Abstract

In this paper, we revisit the well-known Hong–Ou–Mandel (HOM) effect in which two photons, which meet at a beamsplitter, can interfere destructively, leading to null in coincidence counts. In a standard HOM measurement, the coincidence counts across the two output ports of the beamsplitter are monitored as the temporal delay between the two photons prior to the beamsplitter is varied, resulting in the well-known HOM dip. We show, both theoretically and experimentally, that by leaving the delay fixed at a particular value while relying on spectrally resolved coincidence photon counting, we can reconstruct the HOM dip, which would have been obtained through a standard delay-scanning, non-spectrally resolved HOM measurement. We show that our numerical reconstruction procedure exhibits a novel dispersion cancellation effect, to all orders. We discuss how our present work can lead to a drastic reduction in the time required to acquire a HOM interferogram, and specifically discuss how this could be of particular importance for the implementation of efficient quantum-optical coherence tomography devices.

© 2020 Chinese Laser Press

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2020 (1)

2019 (4)

P. Y. Graciano, A. M. A. Martínez, D. Lopez-Mago, G. Castro-Olvera, M. Rosete-Aguilar, J. Garduño-Mejía, R. R. Alarcón, H. C. Ramírez, and A. B. U’Ren, “Interference effects in quantum-optical coherence tomography using spectrally engineered photon pairs,” Sci. Rep. 9, 8954 (2019).
[Crossref]

P.-A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, “Imaging with quantum states of light,” Nat. Rev. Phys. 1, 367–380 (2019).
[Crossref]

C. Agnesi, B. Da Lio, D. Cozzolino, L. Cardi, B. Ben Bakir, K. Hassan, A. Della Frera, A. Ruggeri, A. Giudice, G. Vallone, P. Villoresi, A. Tosi, K. Rottwitt, Y. Ding, and D. Bacco, “Hong-Ou-Mandel interference between independent III-V on silicon waveguide integrated lasers,” Opt. Lett. 44, 271–274 (2019).
[Crossref]

I. R. Berchera and I. P. Degiovanni, “Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology,” Metrologia 56, 024001 (2019).
[Crossref]

2018 (3)

A. Lyons, G. C. Knee, E. Bolduc, T. Roger, J. Leach, E. M. Gauger, and D. Faccio, “Attosecond-resolution Hong-Ou-Mandel interferometry,” Sci. Adv. 4, eaap9416 (2018).
[Crossref]

A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, “Optical sectioning in induced coherence tomography with frequency-entangled photons,” Phys. Rev. A 97, 023824 (2018).
[Crossref]

K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
[Crossref]

2016 (5)

A. Thomas, M. Van Camp, O. Minaeva, D. Simon, and A. V. Sergienko, “Spectrally engineered broadband photon source for two-photon quantum interferometry,” Opt. Express 24, 24947–24958 (2016).
[Crossref]

M. Okano, H. H. Lim, R. Okamoto, N. Nishizawa, S. Kurimura, and S. Takeuchi, “0.54 μm resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography,” Sci. Rep. 5, 18042 (2016).
[Crossref]

M. V. Chekhova and Z. Y. Ou, “Nonlinear interferometers in quantum optics,” Adv. Opt. Photon. 8, 104–155 (2016).
[Crossref]

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou-Mandel interference,” Nat. Photonics 10, 441–444 (2016).
[Crossref]

2015 (2)

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

R.-B. Jin, T. Gerrits, M. Fujiwara, R. Wakabayashi, T. Yamashita, S. Miki, H. Terai, R. Shimizu, M. Takeoka, and M. Sasaki, “Spectrally resolved Hong-Ou-Mandel interference between independent photon sources,” Opt. Express 23, 28836 (2015).
[Crossref]

2014 (1)

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
[Crossref]

2013 (2)

M. Okano, R. Okamoto, A. Tanaka, S. Ishida, N. Nishizawa, and S. Takeuchi, “Dispersion cancellation in high-resolution two-photon interference,” Phys. Rev. A 88, 043845 (2013).
[Crossref]

