## Generation of frequency degenerate twin photons in pulse pumped fiber optical parametric amplifiers: Influence of background noise |

Optics Express, Vol. 22, Issue 3, pp. 2553-2561 (2014)

http://dx.doi.org/10.1364/OE.22.002553

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### Abstract

Using a Sagnac fiber loop functions as a deterministic splitter of photon pairs produced by the frequency degenerate four wave mixing, we show that the background noise of the degenerate photon pairs is contributed by both Raman scattering and frequency non-degenerate four wave mixing. To improve the purity of photon pairs in the high gain regime, in addition to suppressing the noise photons by cooling the nonlinear fiber and by optimizing the detuning between the frequencies of the pump and photon pairs, the walk-off effect of the two pulsed pump fields should be mitigated by managing the dispersion of the fiber. Our investigation is not only the first step towards the generation of multi-mode squeezed vacuum in fiber optical parametric amplifiers pumped with pulsed lights, but also contributes to improving the purity of the fiber sources of degenerate photon pairs.

© 2014 Optical Society of America

1. M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The einstein-podolsky-rosen paradox: From concepts to applications,” Rev. Mod. Phys. **81**, 1727–1751 (2009). [CrossRef]

2. O. Pinel, P. Jian, R. M. Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. **108**, 083601 (2012). [CrossRef] [PubMed]

3. W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: simultaneous squeezing of multimode modes,” Phys. Rev. A **73**, 063819 (2006). [CrossRef]

3. W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: simultaneous squeezing of multimode modes,” Phys. Rev. A **73**, 063819 (2006). [CrossRef]

5. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurement of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. **29**, 1267–1269 (2004). [CrossRef] [PubMed]

6. B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. **101**, 123601 (2008). [CrossRef] [PubMed]

*χ*

^{(2)}crystal based parametric processes [1

1. M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The einstein-podolsky-rosen paradox: From concepts to applications,” Rev. Mod. Phys. **81**, 1727–1751 (2009). [CrossRef]

7. L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed state by parametric down conversion,” Phys. Rev. Lett. **57**, 2520–2523 (1986). [CrossRef] [PubMed]

*χ*

^{(3)}optical fiber also can be used to generate the nonclassical lights [8

8. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photon. Technol. Lett. **14**, 983–985 (2002). [CrossRef]

9. J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett. **27**, 1675–1677 (2002). [CrossRef]

*ω*

_{p}_{1}and

*ω*

_{p}_{2}scatter through the

*χ*

^{(3)}nonlinearity to create the signal and idler photon pairs at frequencies

*ω*and

_{s}*ω*, respectively, such that

_{i}*ω*

_{p}_{1}+

*ω*

_{p}_{2}=

*ω*+

_{s}*ω*and

_{i}*ω*≠

_{s}*ω*. The other is the frequency degenerate FWM (DFWM), in which two pump photons at the different frequencies nonlinearity to create a pair of identical photons at the

_{i}*ω*

_{p}_{1}and

*ω*

_{p}_{2}scatter through the

*χ*

^{(3)}mean frequency

*ω*, such that

_{si}*ω*

_{p}_{1}+

*ω*

_{p}_{2}=

*ω*+

_{s}*ω*and

_{i}*ω*=

_{s}*ω*=

_{i}*ω*. In the former case, the phase matching condition

_{si}*k*

_{p}_{1}+

*k*

_{p}_{2}=

*k*+

_{s}*k*with

_{i}*k*

_{p}_{1(2)}and

*k*

_{s}_{(}

_{i}_{)}respectively denoting the wave-vectors at

*ω*

_{p}_{1(2)}and

*ω*

_{s}_{(}

_{i}_{)}should be satisfied, while for the latter case, the phase matching condition

*k*

_{p}_{1}+

*k*

_{p}_{2}= 2

*k*

_{s}_{(}

_{i}_{)}should be satisfied.

8. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photon. Technol. Lett. **14**, 983–985 (2002). [CrossRef]

13. X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. **101**, 261111 (2012). [CrossRef]

14. J. Fan, A. Dogariu, and L. J. Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. **30**, 1530–1532 (2005). [CrossRef] [PubMed]

15. J. Chen, K. F. Lee, and P. Kumar, “Deterministic quantum splitter based on time-reversed Hong-Ou-Mandel interference,” Phys. Rev. A **76**, 031804 (2007). [CrossRef]

16. J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-not gate in the telecommunications band,” Phys. Rev. Lett. **100**, 133603 (2008). [CrossRef] [PubMed]

^{−1}is cooled in liquid nitrogen (77K) to suppress the RS serves as the nonlinear medium of DFWM, in which two pump photons at the wavelengths

*λ*

_{p}_{1}and

*λ*

_{p}_{2}are scattered into a pair of co-polarized signal and idler photons having the identical mean wavelength

*λ*= 1544.5 nm, which is the same as the experimentally measured zero dispersion wavelength of the DSF. SMF1 and SMF2 function as the dispersive elements of photon pairs. Each linearly polarized pump field,

_{si}*E*(i=1,2), injected into the SFL is split into two pump waves traversing in a counter-propagating manner by FC1, and the two pump fields in the clockwise (CW) and counter-clockwise (CCW) directions respectively produce degenerate photon pairs, |2〉

_{pi}*and |2〉*

_{c}*, where the footnotes*

_{d}*c*and

*d*denote the propagation direction. The SFL is then preceded by a circulator (Cir), which redirects the SFL reflected photons to a separate spatial mode, and the two output modes of SFL are labeled as ”

*a*” and ”

*b*”.

17. N. Zhao, L. Yang, and X. Li, “Passive optical switching of photon pairs using a spontaneous parametric fiber loop,” Opt. Lett. **37**, 1220–1222 (2012). [CrossRef] [PubMed]

*ψ*

_{2}〉 = |1〉

*|1〉*

_{a}*, and the footnotes*

_{b}*a*and

*b*denote the spatial modes of the photons coming out of the SFL. Since the degenerate signal and idler photon pairs inherit the phase of the two pump photons, in Eq. (1), we have

*ϕ*=

*ϕ*

_{p}_{1}+

*ϕ*

_{p}_{2}+

*ϕ*with

_{d}*ϕ*= (

_{d}*k′*

_{p}_{1}+

*k′*

_{p}_{2}− 2

*k′*)

_{si}*L*

_{2}− (

*k*

_{p}_{1}+

*k*

_{p}_{2}− 2

*k*)

_{si}*L*

_{1}denoting the dispersion induced phase difference, where

*ϕ*(

_{pi}*i*= 1, 2) is the phase difference of the pump

*E*(

_{pi}*i*= 1, 2) propagating in the CW and CCW directions,

*L*

_{1}(

*L*

_{2}) is the length of SMF1 (SMF2),

*k*(

_{pi}*k′*) and

_{pi}*k′*(

_{si}*k*) are the wave-vectors of the fields

_{si}*E*and scattered photons at

_{pi}*λ*in SMF1 (SMF2), respectively. Equation (1) shows that we can obtain the state |

_{si}*ψ*〉 = |

*ψ*

_{1}〉 for

*ϕ*= 2

*nπ*, and |

*ψ*〉 = |

*ψ*

_{2}〉 for

*ϕ*= (2

*n*+ 1)

*π*, where

*n*is an integer. In the former case, both the signal and idler photons of a pair come out in the same spatial mode, they are both simultaneously in either mode

*a*or mode

*b*; in the latter case, the signal and idler photons of a pair have different spatial modes, i.e., if one photon emerges in mode

*a*then the other one is in mode

*b*, or vice versa. Moreover, to ensure the deterministic separation of photon pairs is immune to the detuning between the central frequencies of the photon pairs and pump, the dispersion induced phase difference

*ϕ*should equal to 0 [17

_{d}17. N. Zhao, L. Yang, and X. Li, “Passive optical switching of photon pairs using a spontaneous parametric fiber loop,” Opt. Lett. **37**, 1220–1222 (2012). [CrossRef] [PubMed]

*E*

_{p1}and

*E*

_{p2}, which are respectively centering at the wavelengths

*λ*

_{p1}and

*λ*

_{p2}, by taking the 40 MHz train of 150-fs pulses centering at 1550 nm from a mode-locked fiber laser with bandwidth of about 60 nm, dispersing them with the gratings,

*G*

_{1},

*G*

_{2}and

*G*

_{3}, and then spectrally filtering them to obtain two synchronous beams with a tunable wavelength separation of about 10–30 nm. To achieve the required power and to avoid the cross-talk between the two pumps, we first send the two pump pulses with a time delay of about 10 ns into FC2 from its two input ports, then feed one output port of FC2 into the erbium-doped fiber amplifier (EDFA). Photons at the wavelength of

*λ*= 1544.5 nm from the laser that leak through the spectral-dispersion optics and from the amplified spontaneous emission of the EDFA are suppressed by passing the amplified pump pulses through a dual-band filter F1, whose full-width-half-maximum (FWHM) in each band is about 0.6 nm. F1 is a double grating filter [8

_{si}8. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photon. Technol. Lett. **14**, 983–985 (2002). [CrossRef]

*E*

_{p1}and

*E*

_{p2}are adjustable. The gain of DFWM in DSF is maximized by matching the optical paths traversed by the two co-polarized input pump pulses.

