Optics InfoBase > Optics Express > Volume 21 > Issue 5 > Page 5879

## Spectral engineering by Gaussian phase-matching for quantum photonicsP. Ben Dixon, Jeffrey H. Shapiro, and Franco N. C. Wong »View Author Affiliations
P. Ben Dixon,
Jeffrey H. Shapiro,
and Franco N. C. Wong
Corresponding author: bendixon@mit.edu |

Optics Express, Vol. 21, Issue 5, pp. 5879-5890 (2013)

http://dx.doi.org/10.1364/OE.21.005879

View Full Text Article

Enhanced HTML Acrobat PDF (1157 KB)

### Abstract

We demonstrate Gaussian-shaped phase matching of a periodically-poled potassium titanyl phosphate (PPKTP) crystal by imposing a custom duty-cycle pattern on its grating structure while keeping the grating period fixed. The PPKTP’s phase-matching characteristics are verified through optical difference-frequency generation measurements, showing good agreement with expected values based on our design parameters. Our theoretical analysis predicts that under extended phase-matching conditions the custom-poled PPKTP crystal is capable of generating heralded single photons with a spectral purity of 97%, and can reach as high as 99.5% with gentle spectral filtering, something that is highly desirable for photonic quantum information processing applications.

© 2013 OSA

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 21, 2012

Revised Manuscript: February 21, 2013

Manuscript Accepted: February 21, 2013

Published: March 1, 2013

**Citation**

P. Ben Dixon, Jeffrey H. Shapiro, and Franco N. C. Wong, "Spectral engineering by Gaussian phase-matching for quantum photonics," Opt. Express **21**, 5879-5890 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5879

Sort: Author | Year | Journal | Reset

### References

- P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A65, 052104 (2002). [CrossRef]
- T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science316, 726–729 (2007). [CrossRef] [PubMed]
- V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science306, 1330–1336 (2004). [CrossRef] [PubMed]
- M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys.3, 692–695 (2007). [CrossRef]
- R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A79, 040302 (2009). [CrossRef]
- S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” arXiv:1011.3245 [quant-ph] (2010).
- A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys.8, 285–291 (2012). [CrossRef]
- T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hoffenberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature488, 57–60 (2012). [CrossRef] [PubMed]
- A. Muller, W. Fang, J. Lawall, and G. S. Solomon, “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical stark effect,” Phys. Rev. Lett.103, 217402 (2009). [CrossRef]
- J. Chen, K. F. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,” Opt. Lett.31, 2798–2800 (2006). [CrossRef] [PubMed]
- C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A31, 2409–2418 (1985). [CrossRef] [PubMed]
- C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004). [CrossRef]
- 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]
- A. B. U’Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Las. Phys.15, 146 (2005).
- 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]
- R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett.96, 240502 (2006). [CrossRef] [PubMed]
- W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64, 063815 (2001). [CrossRef]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett.101, 153602 (2008). [CrossRef] [PubMed]
- O. Cohen, J. S. Lundeen, B. J. Smith, G. Puentes, P. J. Mosley, and I. A. Walmsley, “Tailored photon-pair generation in optical fibers,” Phys. Rev. Lett.102, 123603 (2009). [CrossRef] [PubMed]
- R. Rangarajan, L. E. Vicent, A. B. U’Ren, and P. G. Kwiat, “Engineering an ideal indistinguishable photon-pair source for optical quantum information processing,” J. Mod. Opt.58, 318–327 (2011). [CrossRef]
- A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19, 55–65 (2011). [CrossRef]
- T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011). [CrossRef] [PubMed]
- E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T. Thew, “Engineering integrated pure narrow-band photon sources,” New J. Phys.14, 033008 (2012). [CrossRef]
- I. Ali Khan and J. C. Howell, “Experimental demonstration of high two-photon time-energy entanglement,” Phys. Rev. A73, 031801 (2006). [CrossRef]
- Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A82, 043826 (2010). [CrossRef]
- R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A81, 053805 (2010). [CrossRef]
- C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: Effective finite Hilbert space and entropy control,” Phys. Rev. Lett.84, 5304–5307 (2000). [CrossRef] [PubMed]
- C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett.92, 127903 (2004). [CrossRef] [PubMed]
- R. Erdmann, D. Branning, W. Grice, and I. A. Walmsley, “Restoring dispersion cancellation for entangled photons produced by ultrashort pulses,” Phys. Rev. A62, 053810 (2000). [CrossRef]
- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Generating entangled two-photon states with coincident frequencies,” Phys. Rev. Lett.88, 183602 (2002).
- O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. Kärtner, “Two-Photon Coincident-Frequency Entanglement via Extended Phase Matching,” Phys. Rev. Lett.94, 083601 (2005). [CrossRef] [PubMed]
- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Extended phase-matching conditions for improved entanglement generation,” Phys. Rev. A66, 043813 (2002). [CrossRef]
- P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New J. Phys.10, 093011 (2008). [CrossRef]
- A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-I PDC with backward-wave amplification,” Opt. Express17, 3441–3446 (2009). [CrossRef] [PubMed]
- M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A72, 023825 (2005). [CrossRef]
- R. Boyd, Nonlinear optics (Academic Press, 1992).
- M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron.28, 2631–2654 (1992). [CrossRef]
- M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett.22, 1341–1343 (1997). [CrossRef]
- M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.100, 183601 (2008). [CrossRef] [PubMed]
- T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, “Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4,” Appl. Opt.26, 2390–2394 (1987). [CrossRef] [PubMed]
- D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett.22, 1553–1555 (1997). [CrossRef]
- K. Fradkin, A. Arie, A. Skliar, and G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett.74, 914–916 (1999). [CrossRef]
- F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett.84, 1644–1646 (2004). [CrossRef]
- S. Popescu and D. Rohrlich, “Thermodynamics and the measure of entanglement,” Phys. Rev. A56, R3319–R3321 (1997). [CrossRef]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Time-resolved single-photon detection by femtosecond upconversion,” Opt. Lett.33, 2257–2259 (2008). [CrossRef] [PubMed]