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Demonstration of high-order dispersion cancellation with an ultrahigh-efficiency sum-frequency correlator,” Phys. Rev. Lett. 111, 193603 (2013).
[Crossref]

2012 (3)

D. Lopez-Mago and L. Novotny, “Quantum-optical coherence tomography with collinear entangled photons,” Opt. Lett. 37, 4077–4079 (2012).
[Crossref]

D. Lopez-Mago and L. Novotny, “Coherence measurements with the two-photon Michelson interferometer,” Phys. Rev. A 86, 023820 (2012).
[Crossref]

M. C. Teich, B. E. A. Saleh, F. N. C. Wong, and J. H. Shapiro, “Variations on the theme of quantum optical coherence tomography: a review,” Quantum Inf. Process. 11, 903–923 (2012).
[Crossref]

2011 (1)

K. A. O’Donnell, “Observations of dispersion cancellation of entangled photon pairs,” Phys. Rev. Lett. 106, 063601 (2011).
[Crossref]

2010 (1)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[Crossref]

2009 (1)

R. Kaltenbaek, J. Lavoie, and K. J. Resch, “Classical analogues of two-photon quantum interference,” Phys. Rev. Lett. 102, 243601 (2009).
[Crossref]

2008 (2)

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys. 4, 864–868 (2008).
[Crossref]

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78, 025804 (2008).
[Crossref]

2007 (1)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

2006 (1)

B. I. Erkmen and J. H. Shapiro, “Phase-conjugate optical coherence tomography,” Phys. Rev. A 74, 041601 (2006).
[Crossref]

2004 (2)

2003 (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref]

2002 (1)

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum-optical coherence tomography with dispersion cancellation,” Phys. Rev. A 65, 053817 (2002).
[Crossref]

2000 (2)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25, 111–113 (2000).
[Crossref]

1999 (1)

I. A. Walmsley, “Measuring ultrafast optical pulses using spectral interferometry,” Opt. Photon. News 10, 28–33 (1999).
[Crossref]

1997 (1)

1996 (1)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[Crossref]

1992 (2)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[Crossref]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[Crossref]

1991 (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[Crossref]

1987 (1)

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]

Abouraddy, A. F.

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum-optical coherence tomography with dispersion cancellation,” Phys. Rev. A 65, 053817 (2002).
[Crossref]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Agnesi, C.

Alarcón, R. R.

P. Y. Graciano, A. M. A. Martínez, D. Lopez-Mago, G. Castro-Olvera, M. Rosete-Aguilar, J. Garduño-Mejía, R. R. Alarcón, H. C. Ramírez, and A. B. U’Ren, “Interference effects in quantum-optical coherence tomography using spectrally engineered photon pairs,” Sci. Rep. 9, 8954 (2019).
[Crossref]

Bacco, D.

Bao, X.-H.

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
[Crossref]

Ben Bakir, B.

Berchera, I. R.

I. R. Berchera and I. P. Degiovanni, “Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology,” Metrologia 56, 024001 (2019).
[Crossref]

Biggerstaff, D. N.

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys. 4, 864–868 (2008).
[Crossref]

Bolduc, E.

A. Lyons, G. C. Knee, E. Bolduc, T. Roger, J. Leach, E. M. Gauger, and D. Faccio, “Attosecond-resolution Hong-Ou-Mandel interferometry,” Sci. Adv. 4, eaap9416 (2018).
[Crossref]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Bowen, W. P.

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Cardi, L.

Carrasco, S.

Castro-Olvera, G.

P. Y. Graciano, A. M. A. Martínez, D. Lopez-Mago, G. Castro-Olvera, M. Rosete-Aguilar, J. Garduño-Mejía, R. R. Alarcón, H. C. Ramírez, and A. B. U’Ren, “Interference effects in quantum-optical coherence tomography using spectrally engineered photon pairs,” Sci. Rep. 9, 8954 (2019).
[Crossref]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Chekhova, M. V.