*λ*= 1544.5 nm is low. To achieve this, we send the photons emerging in the spatial modes

_{si}*a*and

*b*through the filters F2 and F3, respectively. F2 and F3, providing a more than 100 dB rejection to pump, are realized by cascading two WDM filters (Santec, WDM-15), whose central wavelength and FWHM are about 1544.5 nm and 1.1 nm, respectively. To suppress the cross-polarized RS, F2 (F3) is then followed by FPC3 (FPC4) and PBS1 (PBS2) [10

10. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

*b*, the co-polarized photons passing through F3 are measured by SPD3; while in mode

*a*, co-polarized photons passing through F2 are split by FC4, and the two outputs of FC4 are respectively detected by SPD1 and SPD2. All the three SPDs are operated in the gated Geiger mode. The 2.5 ns gate pulses arrive at a rate of about 2.58 MHz, which is 1/16 of the repetition rate of the pump pulses, and the dead time of the gate is set to 10

*μ*s.

*a*or

*b*is constant, while the two-fold coincidence counting rates of photon pairs respectively in the same and different spatial modes

*C*(SPD1 and SPD2) and

^{s}*C*(SPD2 and SPD3) are given by [18

^{d}18. Equations (2) and (3) can be derived by utilizing the method used in Ref. [19] and using the Hamiltonian of the DFWM _{I}, _{pj}, ω_{p0j} and σ_{p0j} are the peak power, central frequency and bandwidth of the pump field _{0}, V_{Q} and n(ω_{si}) are the vacuum permittivity, the quantization volume and the refractive index of the fiber, respectively, and â^{+}(ω_{si}) is the creation operator of the field at frequency ω_{si}.

19. L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A **83**, 053843 (2011). [CrossRef]

*N*(

_{Di}*i*= 1, 2, 3) refers to the individual counting rates of SPDi,

*η*

_{1}and

*η*

_{3}are the total detection efficiency in the channels of SPD1 and SPD3, respectively, and

*ξ*determined by the bandwidths of pump and photon pairs is the collection efficiency of photon pairs [19

_{si}19. L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A **83**, 053843 (2011). [CrossRef]

*λ*, where the spectra of both pump and photon pairs are assumed to be Gaussian shaped with

_{si}*σ*and

_{p}*σ*respectively denoting the FWHM of pump photons and photon pairs. Usually, the term

_{si}*N*

_{D}_{2}

*η*

_{3}

*ξ*in Eq. (3), originated from the quantum correlation of photon pairs, is called the true coincidences. Defining the ratio between the true coincidences and accidental-coincidences as

_{si}*ψ*〉 = |

*ψ*

_{2}〉 (

*ϕ*=

*π*), the ratio

*CAR*

^{(d)}is maximized, while the ratio

*CAR*

^{(s)}is minimized. Additionally, we note that in contrast to the case of the frequency non-degenerate photon pairs [17

17. N. Zhao, L. Yang, and X. Li, “Passive optical switching of photon pairs using a spontaneous parametric fiber loop,” Opt. Lett. **37**, 1220–1222 (2012). [CrossRef] [PubMed]

20. X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All fiber source of frequency-entangled photon pairs,” Phys. Rev. A **79**, 033817 (2009). [CrossRef]

*C*in Eq. (2) does not equal to the accidental coincidence rate due to the bunching effect [21

^{s}21. B. Yurke and M. Potasek, “Obtainment of thermal noise from a pure quantum state,” Phys. Rev. A **36**, 3464–3466 (1987). [CrossRef] [PubMed]

*E*

_{p1}and

*E*

_{p2}, there are also RS and NDFWM originated from the individual pumps

*E*

_{p1}and

*E*

_{p2}, respectively. Therefore, to improve the purity of the degenerated photon pairs, it is necessary to study how to enhance the desired DFWM and to suppress the other deleterious nonlinear processes.