**Aaronson, S.**

- S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” arXiv:1011.3245 [quant-ph] (2010).

**Albota, M. A.**

- O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. Kärtner, “Two-Photon Coincident-Frequency Entanglement via Extended Phase Matching,” Phys. Rev. Lett.94, 083601 (2005). [CrossRef] [PubMed]

**Ali Khan, I.**

- I. Ali Khan and J. C. Howell, “Experimental demonstration of high two-photon time-energy entanglement,” Phys. Rev. A73, 031801 (2006). [CrossRef]

**Altepeter, J. B.**

- Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A82, 043826 (2010). [CrossRef]

**Arbore, M. A.**

**Arie, A.**

- K. Fradkin, A. Arie, A. Skliar, and G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett.74, 914–916 (1999). [CrossRef]

**Arkhipov, A.**

- S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” arXiv:1011.3245 [quant-ph] (2010).

**Aspelmeyer, M.**

- R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A79, 040302 (2009). [CrossRef]
- R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett.96, 240502 (2006). [CrossRef] [PubMed]

**Aspuru-Guzik, A.**

- A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys.8, 285–291 (2012). [CrossRef]

**Baek, B.**

- T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011). [CrossRef] [PubMed]

**Banaszek, K.**

- A. B. U’Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Las. Phys.15, 146 (2005).
- M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A72, 023825 (2005). [CrossRef]

**Bennink, R. S.**

- T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express19, 24434–24447 (2011). [CrossRef] [PubMed]
- R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A81, 053805 (2010). [CrossRef]

**Beveratos, A.**

- M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys.3, 692–695 (2007). [CrossRef]

**Blauensteiner, B.**

- R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett.96, 240502 (2006). [CrossRef] [PubMed]

**Boyd, R.**

- R. Boyd, Nonlinear optics (Academic Press, 1992).

**Branczyk, A. M.**

**Branning, D.**

- R. Erdmann, D. Branning, W. Grice, and I. A. Walmsley, “Restoring dispersion cancellation for entangled photons produced by ultrashort pulses,” Phys. Rev. A62, 053810 (2000). [CrossRef]

**Byer, R.**

- M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron.28, 2631–2654 (1992). [CrossRef]

**Byer, R. L.**

**Calkins, B.**

**Carrasco, S.**

- M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.100, 183601 (2008). [CrossRef] [PubMed]

**Chen, J.**

**Chou, M. H.**

**Christ, A.**

**Cohen, O.**

- O. Cohen, J. S. Lundeen, B. J. Smith, G. Puentes, P. J. Mosley, and I. A. Walmsley, “Tailored photon-pair generation in optical fibers,” Phys. Rev. Lett.102, 123603 (2009). [CrossRef] [PubMed]

**Dorenbos, S.**

**Dowling, J. P.**

- P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A65, 052104 (2002). [CrossRef]