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[Crossref]

Chinn, S. R.

Cozzolino, D.

Cruz-Delgado, D.

K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
[Crossref]

Cruz-Ramirez, H.

K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
[Crossref]

Cruz-Ramírez, H.

Da Lio, B.

Degiovanni, I. P.

I. R. Berchera and I. P. Degiovanni, “Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology,” Metrologia 56, 024001 (2019).
[Crossref]

Della Frera, A.

Dezfooliyan, A.

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Demonstration of high-order dispersion cancellation with an ultrahigh-efficiency sum-frequency correlator,” Phys. Rev. Lett. 111, 193603 (2013).
[Crossref]

Ding, Y.

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

Drexler, W.

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Phase-conjugate optical coherence tomography,” Phys. Rev. A 74, 041601 (2006).
[Crossref]

Faccio, D.

A. Lyons, G. C. Knee, E. Bolduc, T. Roger, J. Leach, E. M. Gauger, and D. Faccio, “Attosecond-resolution Hong-Ou-Mandel interferometry,” Sci. Adv. 4, eaap9416 (2018).
[Crossref]

Fang, B.

K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
[Crossref]

Fejer, M. M.

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Demonstration of high-order dispersion cancellation with an ultrahigh-efficiency sum-frequency correlator,” Phys. Rev. Lett. 111, 193603 (2013).
[Crossref]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

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T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[Crossref]

Shimizu, R.

Simon, D.

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[Crossref]

Stinson, W. G.

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[Crossref]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917–1920 (1996).
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[Crossref]

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[Crossref]

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M. Okano, H. H. Lim, R. Okamoto, N. Nishizawa, S. Kurimura, and S. Takeuchi, “0.54 μm resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography,” Sci. Rep. 5, 18042 (2016).
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A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, “Optical sectioning in induced coherence tomography with frequency-entangled photons,” Phys. Rev. A 97, 023824 (2018).
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S. Carrasco, J. P. Torres, L. Torner, A. Sergienko, B. E. A. Saleh, and M. C. Teich, “Enhancing the axial resolution of quantum optical coherence tomography by chirped quasi-phase matching,” Opt. Lett. 29, 2429–2431 (2004).
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A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, “Optical sectioning in induced coherence tomography with frequency-entangled photons,” Phys. Rev. A 97, 023824 (2018).
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Vallone, G.

Van Camp, M.

Verma, V. B.

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
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Wakabayashi, R.

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I. A. Walmsley, “Measuring ultrafast optical pulses using spectral interferometry,” Opt. Photon. News 10, 28–33 (1999).
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X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
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J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Demonstration of high-order dispersion cancellation with an ultrahigh-efficiency sum-frequency correlator,” Phys. Rev. Lett. 111, 193603 (2013).
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A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
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Wong, F. N. C.

M. C. Teich, B. E. A. Saleh, F. N. C. Wong, and J. H. Shapiro, “Variations on the theme of quantum optical coherence tomography: a review,” Quantum Inf. Process. 11, 903–923 (2012).
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Yamamoto, T.

T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou-Mandel interference,” Nat. Photonics 10, 441–444 (2016).
[Crossref]

Yamashita, T.

T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou-Mandel interference,” Nat. Photonics 10, 441–444 (2016).
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R.-B. Jin, T. Gerrits, M. Fujiwara, R. Wakabayashi, T. Yamashita, S. Miki, H. Terai, R. Shimizu, M. Takeoka, and M. Sasaki, “Spectrally resolved Hong-Ou-Mandel interference between independent photon sources,” Opt. Express 23, 28836 (2015).
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Yang, J.

