Abstract

Quantum frequency conversion (FC) in nonlinear optical media is a powerful tool for temporal-mode selective manipulation of light. Recent attempts at achieving high mode selectivities and/or fidelities have had to resort to multi-dimensional optimization schemes to determine the system’s natural Schmidt modes. Certain combinations of relative-group velocities between the relevant frequency bands, medium length, and temporal pulse widths have been known to achieve good selectivities (exceeding 80%) for temporal modes that are nearly identical to pump pulse shapes, even for high conversion efficiencies. Working in this parameter regime using an off-the-shelf, second-harmonic generation, MgO:PPLN waveguide, and with pulses on the order of 500 fs at wavelengths around 800 nm, we verify experimentally that model-predicted Schmidt modes provide the high temporal-mode selectivity expected. The good agreement between experiment and theory paves the way to the implementation of a proposed two-stage FC scheme that is predicted by the present theory to reach near-perfect (100%) selectivity.

© 2017 Optical Society of America

Full Article  |  PDF Article
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2017 (4)

A. Lenhard, M. Bock, C. Becher, J. Brito, and J. Eschner, “Coherence and entanglement preservation of frequency-converted heralded single photons,” Opt. Express 25, 11187–11199 (2017).
[Crossref]

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[Crossref] [PubMed]

P. Manukar, N. Jain, P. Kumar, and G. S. Kanter, “Programmable optical waveform reshaping on a picosecond timescale,” Opt. Lett. 42, 951–954 (2017).
[Crossref]

M. Karpiński, M. Jachura, L. J. Wright, and B. J. Smith, “Bandwidth manipulation of quantum light by an electrooptic time lens,” Nat. Photonics 11, 53–57 (2017).
[Crossref]

2016 (5)

P. Manurkar, N. Jain, M. Silver, Y.-P. Huang, C. Langrock, M. M. Fejer, P. Kumar, and G. S. Kanter, “Multidimensional mode-separable frequency conversion for high-speed quantum communication,” Optica 3, 1300–1307 (2016).
[Crossref]

L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
[Crossref] [PubMed]

M. Pant and D. Englund, “High-dimensional unitary transformations and boson sampling on temporal modes using dispersive optics,” Phys. Rev. A 93, 043803 (2016).
[Crossref]

N. Quesada and J. E. Sipe, “High efficiency in mode-selective frequency conversion,” Opt. Lett. 41, 364–367 (2016).
[Crossref] [PubMed]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref] [PubMed]

2015 (5)

J. B. Christensen, D. V. Reddy, C. J. McKinstrie, K. Rottwitt, and M. G. Raymer, “Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering,” Opt. Express 23, 23287–23301 (2015).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

J. M. Donohue, M. D. Mazurek, and K. J. Resch, “Theory of high-efficiency sum-frequency generation for single-photon waveform conversion,” Phys. Rev. A 91, 033809 (2015).
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

2014 (6)

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

J. Roslund, R. M. de Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

V. A. Averchenko, V. Thiel, and N. Treps, “Nonlinear photon subtraction from a multimode quantum field,” Phys. Rev. A 89, 063808 (2014).
[Crossref]

A. S. Kowligy, P. Manurkar, N. V. Corzo, V. G. Velev, M. Silver, R. P. Scott, S. J. B. Yoo, P. Kumar, G. S. Kanter, and Y.-P. Huang, “Quantum optical arbitrary waveform manipulation and measurement in real time,” Opt. Express 22, 27942–27957 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
[Crossref] [PubMed]

2013 (4)

P. J. Bustard, R. Lausten, D. G. England, and B. J. Sussman, “Toward quantum processing in molecules: A thz-bandwidth coherent memory for light,” Phys. Rev. Lett. 111, 083901 (2013).
[Crossref] [PubMed]

Y.-P. Huang and P. Kumar, “Mode-resolved photon counting via cascaded quantum frequency conversion,” Opt. Lett. 38, 468–470 (2013).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