**Eberly, J. H.**

- C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett.92, 127903 (2004). [CrossRef] [PubMed]
- C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: Effective finite Hilbert space and entropy control,” Phys. Rev. Lett.84, 5304–5307 (2000). [CrossRef] [PubMed]

**Eckardt, R. C.**

**Eckstein, A.**

**Erdmann, R.**

- A. B. U’Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Las. Phys.15, 146 (2005).
- R. Erdmann, D. Branning, W. Grice, and I. A. Walmsley, “Restoring dispersion cancellation for entangled photons produced by ultrashort pulses,” Phys. Rev. A62, 053810 (2000). [CrossRef]

**Fan, T. Y.**

**Fan, Y. X.**

**Fang, W.**

- A. Muller, W. Fang, J. Lawall, and G. S. Solomon, “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical stark effect,” Phys. Rev. Lett.103, 217402 (2009). [CrossRef]

**Fedrizzi, A.**

**Feigelson, R. S.**

**Fejer, M.**

- M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron.28, 2631–2654 (1992). [CrossRef]

**Fejer, M. M.**

- M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.100, 183601 (2008). [CrossRef] [PubMed]
- M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett.22, 1341–1343 (1997). [CrossRef]

**Fiorentino, M.**

- O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. Kärtner, “Two-Photon Coincident-Frequency Entanglement via Extended Phase Matching,” Phys. Rev. Lett.94, 083601 (2005). [CrossRef] [PubMed]

**Firstenberg, O.**

- T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hoffenberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature488, 57–60 (2012). [CrossRef] [PubMed]

**Fradkin, K.**

- K. Fradkin, A. Arie, A. Skliar, and G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett.74, 914–916 (1999). [CrossRef]

**Galvanauskas, A.**

**Gerrits, T.**

**Gerry, C.**

- C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004). [CrossRef]

**Giovannetti, V.**

- V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science306, 1330–1336 (2004). [CrossRef] [PubMed]
- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Extended phase-matching conditions for improved entanglement generation,” Phys. Rev. A66, 043813 (2002). [CrossRef]
- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Generating entangled two-photon states with coincident frequencies,” Phys. Rev. Lett.88, 183602 (2002).

**Gisin, N.**

- M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys.3, 692–695 (2007). [CrossRef]

**Glancy, S.**

**Gorshkov, A. V.**

- T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hoffenberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature488, 57–60 (2012). [CrossRef] [PubMed]

**Grice, W.**

**Grice, W. P.**

- W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64, 063815 (2001). [CrossRef]

**Hadfield, R. H.**

**Halder, M.**

**Harter, D.**

**Herrmann, H.**

- E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T. Thew, “Engineering integrated pure narrow-band photon sources,” New J. Phys.14, 033008 (2012). [CrossRef]

**Hoffenberth, S.**

**Hong, C. K.**

- 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]
- C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A31, 2409–2418 (1985). [CrossRef] [PubMed]

**Howell, J. C.**

- I. Ali Khan and J. C. Howell, “Experimental demonstration of high two-photon time-energy entanglement,” Phys. Rev. A73, 031801 (2006). [CrossRef]

**Hu, B. Q.**

**Huang, C. E.**

**Huang, Y.-P.**

- Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A82, 043826 (2010). [CrossRef]

**Hum, D. S.**

**Jundt, D.**

**Jundt, D. H.**

**Kaltenbaek, R.**

- R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A79, 040302 (2009). [CrossRef]

**Kärtner, F. X.**

**Klapwijk, T.**

**Knight, P.**

- C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004). [CrossRef]

**Knill, E.**

**Kok, P.**

- P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A65, 052104 (2002). [CrossRef]

**König, F.**

- F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett.84, 1644–1646 (2004). [CrossRef]

**Kumar, P.**

- J. Chen, K. F. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,” Opt. Lett.31, 2798–2800 (2006). [CrossRef] [PubMed]

**Kurimura, S.**

- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Time-resolved single-photon detection by femtosecond upconversion,” Opt. Lett.33, 2257–2259 (2008). [CrossRef] [PubMed]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett.101, 153602 (2008). [CrossRef] [PubMed]

**Kuzucu, O.**

- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett.101, 153602 (2008). [CrossRef] [PubMed]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Time-resolved single-photon detection by femtosecond upconversion,” Opt. Lett.33, 2257–2259 (2008). [CrossRef] [PubMed]