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
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T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou-Mandel interference,” Nat. Photonics 10, 441–444 (2016).
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T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
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T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
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K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
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Adv. Opt. Photon. (1)

J. Mod. Opt. (1)

K. Zielnicki, K. Garay-Palmett, D. Cruz-Delgado, H. Cruz-Ramirez, M. F. O’Boyle, B. Fang, V. O. Lorenz, A. B. U’Ren, and P. G. Kwiat, “Joint spectral characterization of photon-pair sources,” J. Mod. Opt. 65, 1141–1160 (2018).
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Metrologia (1)

I. R. Berchera and I. P. Degiovanni, “Quantum imaging with sub-Poissonian light: challenges and perspectives in optical metrology,” Metrologia 56, 024001 (2019).
[Crossref]

Nat. Photonics (2)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou-Mandel interference,” Nat. Photonics 10, 441–444 (2016).
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Nat. Phys. (1)

R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys. 4, 864–868 (2008).
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Nat. Rev. Phys. (1)

P.-A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, “Imaging with quantum states of light,” Nat. Rev. Phys. 1, 367–380 (2019).
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Nature (2)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
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M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
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Opt. Express (2)

Opt. Lett. (5)

Opt. Photon. News (1)

I. A. Walmsley, “Measuring ultrafast optical pulses using spectral interferometry,” Opt. Photon. News 10, 28–33 (1999).
[Crossref]

Photon. Res. (1)

Phys. Rep. (1)

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

Phys. Rev. A (8)

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78, 025804 (2008).
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D. Lopez-Mago and L. Novotny, “Coherence measurements with the two-photon Michelson interferometer,” Phys. Rev. A 86, 023820 (2012).
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[Crossref]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Quantum-optical coherence tomography with dispersion cancellation,” Phys. Rev. A 65, 053817 (2002).
[Crossref]

A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, “Optical sectioning in induced coherence tomography with frequency-entangled photons,” Phys. Rev. A 97, 023824 (2018).
[Crossref]

M. Okano, R. Okamoto, A. Tanaka, S. Ishida, N. Nishizawa, and S. Takeuchi, “Dispersion cancellation in high-resolution two-photon interference,” Phys. Rev. A 88, 043845 (2013).
[Crossref]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
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B. I. Erkmen and J. H. Shapiro, “Phase-conjugate optical coherence tomography,” Phys. Rev. A 74, 041601 (2006).
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Phys. Rev. Lett. (10)

R. Kaltenbaek, J. Lavoie, and K. J. Resch, “Classical analogues of two-photon quantum interference,” Phys. Rev. Lett. 102, 243601 (2009).
[Crossref]

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Demonstration of high-order dispersion cancellation with an ultrahigh-efficiency sum-frequency correlator,” Phys. Rev. Lett. 111, 193603 (2013).
[Crossref]

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917–1920 (1996).
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K. A. O’Donnell, “Observations of dispersion cancellation of entangled photon pairs,” Phys. Rev. Lett. 106, 063601 (2011).
[Crossref]

T.-M. Zhao, H. Zhang, J. Yang, Z.-R. Sang, X. Jiang, X.-H. Bao, and J.-W. Pan, “Entangling different-color photons via time-resolved measurement and active feed forward,” Phys. Rev. Lett. 112, 103602 (2014).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[Crossref]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. 91, 083601 (2003).
[Crossref]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[Crossref]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[Crossref]

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]

Quantum Inf. Process. (1)

M. C. Teich, B. E. A. Saleh, F. N. C. Wong, and J. H. Shapiro, “Variations on the theme of quantum optical coherence tomography: a review,” Quantum Inf. Process. 11, 903–923 (2012).
[Crossref]

Sci. Adv. (1)

A. Lyons, G. C. Knee, E. Bolduc, T. Roger, J. Leach, E. M. Gauger, and D. Faccio, “Attosecond-resolution Hong-Ou-Mandel interferometry,” Sci. Adv. 4, eaap9416 (2018).
[Crossref]

Sci. Rep. (2)

P. Y. Graciano, A. M. A. Martínez, D. Lopez-Mago, G. Castro-Olvera, M. Rosete-Aguilar, J. Garduño-Mejía, R. R. Alarcón, H. C. Ramírez, and A. B. U’Ren, “Interference effects in quantum-optical coherence tomography using spectrally engineered photon pairs,” Sci. Rep. 9, 8954 (2019).
[Crossref]

M. Okano, H. H. Lim, R. Okamoto, N. Nishizawa, S. Kurimura, and S. Takeuchi, “0.54 μm resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography,” Sci. Rep. 5, 18042 (2016).
[Crossref]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Other (2)

Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, 2007).