A. Christ, B. Brecht, W. Mauerer, and C. Silberhorn, “Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime,” New J. Phys. 15, 053038 (2013).
[Crossref]

2012 (4)

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 695–697 (2012).
[Crossref]

K. F. Reim, J. Nunn, X.-M. Jin, P. S. Michelberger, T. F. M. Champion, D. G. England, K. C. Lee, W. S. Kolthammer, N. K. Langford, and I. A. Walmsley, “Multipulse addressing of a raman quantum memory: Configurable beam splitting and efficient readout,” Phys. Rev. Lett. 108, 263602 (2012).
[Crossref] [PubMed]

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today 65, 32–37 (2012).
[Crossref]

2011 (4)

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13370–13778 (2011).
[Crossref]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13, 065029 (2011).
[Crossref]

H. J. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Wavelength translation across 210 nm in the visible using vector Bragg scattering in a birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 23, 109–111 (2011).
[Crossref]

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

2010 (3)

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum Frequency Translation of Single-Photon States in a Photonic Crystal Fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

2009 (1)

2007 (3)

E. Frumker and Y. Silberberg, “Phase and amplitude pulse shaping with two-dimensional phase-only spatial light modulators,” J. Opt. Soc. Am. B 24, 2940–2947 (2007).
[Crossref]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Review of Scientific Instruments 71, 1929–1960 (2000).
[Crossref]

1992 (1)

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68, 2153–2156 (1992).
[Crossref] [PubMed]

1990 (1)

1961 (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Acioli, L.

L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
[Crossref] [PubMed]

Allgaier, M.

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

V. Ansari, G. Herder, M. Allgaier, B. Brecht, and C. Silberhorn, “Temporal-mode detector tomography of a quantum pulse gate,” arXiv:1702.03336 (2017).

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

Ansari, V.

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

V. Ansari, G. Herder, M. Allgaier, B. Brecht, and C. Silberhorn, “Temporal-mode detector tomography of a quantum pulse gate,” arXiv:1702.03336 (2017).

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

Averchenko, V.

V. Averchenko, D. Sych, and G. Leuchs, “Heralded temporal shaping of single photons enabled by entanglement,” arXiv:1610.03794 (2016).

Averchenko, V. A.

V. A. Averchenko, V. Thiel, and N. Treps, “Nonlinear photon subtraction from a multimode quantum field,” Phys. Rev. A 89, 063808 (2014).
[Crossref]

Barbieri, M.

P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
[Crossref] [PubMed]

Becher, C.

Bellini, M.

L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
[Crossref] [PubMed]

Bock, M.

Brecht, B.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

A. Christ, B. Brecht, W. Mauerer, and C. Silberhorn, “Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime,” New J. Phys. 15, 053038 (2013).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13370–13778 (2011).
[Crossref]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13, 065029 (2011).
[Crossref]

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

V. Ansari, G. Herder, M. Allgaier, B. Brecht, and C. Silberhorn, “Temporal-mode detector tomography of a quantum pulse gate,” arXiv:1702.03336 (2017).

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

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L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
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T. Zhong, J. M. Kindem, J. Rochman, and A. Faraon, “Interfacing broadband photonic qubits to on-chip cavity-protected rare-earth ensembles,” Nat. Commun. 8, 14107 (2017).
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P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
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K. F. Reim, J. Nunn, X.-M. Jin, P. S. Michelberger, T. F. M. Champion, D. G. England, K. C. Lee, W. S. Kolthammer, N. K. Langford, and I. A. Walmsley, “Multipulse addressing of a raman quantum memory: Configurable beam splitting and efficient readout,” Phys. Rev. Lett. 108, 263602 (2012).
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H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
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C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
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H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
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D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
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C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
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L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 695–697 (2012).
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L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
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K. F. Reim, J. Nunn, X.-M. Jin, P. S. Michelberger, T. F. M. Champion, D. G. England, K. C. Lee, W. S. Kolthammer, N. K. Langford, and I. A. Walmsley, “Multipulse addressing of a raman quantum memory: Configurable beam splitting and efficient readout,” Phys. Rev. Lett. 108, 263602 (2012).
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T. Kobayashi, D. Yamazaki, K. Matsuki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Kaoshi, and N. Imoto, “Mach-Zehnder interferometer using frequency-domain beamsplitter,” arXiv:1703.08114 (2017).

