well-known interference pattern is observed in the single-photon detector placed in the output mode

*f*. (We attenuated the laser beam with neutral density filters so that we can utilize single-photon detectors.) The envelope of the interference pattern around

*x*

_{2}=0 provides the spectral bandwidth of the laser. Given that the full width at half maximum (FWHM) value of the central wave packet is 216

*µ*m, we estimate that the pump laser has the FWHM spectral bandwidth of 0.67 nm [17

17. The Wiener-Khinchine theorem states that the
spectral power density of an optical field is related to its autocorrelation. They
are, in fact, a Fourier transform pair. It is not difficult to show that the
following relation holds,
Δλ_{FWHM}=(4ln2/π)λ^{2}_{center}/*L*_{FWHM}. Here Δλ_{FWHM} is the FWHM bandwidth of the
field, λ_{center} is the central wavelength of the laser (405 nm),
and *L*_{FWHM} is the FWHM width of the autocorrelation (interferogram) in Fig. 2.

19. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of
the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays
Greater than the Coherence Time,” Jpn. J. Appl.
Phys. **46**, 7720–7723
(2007). [CrossRef]

*L*=5668

_{p}*µ*m, the mode spacing is calculated to be Δ

*λ*=

*λ*

^{2}

_{0}/

*L*=0.0282 nm [19

_{p}19. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of
the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays
Greater than the Coherence Time,” Jpn. J. Appl.
Phys. **46**, 7720–7723
(2007). [CrossRef]

*ρ*which is given as

_{p}*𝓢*(

*ω*) is the spectral power density and should be described as a discrete sum of all the frequency modes weighted by the spectral profile. Thus, the spectral power density function is written as

_{p}*ω*

_{p0}is the central frequency of the pump, Δ

*ω*is the mode spacing, and

_{p}*n*is the mode number. We assume that the spectral profile is Gaussian,

*δω*is the pump bandwidth.

_{p}*a*, |

*ω*〉=

_{p}*a*

^{†}(

*ω*)|0〉 where

_{p}*a*

^{†}(

*ω*) is the creation operator for a photon of frequency

_{p}*ω*in mode

_{p}*a*. The normalized detection probability for the single-photon detector placed at the output mode

*f*is given as

*E*

^{(+)}

*(*

_{f}*t*)=(

*iE*

^{(+)}

*(*

_{a}*t*−

*τ*

_{2})+

*iE*

^{(+)}

*(*

_{a}*t*)+

*E*

^{(+)}

*b*(

*t*−

*τ*

_{2})−

*E*(+)

*b*(

*t*))/2 with

*τ*

_{2}=

*x*

_{2}/

*c, E*

^{(+)}

*a*

^{(t)}=∫

*dω a*(

*ω*)

*e*, and

^{−iωt}*E*

^{(+)}

*(*

_{b}*t*)=∫

*dω*

*b*(

*ω*)

*e*

*. Here*

^{−iωt}*a*(

*ω*) and

*b*(

*ω*) are the annihilation operators for a photon of frequency

*ω*in modes

*a*and

*b*, respectively.

*𝓒*(

_{p}*τ*

_{2}) is the coherence function of the multi-mode cw pump laser,

## 3. Hong-Ou-Mandel interference with multimode-pumped SPDC

*a*in the axial direction (

*x*

_{1}). The fiber polarization controllers (FPC) are used to ensure that the polarization states of the photons are identical at the input ports of the interferometer.

20. Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon
states,” Phys. Rev. Lett. **91**, 163602 (2003). [CrossRef] [PubMed]

21. M. A. Sagioro, C. Olindo, C. H. Monken, and S. Pádua, “Time control of two-photon
interference,” Phys. Rev. A **69**, 053817 (2004). [CrossRef]

22. A. Zavatta, S. Viciani, and M. Bellini, “Recurrent fourth-order interference dips and
peaks with a comblike two-photon entangled state,”
Phys. Rev. A **70**, 023806 (2004). [CrossRef]

*c*and

*d*), and the coincidence counting rate between the two detectors is recorded as a function of the relative input delay

*x*

_{1}. The experimental data are shown in Fig. 4 and it is clear the Hong-Ou-Mandel dip is observed only when the photons arrive the beam splitter BS1 simultaneously [23

23. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals
between two photons by interference,” Phys. Rev.
Lett. **59**, 2044–2046
(1987). [CrossRef] [PubMed]

20. Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon
states,” Phys. Rev. Lett. **91**, 163602 (2003). [CrossRef] [PubMed]