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

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Figures (9)

Fig. 1.
Fig. 1. (a) Simulation of frequency-delay interferogram r c ( τ , Ω ) . (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Result of integrating the interferogram over τ , yielding a HOM-like dip in the frequency variable Ω . (d) Fourier transform of (a), so as to yield the time-domain interferogram r ˜ c ( τ , T ) . (e) Evaluation of r ˜ c ( τ , T ) at T = 0 , yielding the HOM interferogram. (f) Evaluation of r ˜ c ( τ , T ) at τ = 1    ps . (g) Function A ( Ω ) . (h) Function B ( Ω ) .
Fig. 2.
Fig. 2. (a) Frequency-delay interferogram r c ( τ , Ω ) for two-interface sample (borosilicate coverslip of 170 μm thickness). (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Fourier transform of (a) yielding the time-domain interferogram r ˜ c ( τ , T ) .
Fig. 3.
Fig. 3. (a) and (d) Simulation of the temporal-domain interferogram | r ˜ c ( τ , T ) | for a three-layer sample (intermediate layer at 40% of the sample thickness, in addition to the two extremal interfaces); in (a) we show the case of an SPDC source centered at 775 nm with a narrowband pump (0.1 nm), while in (d) we increase the pump bandwidth to 10 nm. (b) and (e) Evaluation of | r ˜ c ( τ , T ) | at τ 0 = 1.7    ps ; while (b) corresponds to a narrow pump bandwidth (0.1 nm), (e) shows the effect of increasing the bandwidth to 10 nm. (c) and (f) HOM interferogram resulting for the above two cases; (c) for a narrow pump bandwidth (0.1 nm) and (f) for a pump bandwidth of 10 nm.
Fig. 4.
Fig. 4. Experimental setup. Ti:Sa, titanium–sapphire laser; TC, temperature controller; L, plano-convex spherical lens; PPLN, periodically poled lithium niobate nonlinear crystal; SF, set of bandpass and long-pass filters; MPC, manual fiber polarization controller; PMC, polarization-maintaining optical circulator; FC, compensating fiber; S, sample; RM, reference mirror; BS, beamsplitter; FSs, fiber spools; TDC, time-to-digital converter; APD, avalanche photodetectors.
Fig. 5.
Fig. 5. (a) Experimental measurement of the delay-frequency interferogram r c ( τ , Ω ) , for a single-layer sample (plain mirror). (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Result of integrating the interferogram over τ , yielding a HOM-like dip in the frequency variable Ω . (d) Numerical Fourier transform of (a), yielding the time-domain interferogram | r ˜ c ( τ , T ) | . (e) Evaluation of | r ˜ c ( τ , T ) | at T = 0 , yielding the HOM interferogram. (f) Evaluation of | r ˜ c ( τ , T ) | at τ = 1    ps .
Fig. 6.
Fig. 6. Reconstruction procedure for the functions A ( Ω ) and B ( Ω ) , from which we can compute the HOM interferogram through Eq. (6). (a) Evaluation of the delay-frequency interferogram r c ( τ , Ω ) at τ = 1    ps . (b) Numerical Fourier transform of (a), yielding | r ˜ c ( τ 0 , T ) | with τ 0 = 1    ps . (c) and (d) Peaks 1 and 2 isolated from | r ˜ c ( τ 0 , T ) | by restricting the T variable to the two windows indicated in panel (b). (e) Function A ( Ω ) obtained as the inverse Fourier transform of peak 1. (f) Function B ( Ω ) obtained as the inverse Fourier transform of peak 2, multiplied by the phase exp ( i Ω τ 0 ) ; both amplitude and phase are shown.
Fig. 7.
Fig. 7. Reconstructed HOM dip (red line) and conventional HOM dip obtained through scanning the delay with non-frequency-resolved coincidence counting (black dots).
Fig. 8.
Fig. 8. (a) Experimental measurement of the delay-frequency interferogram r c ( τ , Ω ) for a two-layer sample (borosilicate glass coverslip of 170 μm thickness). (b) Result of integrating the interferogram over Ω , yielding the QOCT interferogram. (c) Numerical Fourier transform of (a), yielding the time-domain interferogram | r ˜ c ( τ , T ) | .
Fig. 9.
Fig. 9. Reconstruction of the sample morphology and QOCT interferogram for a two-layer sample (borosilicate glass coverslip of 170 μm thickness). (a) Experimental measurement of the function r c ( τ 0 , Ω ) at a fixed delay τ 0 = 0.363    ps . (b) Numerical Fourier transform of (a), yielding | r ˜ c ( τ 0 , T ) | ; here we have labeled five of the resulting peaks with the numbers 1–5. (c) Reconstructed QOCT interferogram (red line) and conventional delay-scanning, non-spectrally resolved HOM measurement (black points).