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Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
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J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

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P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
[Crossref] [PubMed]

K. F. Reim, J. Nunn, X.-M. Jin, P. S. Michelberger, T. F. M. Champion, D. G. England, K. C. Lee, W. S. Kolthammer, N. K. Langford, and I. A. Walmsley, “Multipulse addressing of a raman quantum memory: Configurable beam splitting and efficient readout,” Phys. Rev. Lett. 108, 263602 (2012).
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[Crossref]

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

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M. Pant and D. Englund, “High-dimensional unitary transformations and boson sampling on temporal modes using dispersive optics,” Phys. Rev. A 93, 043803 (2016).
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L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
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J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

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K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

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Quiring, V.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

Ra, Y.-S.

Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” arXiv:1702.02082 (2017).

Radic, S.

H. J. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Wavelength translation across 210 nm in the visible using vector Bragg scattering in a birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 23, 109–111 (2011).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum Frequency Translation of Single-Photon States in a Photonic Crystal Fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

Ramelow, S.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref] [PubMed]

Raymer, M.

H. J. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Wavelength translation across 210 nm in the visible using vector Bragg scattering in a birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 23, 109–111 (2011).
[Crossref]

M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

Raymer, M. G.

J. B. Christensen, D. V. Reddy, C. J. McKinstrie, K. Rottwitt, and M. G. Raymer, “Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering,” Opt. Express 23, 23287–23301 (2015).
[Crossref] [PubMed]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 695–697 (2012).
[Crossref]

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today 65, 32–37 (2012).
[Crossref]

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum Frequency Translation of Single-Photon States in a Photonic Crystal Fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

Reddy, D. V.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
[Crossref]

J. B. Christensen, D. V. Reddy, C. J. McKinstrie, K. Rottwitt, and M. G. Raymer, “Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering,” Opt. Express 23, 23287–23301 (2015).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

Reim, K. F.

K. F. Reim, J. Nunn, X.-M. Jin, P. S. Michelberger, T. F. M. Champion, D. G. England, K. C. Lee, W. S. Kolthammer, N. K. Langford, and I. A. Walmsley, “Multipulse addressing of a raman quantum memory: Configurable beam splitting and efficient readout,” Phys. Rev. Lett. 108, 263602 (2012).
[Crossref] [PubMed]

Resch, K. J.

J. M. Donohue, M. D. Mazurek, and K. J. Resch, “Theory of high-efficiency sum-frequency generation for single-photon waveform conversion,” Phys. Rev. A 91, 033809 (2015).
[Crossref]

Ricken, R.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

Rochman, J.

T. Zhong, J. M. Kindem, J. Rochman, and A. Faraon, “Interfacing broadband photonic qubits to on-chip cavity-protected rare-earth ensembles,” Nat. Commun. 8, 14107 (2017).
[Crossref] [PubMed]

Roslund, J.

J. Roslund, R. M. de Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

Rottwitt, K.

J. B. Christensen, D. V. Reddy, C. J. McKinstrie, K. Rottwitt, and M. G. Raymer, “Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering,” Opt. Express 23, 23287–23301 (2015).
[Crossref] [PubMed]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 695–697 (2012).
[Crossref]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

Sansoni, L.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

Sasoni, L.

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

Saunders, D. J.

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

Scott, R. P.

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Silberberg, Y.