21. M. A. Sagioro, C. Olindo, C. H. Monken, and S. Pádua, “Time control of two-photon
interference,” Phys. Rev. A **69**, 053817 (2004). [CrossRef]

22. A. Zavatta, S. Viciani, and M. Bellini, “Recurrent fourth-order interference dips and
peaks with a comblike two-photon entangled state,”
Phys. Rev. A **70**, 023806 (2004). [CrossRef]

## 4. Photonic de Broglie wave interference with multimode-pumped SPDC

24. J. Jacobson, G. Bjork, I. Chuang, and Y. Yamamoto, “Photonic de Broglie
waves,” Phys. Rev. Lett. **74**, 4835–4838
(1995). [CrossRef] [PubMed]

25. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the Photonic de
BroglieWavelength of Entangled Photon Pairs Generated by Spontaneous Parametric
Down-Conversion,” Phys. Rev. Lett. **89**, 213601 (2002). [CrossRef] [PubMed]

*a*and

*b*, of the interferometer and the relative input time delay

*t*

_{1}=

*x*

_{1}/

*c*is adjusted by axially moving one output collimator of the single-mode fiber. A two-photon detector, consisting of a 50:50 beam splitter, two single-photon detectors, and a coincidence circuit with a 3 ns coincidence window, is placed at the output mode

*e*of the interferometer, as shown in Fig. 1. The output of the two-photon detector (i.e., the coincidence count rate) is recorded as functions of

*x*

_{1}and

*x*

_{2}. Note that, for observing the photonic de Broglie wave interference, it is necessary to put a two-photon detector at one output port of the interferometer [25

25. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the Photonic de
BroglieWavelength of Entangled Photon Pairs Generated by Spontaneous Parametric
Down-Conversion,” Phys. Rev. Lett. **89**, 213601 (2002). [CrossRef] [PubMed]

25. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the Photonic de
BroglieWavelength of Entangled Photon Pairs Generated by Spontaneous Parametric
Down-Conversion,” Phys. Rev. Lett. **89**, 213601 (2002). [CrossRef] [PubMed]

26. J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder
interferometer,” Phys. Rev. Lett. **65**, 1348–1351
(1990). [CrossRef] [PubMed]

27. Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order
interference,” Phys. Rev. A **42**, 2957–2965
(1990). [CrossRef] [PubMed]

*x*

_{2}with the condition

*x*

_{1}=0

*µ*m. Note that, at this condition, the scheme is equivalent to measuring the biphoton photonic de Broglie wavelength as

*x*

_{1}=0

*µ*m condition leads to the photon number-path entangled state or the NOON state,

*x*2=

*L*, where

_{p}*L*is shown in Fig. 2. Second, the shapes of the individual wave packets are nearly identical to the pump wave packet demonstrated in Fig. 2. Third, the interference fringes exhibit the maximum visibility of ~98% and the period of oscillation is

_{p}*λ/N*(

*N*=2), which is a signature of the biphoton NOON state. The data, therefore, suggest that the pump coherence properties are completely transferred to the biphoton de Broglie wave interference. Note that the biphoton interference revival phenomena reported in Fig. 5(a) is somewhat analogous to the biphoton interference with SPDC generated from mode-locked ultrafast pump pulses where

*L*is the time interval between adjacent pulses [16

_{p}/c16. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P Kulik, “Biphoton interference with a multimode
pump,” Phys. Rev. A **63**, 053801 (2001). [CrossRef]

28. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon
Source for Quantum Communication,” Phys. Rev.
Lett. **82**, 2594–2597
(1999). [CrossRef]

29. Y.-H. Kim, V. Berardi, M. V. Chekhova, A. Garuccio, and Y. H. Shih, “Temporal indistinguishability and quantum
interference,” Phys. Rev. A **62**, 43820 (2000). [CrossRef]

*x*

_{1}≠0. These data are reported in Fig. 5(b), Fig. 5(c), and Fig. 5(d) and they correspond to the conditions

*x*

_{1}=73

*µ*m,

*x*

_{1}=2834

*µ*m, and

*x*

_{1}=5668

*µ*m, respectively. For

*x*

_{1}=50

*µ*m, the pair photons do not arrive at the interferometer simultaneously, but still within the coherence time (see Fig. 4). The conditions

*x*

_{1}=2834

*µ*m and

*x*

_{1}=5668

*µ*m roughly correspond to

*x*

_{1}≈

*L*/2 and

_{p}*x*

_{1}≈

*L*, respectively.