*ψ*〉 = |

*ψ*

_{2}〉 = |1〉

*|1〉*

_{a}*. To realize the required phase difference*

_{b}*ϕ*=

*ϕ*

_{p}_{1}+

*ϕ*

_{p}_{2}=

*π*and mode matching, we first adjust FPC2 to ensure the SFL functions as a 50/50 power splitter of the pump fields

*E*

_{p1}and

*E*

_{p2}, then adjust FPC1 to guarantee the two-fold coincidence rate of SPD1 and SPD2 is minimized [20

20. X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All fiber source of frequency-entangled photon pairs,” Phys. Rev. A **79**, 033817 (2009). [CrossRef]

*CAR*

^{(s)}is about 1.8. The measured value of

*CAR*

^{(s)}is slightly higher than that calculated by using Eq. (2). This is because the spectra of the filters F2 and F3 are super-Gaussian shaped, which are different from the assumptions used to deduce the expression of

*g*

^{(2)}in Eq. (2). Hence, the result implies that the coincidence rate of the photons emerging from the two output ports of FC4 is originated from the photon bunching effect but not the quantum correlation of photon pairs [18

18. Equations (2) and (3) can be derived by utilizing the method used in Ref. [19] and using the Hamiltonian of the DFWM _{I}, _{pj}, ω_{p0j} and σ_{p0j} are the peak power, central frequency and bandwidth of the pump field _{0}, V_{Q} and n(ω_{si}) are the vacuum permittivity, the quantization volume and the refractive index of the fiber, respectively, and â^{+}(ω_{si}) is the creation operator of the field at frequency ω_{si}.

22. X. Ma, X. Li, L. Cui, X. Guo, and L. Yang, “Effect of chromatic-dispersion-induced chirp on the temporal coherence properties of individual beams from spontaneous four-wave mixing,” Phys. Rev. A **84**, 023829 (2011). [CrossRef]

*E*

_{p1}and

*E*

_{p2}are

*λ*

_{p1}= 1539.5 nm and

*λ*

_{p2}= 1549.5 nm, respectively. We record the counting rate of SPD3 as a function of the pump power for three cases: only the individual pump field of (i)

*E*

_{p1}and (ii)

*E*

_{p2}is launched into SFL, and (iii) both

*E*

_{p1}and

*E*

_{p2}with equal power are launched into SFL. For cases (i) ((ii)), we fit the measured data with the second order polynomial function

*P*

_{1(2)}is the average power of the field

*E*

_{p1}(

*E*

_{p2}), and the fitting coefficients of the linear and quadratic terms,

*E*

_{p1}(

*E*

_{p2}) [8

**14**, 983–985 (2002). [CrossRef]

23. X. Li, P. Voss, J. Chen, K. Lee, and P. Kumar, “Measurement of co- and cross-polarized raman spectra in silica fiber for small detunings,” Opt. Express **13**, 2236–2244 (2005). [CrossRef] [PubMed]

*E*

_{p1}and

*E*

_{p2}also contribute to the detected photons. For the RS at 1544.5 nm, the Bose population factor of optical phonon for

*E*

_{p2}is less than that for

*E*

_{p1}[23

23. X. Li, P. Voss, J. Chen, K. Lee, and P. Kumar, “Measurement of co- and cross-polarized raman spectra in silica fiber for small detunings,” Opt. Express **13**, 2236–2244 (2005). [CrossRef] [PubMed]

*λ*

_{p1}= 1539.5 nm, which is in the normal dispersion regime of DSF. However, the intensity of the detected photons contributed by NDFWM of the field

*E*

_{p1}with a given power is unexpectedly greater than that of

*E*

_{p2}. We think this is because the dispersion property of the DSF is inhomogeneous and the measured value of zero dispersion wavelength ∼1544.5 nm is actually an averaged result of the 300-m-long DSF.

*N*of SPD3 versus the power of two pump fields

_{t}*P*

_{1}+

*P*

_{2}for case (iii). The main plot of Fig. 2(c), obtained by subtracting the background noise

*N*and

_{s}*N*of individual pump fields from

_{a}*N*, shows the counting rate of detected photons originated from DFWM

_{t}*N*versus pump power. Moreover,

_{d}*N*fits the function

_{d}*N*=

_{d}*s*

_{2}(

*P*

_{1}+

*P*

_{2})

^{2}very well, where the fitting coefficient

*s*

_{2}is proportional to the gain of DFWM. Comparing Fig. 2(c) with Figs. 2(a) and 2(b), one sees that in the low (high) gain regime of DFWM, the background of photon pairs is mainly contributed by RS (NDFWM), because the noise photons originated from RS (NDFWM) are greater than that from NDFWM (RS).