Silberhorn, C.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

A. Christ, B. Brecht, W. Mauerer, and C. Silberhorn, “Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime,” New J. Phys. 15, 053038 (2013).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13370–13778 (2011).
[Crossref]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13, 065029 (2011).
[Crossref]

K. Laiho, K. N. Cassemiro, and C. Silberhorn, “Producing high fidelity single photons with optimal brightness via waveguided parametric down-conversion,” Opt. Express 17, 22823–22837 (2009).
[Crossref]

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

V. Ansari, G. Herder, M. Allgaier, B. Brecht, and C. Silberhorn, “Temporal-mode detector tomography of a quantum pulse gate,” arXiv:1702.03336 (2017).

Silver, M.

Sipe, J. E.

Smith, B. J.

M. Karpiński, M. Jachura, L. J. Wright, and B. J. Smith, “Bandwidth manipulation of quantum light by an electrooptic time lens,” Nat. Photonics 11, 53–57 (2017).
[Crossref]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

Sørensen, A. S.

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
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Srinivasan, K.

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today 65, 32–37 (2012).
[Crossref]

Strang, G.

G. Strang, Introduction to Linear Algebra (Wellesley-Cambridge Press, 1998), 3rd ed.

Suche, H.

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13, 065029 (2011).
[Crossref]

Surmacz, K.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

Sussman, B. J.

P. J. Bustard, R. Lausten, D. G. England, and B. J. Sussman, “Toward quantum processing in molecules: A thz-bandwidth coherent memory for light,” Phys. Rev. Lett. 111, 083901 (2013).
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V. Averchenko, D. Sych, and G. Leuchs, “Heralded temporal shaping of single photons enabled by entanglement,” arXiv:1610.03794 (2016).

Terai, H.

T. Kobayashi, D. Yamazaki, K. Matsuki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Kaoshi, and N. Imoto, “Mach-Zehnder interferometer using frequency-domain beamsplitter,” arXiv:1703.08114 (2017).

Thiel, V.

V. A. Averchenko, V. Thiel, and N. Treps, “Nonlinear photon subtraction from a multimode quantum field,” Phys. Rev. A 89, 063808 (2014).
[Crossref]

Thomas, S.

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

Treps, N.

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

V. A. Averchenko, V. Thiel, and N. Treps, “Nonlinear photon subtraction from a multimode quantum field,” Phys. Rev. A 89, 063808 (2014).
[Crossref]

J. Roslund, R. M. de Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
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Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” arXiv:1702.02082 (2017).

V. Ansari, M. Allgaier, L. Sasoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Temporal-mode tomography of single photons,” arXiv:1607.03001 (2016).

van Enk, S.

M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

Velev, V. G.

Vigh, G.

M. Allgaier, G. Vigh, V. Ansari, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, “Fast time-domain measurements on telecom single photons,” arXiv:1702.03240 (2017).

Waldermann, F. C.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

Walmsley, I. A.

P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
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J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

J. Nunn, S. Thomas, J. H. D. Munns, K. T. Kaczmarek, C. Qiu, A. Feizpour, E. Poem, B. Brecht, D. J. Saunders, P. M. Ledingham, D. V. Reddy, M. G. Raymer, and I. A. Walmsley, “Theory of noise suppression in Λ-type quantum memories by means of a cavity,” arXiv:1601.00157 (2016).

Wang, Z.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
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M. Karpiński, M. Jachura, L. J. Wright, and B. J. Smith, “Bandwidth manipulation of quantum light by an electrooptic time lens,” Nat. Photonics 11, 53–57 (2017).
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T. Kobayashi, D. Yamazaki, K. Matsuki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Kaoshi, and N. Imoto, “Mach-Zehnder interferometer using frequency-domain beamsplitter,” arXiv:1703.08114 (2017).

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T. Kobayashi, D. Yamazaki, K. Matsuki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Kaoshi, and N. Imoto, “Mach-Zehnder interferometer using frequency-domain beamsplitter,” arXiv:1703.08114 (2017).