Equations (16)

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| ψ = | 0 s | 0 i + η d Ω f ( Ω ) | ω 0 + Ω s | ω 0 Ω i ,
f ( Ω ) = f 0 sinc [ L 2 Δ k ( Ω ) ] exp [ i L 2 Δ k ( Ω ) ] F f ( Ω ) ,
R c ( τ ) = R 0 2 d Ω | f ( Ω ) f ( Ω ) e i Ω τ | 2 .
r c ( τ , Ω ) = 1 2 | f ( Ω ) f ( Ω ) e i Ω τ | 2 ,
R c ( τ ) = R 0 d Ω r c ( τ , Ω ) .
r c ( τ , Ω ) = 1 2 [ A ( Ω ) + B ( Ω ) e i Ω τ + B * ( Ω ) e i Ω τ ] ,
A ( Ω ) = | f ( Ω ) | 2 + | f ( Ω ) | 2 ,
B ( Ω ) = f ( Ω ) f * ( Ω ) .
r ˜ c ( τ , T ) = 1 2 π d Ω r c ( τ , Ω ) e i T Ω ,
r ˜ c ( τ , T ) = 1 2 [ A ˜ ( T ) + B ˜ ( T τ ) + B ˜ ( T τ ) ] .
| τ | < π δ ω .
N = 2 L n M c Δ τ .
r ˜ c ( τ , T ) = F ˜ ( T ) 1 2 F ˜ ( T τ ) + cos ( ω 0 T s ) F ˜ ( T T s / 2 ) cos ( ω 0 T s ) F ˜ [ T ( τ T s / 2 ) ] 1 2 F ˜ [ T ( τ T s ) ] 1 2 F ˜ ( T + τ ) + cos ( ω 0 T s ) F ˜ ( T + T s / 2 ) cos ( ω 0 T s ) F ˜ [ T + ( τ T s / 2 ) ] 1 2 F ˜ [ T + ( τ T s ) ] .
R c ( τ ) = R 0 2 d Ω | f ( Ω ) | 2 | H ( Ω ) H ( Ω ) e i Ω τ | 2 ,
H ( Ω ) = j = 0 N 1 r ( j ) e i ( ω 0 + Ω ) T s ( j ) = r ( 0 ) + r ( 1 ) e i ( ω 0 + Ω ) T s ( 1 ) + ,
H ( Ω ) = j = 0 N 1 r ( j ) e i [ ( ω 0 + Ω ) T s ( j ) + Φ j ( Ω ) ] .

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