*E*

_{p1}(

*E*

_{p2}) as a function of

*c*is the speed of light in vacuum. As a comparison, the fitting coefficient proportional to the gain of DFWM

*s*

_{2}versus the detuning

*λ*

_{p2}−

*λ*| < 10 nm but will start to decrease slightly for |

_{si}*λ*

_{p2}−

*λ*| > 10 nm [23

_{si}23. X. Li, P. Voss, J. Chen, K. Lee, and P. Kumar, “Measurement of co- and cross-polarized raman spectra in silica fiber for small detunings,” Opt. Express **13**, 2236–2244 (2005). [CrossRef] [PubMed]

*s*

_{2}decreases gradually with the increase of detuning due to the walk-off effect of the two pulsed pump fields. Obviously,

*s*

_{2}in Fig. 3(c) is greater than

10. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

11. H. Takesue and K. Inoue, “1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express **13**, 7832–7839 (2005). [CrossRef] [PubMed]

*R*versus the detunings under different pump power levels

*P*

_{1}+

*P*

_{2}by using our experimentally measured results

*N*,

_{s}*N*and

_{a}*N*, as shown in Fig. 4(a). For the low pump power of

_{d}*P*

_{1}+

*P*

_{2}= 0.05 mW, the value of

*R*is the highest for the small detuning of Ω = 0.63 THz (

*R*increase. For example, for the pump power of

*P*

_{1}+

*P*

_{2}= 0.34 mW, the highest

*R*corresponds to Ω = 0.88 THz (

*P*

_{1}+

*P*

_{2}is increased to 0.55 mW, the highest

*R*still corresponds to Ω = 0.88 THz, and the value of

*R*starts to decrease with the increase of detuning. The results indicate that when the detuning is greater than a certain value, which is determined by the dispersion of DSF, the ratio

*R*will decrease with the increase of detuning because the walk-off effect of the two pump fields results in a decreased gain of DFWM (see Fig. 3(c)).

10. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

*P*

_{1}+

*P*

_{2}is varied. The results in Fig. 4(b) are obtained for the detuning Ω of about 0.63 and 0.88 THz, respectively. One sees that for a given pump in the low power regime, although the pair production rate for detuning of 0.63 THz is slightly higher than that for detuning of 0.88 THz (see Fig. 3(c)), the value of CAR for the detuning of 0.63 THz is higher. With the increase of pump power, the difference between the values of CAR of the two kinds of detunings decreases for

*P*

_{1}+

*P*

_{2}less than 0.15 mW. However, when

*P*

_{1}+

*P*

_{2}is greater than 0.15 mW, for a given pump power, the value of CAR for the detuning of 0.88 THz is always higher because the noise photons contributed by NDFWM is less than that for detuning of 0.63 THz. The results are in consistent with Eqs. (6)–(8).

*E*

_{p1}and

*E*

_{p2}. When the total power of the two pump fields are low, the purity of photon pairs are mainly influenced by RS. However, when the total power of the two pump fields are high, which is the necessary condition for generating squeezed vacuum in DSF [24

24. C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” IEEE J. Sel. Top. Quantum Electron. **18**, 958–969 (2012). [CrossRef]

## Acknowledgments

## References and links

1. | M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The einstein-podolsky-rosen paradox: From concepts to applications,” Rev. Mod. Phys. |

2. | O. Pinel, P. Jian, R. M. Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. |

3. | W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: simultaneous squeezing of multimode modes,” Phys. Rev. A |

4. | R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. |

5. | J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurement of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. |

6. | B. Lamine, C. Fabre, and N. Treps, “Quantum improvement of time transfer between remote clocks,” Phys. Rev. Lett. |

7. | L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed state by parametric down conversion,” Phys. Rev. Lett. |

8. | M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” Photon. Technol. Lett. |

9. | J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett. |

10. | X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express |

11. | H. Takesue and K. Inoue, “1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express |

12. | J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express |

13. | X. Guo, X. Li, N. Liu, L. Yang, and Z. Y. Ou, “An all-fiber source of pulsed twin beams for quantum communication,” Appl. Phys. Lett. |

14. | J. Fan, A. Dogariu, and L. J. Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. |