Yamazaki, D.

T. Kobayashi, D. Yamazaki, K. Matsuki, R. Ikuta, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Kaoshi, and N. Imoto, “Mach-Zehnder interferometer using frequency-domain beamsplitter,” arXiv:1703.08114 (2017).

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
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Zavatta, A.

L. S. Costanzo, A. S. Coelho, D. Pellegrino, M. S. Mendes, L. Acioli, K. N. Cassemiro, D. Felinto, A. Zavatta, and M. Bellini, “Zero-area single-photon pulses,” Phys. Rev. Lett. 116, 023602 (2016).
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Zheng, Z.

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

Zhong, T.

T. Zhong, J. M. Kindem, J. Rochman, and A. Faraon, “Interfacing broadband photonic qubits to on-chip cavity-protected rare-earth ensembles,” Nat. Commun. 8, 14107 (2017).
[Crossref] [PubMed]

IEEE Photon. Technol. Lett. (1)

H. J. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Wavelength translation across 210 nm in the visible using vector Bragg scattering in a birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 23, 109–111 (2011).
[Crossref]

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

Nat. Commun. (1)

T. Zhong, J. M. Kindem, J. Rochman, and A. Faraon, “Interfacing broadband photonic qubits to on-chip cavity-protected rare-earth ensembles,” Nat. Commun. 8, 14107 (2017).
[Crossref] [PubMed]

Nat. Photonics (2)

J. Roslund, R. M. de Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

M. Karpiński, M. Jachura, L. J. Wright, and B. J. Smith, “Bandwidth manipulation of quantum light by an electrooptic time lens,” Nat. Photonics 11, 53–57 (2017).
[Crossref]

New J. Phys. (3)

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13, 065029 (2011).
[Crossref]

A. Christ, B. Brecht, W. Mauerer, and C. Silberhorn, “Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime,” New J. Phys. 15, 053038 (2013).
[Crossref]

Opt. Commun. (1)

M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

Opt. Express (8)

J. B. Christensen, D. V. Reddy, C. J. McKinstrie, K. Rottwitt, and M. G. Raymer, “Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering,” Opt. Express 23, 23287–23301 (2015).
[Crossref] [PubMed]

K. Laiho, K. N. Cassemiro, and C. Silberhorn, “Producing high fidelity single photons with optimal brightness via waveguided parametric down-conversion,” Opt. Express 17, 22823–22837 (2009).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13370–13778 (2011).
[Crossref]

A. Lenhard, M. Bock, C. Becher, J. Brito, and J. Eschner, “Coherence and entanglement preservation of frequency-converted heralded single photons,” Opt. Express 25, 11187–11199 (2017).
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A. S. Kowligy, P. Manurkar, N. V. Corzo, V. G. Velev, M. Silver, R. P. Scott, S. J. B. Yoo, P. Kumar, G. S. Kanter, and Y.-P. Huang, “Quantum optical arbitrary waveform manipulation and measurement in real time,” Opt. Express 22, 27942–27957 (2014).
[Crossref] [PubMed]

H. J. McGuinness, M. G. Raymer, and C. J. McKinstrie, “Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color,” Opt. Express 19, 17876–17907 (2011).
[Crossref] [PubMed]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 695–697 (2012).
[Crossref]

D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013).
[Crossref] [PubMed]

Opt. Lett. (5)

Optica (1)

Phys. Rev. (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Phys. Rev. A (8)

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

M. Pant and D. Englund, “High-dimensional unitary transformations and boson sampling on temporal modes using dispersive optics,” Phys. Rev. A 93, 043803 (2016).
[Crossref]

B. Brecht, A. Eckstein, R. Ricken, V. Quiring, H. Suche, L. Sansoni, and C. Silberhorn, “Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion,” Phys. Rev. A 90, 030302 (2014).
[Crossref]