**Kwiat, P. G.**

- R. Rangarajan, L. E. Vicent, A. B. U’Ren, and P. G. Kwiat, “Engineering an ideal indistinguishable photon-pair source for optical quantum information processing,” J. Mod. Opt.58, 318–327 (2011). [CrossRef]

**Law, C. K.**

- C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett.92, 127903 (2004). [CrossRef] [PubMed]
- C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: Effective finite Hilbert space and entropy control,” Phys. Rev. Lett.84, 5304–5307 (2000). [CrossRef] [PubMed]

**Lawall, J.**

- A. Muller, W. Fang, J. Lawall, and G. S. Solomon, “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical stark effect,” Phys. Rev. Lett.103, 217402 (2009). [CrossRef]

**Lee, H.**

**Lee, K. F.**

**Liang, C.**

**Liang, Q.-Y.**

**Lita, A.**

**Lloyd, S.**

- V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science306, 1330–1336 (2004). [CrossRef] [PubMed]

**Lukin, M. D.**

**Lundeen, J. S.**

- O. Cohen, J. S. Lundeen, B. J. Smith, G. Puentes, P. J. Mosley, and I. A. Walmsley, “Tailored photon-pair generation in optical fibers,” Phys. Rev. Lett.102, 123603 (2009). [CrossRef] [PubMed]
- 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]
- P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New J. Phys.10, 093011 (2008). [CrossRef]

**Maccone, L.**

- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Extended phase-matching conditions for improved entanglement generation,” Phys. Rev. A66, 043813 (2002). [CrossRef]
- V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Generating entangled two-photon states with coincident frequencies,” Phys. Rev. Lett.88, 183602 (2002).

**Magel, G.**

**Mandel, L.**

- 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]
- C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A31, 2409–2418 (1985). [CrossRef] [PubMed]

**Mirin, R. P.**

**Mosley, P. J.**

- A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-I PDC with backward-wave amplification,” Opt. Express17, 3441–3446 (2009). [CrossRef] [PubMed]
- 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]
- P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New J. Phys.10, 093011 (2008). [CrossRef]

**Muller, A.**

**Nagata, T.**

- T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science316, 726–729 (2007). [CrossRef] [PubMed]

**Nam, S. W.**

**Nasr, M. B.**

**Noh, J.**

- M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A72, 023825 (2005). [CrossRef]

**O’Brien, J. L.**

- T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science316, 726–729 (2007). [CrossRef] [PubMed]

**Okamoto, R.**

**Osorio, C. I.**

- E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T. Thew, “Engineering integrated pure narrow-band photon sources,” New J. Phys.14, 033008 (2012). [CrossRef]

**Ou, Z. Y.**

**Peyronel, T.**

**Pohl, T.**

**Pomarico, E.**

**Popescu, S.**

- S. Popescu and D. Rohrlich, “Thermodynamics and the measure of entanglement,” Phys. Rev. A56, R3319–R3321 (1997). [CrossRef]

**Prevedel, R.**

**Puentes, G.**

**Ralph, T. C.**

**Rangarajan, R.**

- R. Rangarajan, L. E. Vicent, A. B. U’Ren, and P. G. Kwiat, “Engineering an ideal indistinguishable photon-pair source for optical quantum information processing,” J. Mod. Opt.58, 318–327 (2011). [CrossRef]

**Raymer, M. G.**

**Rohrlich, D.**

- S. Popescu and D. Rohrlich, “Thermodynamics and the measure of entanglement,” Phys. Rev. A56, R3319–R3321 (1997). [CrossRef]

**Rosenman, G.**

**Saleh, B. E. A.**

**Sanguinetti, B.**

**Sasaki, K.**

**Scarani, V.**

**Sergienko, A. V.**

**Shapiro, J. H.**

**Silberhorn, C.**

- A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-I PDC with backward-wave amplification,” Opt. Express17, 3441–3446 (2009). [CrossRef] [PubMed]

**Simon, C.**

**Skliar, A.**

**Smith, B. J.**

**Solomon, G. S.**

**Stace, T. M.**

**Stevens, M. J.**

**Takeuchi, S.**

**Teich, M. C.**

**Thew, R. T.**

**Torner, L.**

**Torres, J. P.**

**Tovstonog, S.**

**U’Ren, A. B.**

- W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64, 063815 (2001). [CrossRef]

**Vicent, L. E.**

**Vuletic, V.**

**Walmsley, I. A.**

**Walther, P.**

- A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys.8, 285–291 (2012). [CrossRef]