15. | J. Chen, K. F. Lee, and P. Kumar, “Deterministic quantum splitter based on time-reversed Hong-Ou-Mandel interference,” Phys. Rev. A |

16. | J. Chen, J. B. Altepeter, M. Medic, K. F. Lee, B. Gokden, R. H. Hadfield, S. W. Nam, and P. Kumar, “Demonstration of a quantum controlled-not gate in the telecommunications band,” Phys. Rev. Lett. |

17. | N. Zhao, L. Yang, and X. Li, “Passive optical switching of photon pairs using a spontaneous parametric fiber loop,” Opt. Lett. |

18. | Equations (2) and (3) can be derived by utilizing the method used in Ref. [19] and using the Hamiltonian of the DFWM |

19. | L. Yang, X. Ma, X. Guo, L. Cui, and X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A |

20. | X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, and D. Yu, “All fiber source of frequency-entangled photon pairs,” Phys. Rev. A |

21. | B. Yurke and M. Potasek, “Obtainment of thermal noise from a pure quantum state,” Phys. Rev. A |

22. | X. Ma, X. Li, L. Cui, X. Guo, and L. Yang, “Effect of chromatic-dispersion-induced chirp on the temporal coherence properties of individual beams from spontaneous four-wave mixing,” Phys. Rev. A |

23. | X. Li, P. Voss, J. Chen, K. Lee, and P. Kumar, “Measurement of co- and cross-polarized raman spectra in silica fiber for small detunings,” Opt. Express |

24. | C. J. McKinstrie and J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” IEEE J. Sel. Top. Quantum Electron. |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Fiber Optics

**History**

Original Manuscript: December 4, 2013

Revised Manuscript: January 15, 2014

Manuscript Accepted: January 16, 2014

Published: January 29, 2014

**Citation**

Lei Yang, Fengwei Sun, Ningbo Zhao, and Xiaoying Li, "Generation of frequency degenerate twin photons in pulse pumped fiber optical parametric amplifiers: Influence of background noise," Opt. Express **22**, 2553-2561 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2553

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### References

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- Equations (2) and (3) can be derived by utilizing the method used in Ref. [19] and using the Hamiltonian of the DFWM HI=αχ(3)∫dV(Ep1+Ep2+E^si−E^si−+H.c.), where α is the constant determined by experimental details. In the expression of Hamiltonian HI, Epj+∝e−iγPpjz∫dωpje−(ωpj−ωp0j)2/2σpj2eikpjz−iωpjt(j= 1, 2) denotes the strong pump pulse, where Ppj, ωp0j and σp0j are the peak power, central frequency and bandwidth of the pump field Epj+, respectively; E^si−=∫dωsih¯ωsi2ε0VQa^+(ωsi)n(ωsi)e−i(ksiz−ωsit)represents the quantized electromagnetic signal (idler) field expanded in multi-mode, where ε0, VQ and n(ωsi) are the vacuum permittivity, the quantization volume and the refractive index of the fiber, respectively, and â+(ωsi) is the creation operator of the field at frequency ωsi.
- L. Yang, X. Ma, X. Guo, L. Cui, X. Li, “Characterization of a fiber-based source of heralded single photons,” Phys. Rev. A 83, 053843 (2011). [CrossRef]
- X. Li, L. Yang, X. Ma, L. Cui, Z. Y. Ou, D. Yu, “All fiber source of frequency-entangled photon pairs,” Phys. Rev. A 79, 033817 (2009). [CrossRef]
- B. Yurke, M. Potasek, “Obtainment of thermal noise from a pure quantum state,” Phys. Rev. A 36, 3464–3466 (1987). [CrossRef] [PubMed]
- X. Ma, X. Li, L. Cui, X. Guo, L. Yang, “Effect of chromatic-dispersion-induced chirp on the temporal coherence properties of individual beams from spontaneous four-wave mixing,” Phys. Rev. A 84, 023829 (2011). [CrossRef]
- X. Li, P. Voss, J. Chen, K. Lee, P. Kumar, “Measurement of co- and cross-polarized raman spectra in silica fiber for small detunings,” Opt. Express 13, 2236–2244 (2005). [CrossRef] [PubMed]
- C. J. McKinstrie, J. P. Gordon, “Field fluctuations produced by parametric processes in fibers,” IEEE J. Sel. Top. Quantum Electron. 18, 958–969 (2012). [CrossRef]

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