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, “Mapping broadband single-photon wave packets into an atomic memory,” Phys. Rev. A 75, 011401 (2007).
[Crossref]

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

V. A. Averchenko, V. Thiel, and N. Treps, “Nonlinear photon subtraction from a multimode quantum field,” Phys. Rev. A 89, 063808 (2014).
[Crossref]

J. M. Donohue, M. D. Mazurek, and K. J. Resch, “Theory of high-efficiency sum-frequency generation for single-photon waveform conversion,” Phys. Rev. A 91, 033809 (2015).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion,” Phys. Rev. A 91, 012323 (2015).
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Figures (11)

Fig. 1
Fig. 1 Numerically simulated results for γ ˜ = 0.141, ζ = 20, and ξ = ∞ (perfect group-velocity matching) with Gaussian-shaped pump pulse. (a) The first two s-band input Schmidt modes. (b) The first two r-band output Schmidt modes. (c) Conversion efficiencies of first four dominant Schmidt modes (Selectivity S = 0.071). Note that ϕ1(t′) closely resembles the pump shape, and the temporal width of Ψ1(t) is larger by a factor of ζ = 20.
Fig. 2
Fig. 2 Numerically simulated, dominant Schmidt modes and conversion efficiencies for γ ˜ = 0.707, ζ = 20, and ξ = ∞ (perfect group-velocity matching) with Gaussian (a, b, c) and first-order Hermite-Gaussian (d, e, f) pump pulses. Due to the lack of any complex phase structure in the pumps, the Schmidt modes end up being real valued (up to overall phase). Note that the first (n = 1) s-band input Schmidt modes (a, d) resemble the group-velocity matched, pump-pulse shapes up to temporal skewing, whereas the first r-band output Schmidt modes (b, e) get stretched relative to pump width by factor ζ. Also note the independence of the dominant Schmidt coefficients (c, f) from pump-pulse shape. Here, selectivity S = 0.77.
Fig. 3
Fig. 3 Numerically simulated, first (n = 1) s-band input Schmidt modes (ϕ1(t′)) for ζ = 20, ξ = ∞, and various γ ˜ with (a) Gaussian pump pulses, and (b) first-order Hermite-Gaussian pump pulses. These plots demonstrate the γ ˜-dependent temporal skewing effect. (c) The conversion efficiencies for the first four dominant Schmidt modes. Plot (c) is identical for both pump-pulse shapes. The selectivities are given in the legend.
Fig. 4
Fig. 4 Numerically simulated, 3D surface plots of conversion efficiencies (CE) vs. input pump-signal time delay by pump width (τd/τp) for various γ ˜ ( P pump ) for (a) Gaussian pump and signal, (b) Gaussian pump and first-order Hermite-Gaussian signal, (c) first-order Hermite-Gaussian pump and Gaussian signal, and (d) first-order Hermite-Gaussian pump and signal pulse shapes. Note the temporal skewness at higher γ ˜, reflected in shift of CE maxima with respect to mesh grid, as well as asymmetry in lobe peak heights.
Fig. 5
Fig. 5 (a) The wavenumber (β) and the group velocity (vg = /) vs. wavelength (λ) for a typical 5 µm wide, periodically-poled, MgO:LN waveguide. Also shown are the r-, s-, and p− bands that we utilize for SFG. (b) Numerically computed, peak normalized joint-spectral amplitude of the degenerate, Type-0 SPDC photon pairs that would be generated in 5 mm of such a waveguide when pumped with 0.1 nm wide blue light in the r-band. Also shown are the signal (s) and pump (p) bands for the SFG process, which are situated symmetrically on either side of the red second-harmonic generation pump wavelength at 816.6 nm. Due to the frequency anti-correlatedness of the SPDC joint-spectral amplitude, both s- and p-bands need to contain non-zero optical energies for SFG to occur into the r-band.
Fig. 6