**Wasylczyk, P.**

**White, A. G.**

**Wong, F. N. C.**

- F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett.84, 1644–1646 (2004). [CrossRef]

**Zbinden, H.**

**Zeilinger, A.**

**Zijlstra, T.**

**Zukowski, M.**

**Zwiller, V.**

### Appl. Opt.

- T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, “Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO4,” Appl. Opt.26, 2390–2394 (1987). [CrossRef] [PubMed]

### Appl. Phys. Lett.

### IEEE J. Quant.Electron.

### J. Mod. Opt.

### Las. Phys.

### Nat. Phys.

### Nature

### New J. Phys.

### Opt. Express

- A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19, 55–65 (2011). [CrossRef]

### Opt. Lett.

- M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett.22, 1341–1343 (1997). [CrossRef]
- D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett.22, 1553–1555 (1997). [CrossRef]
- J. Chen, K. F. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,” Opt. Lett.31, 2798–2800 (2006). [CrossRef] [PubMed]

### Phys. Rev. A

- R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A81, 053805 (2010). [CrossRef]

### Phys. Rev. Lett.

### Science

### Other

- C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004). [CrossRef]
- R. Boyd, Nonlinear optics (Academic Press, 1992).

**2012, Aspuru-Guzik, Nat. Phys.**

**2012, Peyronel, Nature**

**2012, Pomarico, New J. Phys.**

**2011, Rangarajan, J. Mod. Opt.**

**2011, Branczyk, Opt. Express**

**2011, Gerrits, Opt. Express**

**2010, Huang, Phys. Rev. A**

**2010, Bennink, Phys. Rev. A**

**2009, Cohen, Phys. Rev. Lett.**

**2009, Christ, Opt. Express**

**2009, Kaltenbaek, Phys. Rev. A**

**2009, Muller, Phys. Rev. Lett.**

**2008, Kuzucu, Phys. Rev. Lett.**

**2008, Mosley, Phys. Rev. Lett.**

**2008, Mosley, New J. Phys.**

**2008, Nasr, Phys. Rev. Lett.**

**2008, Kuzucu, Opt. Lett.**

**2007, Nagata, Science**

**2007, Halder, Nat. Phys.**

**2006, Chen, Opt. Lett.**

**2006, Kaltenbaek, Phys. Rev. Lett.**

**2006, Ali Khan, Phys. Rev. A**

**2005, Kuzucu, Phys. Rev. Lett.**

**2005, Raymer, Phys. Rev. A**

**2005, U’Ren, Las. Phys.**

**2004, Giovannetti, Science**

**2004, Law, Phys. Rev. Lett.**

**2004, König, Appl. Phys. Lett.**

**2002, Giovannetti, Phys. Rev. A**

**2002, Kok, Phys. Rev. A**

**2001, Grice, Phys. Rev. A**

**2000, Erdmann, Phys. Rev. A**

**2000, Law, Phys. Rev. Lett.**

**1999, Fradkin, Appl. Phys. Lett.**

**1997, Popescu, Phys. Rev. A**

**1997, Arbore, Opt. Lett.**

**1997, Jundt, Opt. Lett.**

**1992, Fejer, IEEE J. Quant.Electron.**

**1987, Fan, Appl. Opt.**

**1987, Hong, Phys. Rev. Lett.**

**1985, Hong, Phys. Rev. A**

**1836, Giovannetti, Phys. Rev. Lett.**

## 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.

### Related Journal Articles

- Generating entangled photons via enhanced spontaneous parametric downconversion in AlGaAs microring resonators (OL)
- Generation of indistinguishable and pure heralded single photons with tunable bandwidth (OL)
- On the distinguishability of downconverted modes with orbital angular momentum (OL)
- Tunable narrowband entangled photon pair source for resonant single-photon single-atom interaction (OL)
- A versatile waveguide source of photon pairs for chip-scale quantum information processing (OE)

### Related Conference Papers

- “Backward Heisenberg Picture” Approach for Spontaneous Parametric Down-Conversion
- “Backward Heisenberg Picture” Approach for Spontaneous Parametric Down-Conversion
- Single Photons with Arbitrary Waveforms
- Experimental Implementation of Entanglement Concentration Using Schmidt Projection
- One-Way Quantum Computation with Two-Photon Multiqubit Cluster States

« Previous Article | Next Article »

OSA is a member of CrossRef.

- Firefox 11+
- Google Chrome 17+
- Internet Explorer 9+
- Safari 5+