_{p}*x*

_{2}=0) become asymmetrical (with respect to the random coincidence rate). The side peaks (recurring biphoton wave packets) also become asymmetrical but in the opposite sense, see Fig. 5(d). Third, the visibilities of the central wave packets, interestingly, remain the same as that of Fig. 5(a). The side-peaks, however, start to lose visibilities. It is also interesting to note that two small peaks (without modulations) appear where

*x*

_{2}=±

*x*

_{1}, marked with arrows in Fig. 5(c).

## 5. Biphoton interference of multimode-pumped SPDC: Theory

30. S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon
pairs generated via frequency-degenerate type-I spontaneous parametric
down-conversion,” Phys. Rev. A **77**, 043807 (2008). [CrossRef]

*p*refers to the pump photon. The signal and the idler photons of SPDC are referred with subscripts

*s*and

*i*, respectively. Additionally,

*L*is the thickness of the SPDC crystal, Δ

*ω*=

*ω*−

_{p}*ω*−

_{s}*ω*, and Δ

_{i}*=*

_{k}*k*.

_{p}−k_{s}−k_{i}*E*

^{(+)}

*(*

_{a}*t*)=∫

*dωa*(

*ω*)

*ϕ*(

*ω*)

*e*

^{−iωt}, where

*a*(

*ω*) is the annihilation operator for the signal photon in mode

*a*and

*E*

^{(+)}

*(*

_{b}*t*) for the idler photon in mode

*b*is similarly defined. The filter transmission is assumed

*ω*

_{0}is the central frequency of the SPDC photon (

*λ*

_{0}=810 nm) and ∫|

*ϕ*(

*ω*)|

^{2}

*dω*=1 [31

31. We have measured the transmission function of the interference filters used in this experiment with an Agilent 8453 UV/VIS spectro-photometer. We have found that the transmission function is indeed very close Gaussian centered at 810 nm as assumed in eq. (10).

*R*between the single-photon detectors in modes

_{cd}*c*and

*d*is proportional to,

*E*

^{(+)}

*(*

_{c}*t*)=(

*iE*

^{(+)}

*(*

_{a}*t*−

*τ*

_{1})+

*E*

^{(+)}

*(*

_{b}*t*))/√2,

*E*

^{(+)}

*(*

_{d}*t*)=(

*E*

^{(+)}

*(*

_{a}*t*−

*τ*

_{1})+

*iE*

^{(+)}

*(*

_{b}*t*))/

*√*

_{2}, and

*τ*

_{1}=

*x*

_{1}/

*c*. Since, in our experiment, the natural bandwidth of SPDC, sinc(Δ

_{k}*L*/2), is much broader than the spectral filter bandwidth Δ

*ω*, the above equation is calculated to be

*e*of the Mach-Zehnder interferometer

*R*is proportional to

_{ee}*E*

^{(+)}

*(*

_{e}*t*)=(

*iE*

^{(+)}

*(*

_{c}*t*)+

*E*

^{(+)}

*(*

_{d}*t*−

*τ*

_{2}))/√2.

**89**, 213601 (2002). [CrossRef] [PubMed]

*ω*=

_{p}*ω*

_{p0}+

*n*Δ

*ω*. Note that

_{p}*ω*

_{p0}is the central frequency of the pump laser,

*ω*

_{0}is the central frequency of the SPDC photon such that

*ω*

_{p0}=2

*ω*

_{0}(i.e., assumed to be degenerate),

*n*is the mode number, Δ

*ω*is the mode spacing, and Δ

_{p}*ω*is the bandwidth of the Gaussian spectral filter for the SPDC photons (assumed to be narrower than the natural bandwidth of SPDC).

*𝓢*

_{eff}(

*ω*)=exp(−(

_{p}*ω*−2

_{p}*ω*

_{0})

^{2}/Δ

*ω*

^{2}

*) with 1/Δ*

_{e}*ω*

^{2}

*=1/2*

_{e}*δω*

^{2}

*+1/2Δ*

_{p}*ω*

^{2}. Note again that 2

*ω*

_{0}=

*ω*

_{p0}and

*δω*is the bandwidth of the pump laser.

_{p}*λ/N*(

*N*=2) modulation, and the shape of the wave packet is determined by

*τ*

_{1},

*τ*

_{2}, and Δ

*ω*. Equation (18) is plotted in Fig. 6 for comparison with the experimental data in Fig. 5. The theoretical description of the biphoton interference of multimode cw-pumped SPDC is thus in excellent agreement with the experimental observation.