Fig. 6 Experimental setup. The holographic grating was used in near-Littrow mode for both incoming and outgoing beams. The m = 1 order reflection from two separated vertical blazed gratings rendered on the SLM was recombined on the holographic grating. Both the input and output couplers of the 5 µm wide, 5 mm long MgO:PPLN waveguide were single-element aspheric lenses of focal length f = 11 mm. DM stands for dichroic mirror. Some frequency filters are not shown.
Fig. 7
Fig. 7 (a) Typical 8-bit grayscale phase mask applied to the SLM to generate a Gaussian shaped signal pulse (left band) and a first-order Hermite-Gaussian pump pulse (right band). Here, the horizontal coordinate maps to different wavelengths. The phase-contrast of the vertical gratings determines amplitude. Vertically shifting the gratings can affect phase (note relative shift between the two grating patterns generating the two frequency lobes of the pump). The curved pattern is for chirp compensation (measured using a commercial FROG/GRENOUILLE 8-50-USB), and the linear spectral phase on the signal shifts it in time relative to the pump. (b) Spectra of original Ti:Sapph laser, the signal, and the pump (first-order Hermite Gaussian, for example) generated by the SLM phase mask in (a). The three different spectra were captured under different conditions and hence, the relative heights are not to scale.
Fig. 8
Fig. 8 Blue light spectra generated from the waveguide in a typical run. The SFG peak requires both the pump and signal to be present at the input, whereas the pump-only SHG peak remains even without the signal, and occurs due to imperfections in poling. The latter peak can compete with the former at higher pump powers. To use very weak signals (say sub-single-photon level), very tight spectral filtering will be needed at the blue output arm.
Fig. 9
Fig. 9 Experimental data: 3D point plots of conversion efficiencies (CE) vs. input pump-signal time delay (τd) for various γ ˜ = σ P pump (where σ = 18 / W, and Ppump is average pump power) for (a) Gaussian pump and signal, (b) Gaussian pump and first-order Hermite-Gaussian signal, (c) first-order Hermite-Gaussian pump and Gaussian signal, and (d) first-order Hermite-Gaussian pump and signal pulse shapes. Note the temporal skewness at higher γ ˜, as well as asymmetry in lobe peak heights, matching the theoretically predicted trends from Fig. 4. Vertical error bars are all of order 10−3, not shown.
Fig. 10
Fig. 10 CE (conversion efficiency) vs. γ ˜ ( P pump ) for various pump and signal input pulse shapes at “zero” delay (defined as delay that maximizes CE at low pump power). The legend label (HGj, HGk) denotes j-th order Hermite-Gaussian pump pulse, and k-th order Hermite-Gaussian signal pulse. The solid lines are theory and the markers are measurements.
Fig. 11
Fig. 11 CE (conversion efficiency) vs. γ ˜ ( P pump ) for j-th order Hermite-Gaussian pump pulses (HGj) and the corresponding first input Schmidt modes (SMj). Also shown are CE with the pump shapes swapped for j ∈ {0, 1}. Solid lines are theory, and markers are experiment (type: “exp.”). Error bars (not shown) are of order 10−3.

Equations (5)

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( z + β r t ) A ^ r ( z , t ) = i γ A p ( t β p z ) A ^ s ( z , t ) ,
( z + β s t ) A ^ s ( z , t ) = i γ A p ( t β p z ) A ^ r ( z , t ) .
A ^ j ( L , t ) = k = r , s G j k ( t , t ) A ^ k ( 0 , t ) d t .
[ G r r ( t , t ) G r s ( t , t ) G s r ( t , t ) G s s ( t , t ) ] = [ n τ n Ψ n ( t ) ψ n ( t ) n ρ n Ψ n ( t ) ϕ n ( t ) n ρ n Φ n ( t ) ψ n ( t ) n τ n Φ n ( t ) ϕ n ( t ) ] .
γ ˜ = γ L β r s , ζ = β r s L τ p , and ξ = β p r β p s ,

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