## 6. Conclusion

## Acknowledgements

## References and links

1. | J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum
revolution,” Phil. Trans. R. Soc. Lond. A |

2. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum
cryptography,” Rev. Mod. Phys. |

3. | P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with
photonic qubits,” Rev. Mod. Phys. |

4. | Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm
Experiment Using Pairs of Light Quants Produced by Optical Parametric Down
Conversion,” Phys. Rev. Lett. |

5. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of
Polarization-Entangled Photon Pairs,” Phys. Rev.
Lett. |

6. | Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and
universal Bell-state synthesizer,” Phys. Rev.
A |

7. | J. G. Rarity and P. R. Tapster, “Experimental Violation of Bell’s
Inequality Based on Phase and Momentum,” Phys.
Rev. Lett. |

8. | D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, “Postselection-free energy-time
entanglement,” Phys. Rev. A |

9. | W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Elimanating frequency and space-tie
corelations in multiphoton states,” Phys. Rev.
A |

10. | Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled
two-photon state via temporal and spectral engineering,”
J. Mod. Opt. |

11. | A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled
Photons,” Phys. Rev. Lett. |

12. | P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded Generation of Ultrafast Single
Photons in Pure Quantum States,” Phys. Rev.
Lett. |

13. | P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled
photons,” Phys. Rev. A |

14. | Y.-H. Kim, M. V. Chekhova, S. P. Kulik, M. H. Rubin, and Y. Shih, “Interferometric Bell-state preparation using
femtosecond-pulse-pumped spontaneous parametric
down-conversion,” Phys. Rev. A |

15. | Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of
the two-photon state generated via type II spontaneous parametric
downconversion,” Opt. Lett. |

16. | A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P Kulik, “Biphoton interference with a multimode
pump,” Phys. Rev. A |

17. | The Wiener-Khinchine theorem states that the
spectral power density of an optical field is related to its autocorrelation. They
are, in fact, a Fourier transform pair. It is not difficult to show that the
following relation holds,
Δλ |

18. | J. W. Goodman, |

19. | S.-Y. Baek, O. Kwon, and Y.-H. Kim, “High-Resolution Mode-Spacing Measurement of
the Blue-Violet Diode Laser Using Interference of Felds Created with Time Delays
Greater than the Coherence Time,” Jpn. J. Appl.
Phys. |

20. | Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon
states,” Phys. Rev. Lett. |

21. | M. A. Sagioro, C. Olindo, C. H. Monken, and S. Pádua, “Time control of two-photon
interference,” Phys. Rev. A |

22. | A. Zavatta, S. Viciani, and M. Bellini, “Recurrent fourth-order interference dips and
peaks with a comblike two-photon entangled state,”
Phys. Rev. A |

23. | C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals
between two photons by interference,” Phys. Rev.
Lett. |

24. | J. Jacobson, G. Bjork, I. Chuang, and Y. Yamamoto, “Photonic de Broglie
waves,” Phys. Rev. Lett. |

25. | K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the Photonic de
BroglieWavelength of Entangled Photon Pairs Generated by Spontaneous Parametric
Down-Conversion,” Phys. Rev. Lett. |

26. | J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder
interferometer,” Phys. Rev. Lett. |

27. | Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order
interference,” Phys. Rev. A |

28. | J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon
Source for Quantum Communication,” Phys. Rev.
Lett. |

29. | Y.-H. Kim, V. Berardi, M. V. Chekhova, A. Garuccio, and Y. H. Shih, “Temporal indistinguishability and quantum
interference,” Phys. Rev. A |

30. | S.-Y. Baek and Y.-H. Kim, “Spectral properties of entangled photon
pairs generated via frequency-degenerate type-I spontaneous parametric
down-conversion,” Phys. Rev. A |

31. | We have measured the transmission function of the interference filters used in this experiment with an Agilent 8453 UV/VIS spectro-photometer. We have found that the transmission function is indeed very close Gaussian centered at 810 nm as assumed in eq. (10). |

**OCIS Codes**

(270.1670) Quantum optics : Coherent optical effects

(270.5290) Quantum optics : Photon statistics

(270.5565) Quantum optics : Quantum communications

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: June 5, 2009

Revised Manuscript: July 9, 2009

Manuscript Accepted: July 9, 2009

Published: July 15, 2009

**Citation**

Osung Kwon, Young-Sik Ra, and Yoon-Ho Kim, "Coherence properties of spontaneous parametric down-conversion pumped by a multi-mode cw diode laser," Opt. Express **17**, 13059-13069 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13059

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### References

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