Abstract

The low-decoherence regime plays a key role in constructing multi-particle quantum systems and has therefore been constantly pursued in order to build quantum simulators and quantum computers in a scalable fashion. Quantum error correction and quantum topological computing have been proved to be able to protect quantumness but have not yet been experimentally realized. Recently, topological boundary states are found to be inherently stable and are capable of protecting physical fields from dissipation and disorder, which inspires the application of such topological protection on quantum correlation. Here we present an experimental demonstration of topological protection of two-photon quantum states against the decoherence in diffusion on a photonic chip. By analyzing the quantum correlation of photons out from the topologically nontrivial boundary state, we obtain a high cross-correlation and a strong violation of Cauchy–Schwarz inequality up to 30 standard deviations. We further prepare different quantum sources and experimentally confirm that the topological protection is robust to the wavelength difference as well as distinguishability of two photons. Our results, together with our integrated implementation, provide an alternative way of protecting quantumness and may inspire many more explorations in “quantum topological photonics”, a crossover between topological photonics and quantum information.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, H. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91, 015006 (2019).
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Y. Wang, Y.-H. Lu, F. Mei, J. Gao, Z.-M. Li, H. Tang, S.-L. Zhu, S. Jia, and X.-M. Jin, “Direct observation of topology from single-photon dynamics,” Phys. Rev. Lett. 122, 193903 (2019).
[Crossref]

Y. Wang, J. Gao, X. L. Pang, Z. Q. Jiao, H. Tang, Y. Chen, L. F. Qiao, Z. W. Gao, J. P. Dou, A. L. Yang, and X. M. Jin, “Parity-induced thermalization gap in disordered ring lattices,” Phys. Rev. Lett. 122, 013903 (2019).
[Crossref]

2018 (5)

A. Blanco-Redondo, B. Bell, D. Oren, B. J. Eggleton, and M. Segev, “Topological protection of biphoton states,” Science 362, 568–571 (2018).
[Crossref]

S. Mittal, E. A. Goldschmidt, and M. Hafezi, “A topological source of quantum light,” Nature 561, 502–506 (2018).
[Crossref]

J. L. Tambasco, G. Corrielli, R. J. Chapman, A. Crespi, O. Zilberberg, R. Osellame, and A. Peruzzo, “Quantum interference of topological states of light,” Sci. Adv. 4, eaat3187 (2018).
[Crossref]

H. Tang, X. F. Lin, Z. Feng, J. Y. Chen, J. Gao, X. Y. Xu, Y. Wang, L. F. Qiao, A. L. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref]

H. Tang, C. D. Franco, Z. Y. Shi, T. S. He, Z. Feng, J. Gao, K. Sun, Z. M. Li, Z. Q. Jiao, T. Y. Wang, M. S. Kim, and X. M. Jin, “Experimental quantum fast hitting on hexagonal graphs,” Nat. Photonics 12, 754–758 (2018).
[Crossref]

2017 (1)

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13, 611–617 (2017).
[Crossref]

2016 (3)

2015 (3)

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349, 622–624 (2015).
[Crossref]

B. M. Terhal, “Quantum error correction for quantum memories,” Rev. Mod. Phys. 87, 307–346 (2015).
[Crossref]

Z. Chaboyer, T. Meany, L. G. Helt, M. J. Withford, and M. J. Steel, “Tunable quantum interference in a 3D integrated circuit,” Sci. Rep. 5, 9601 (2015).
[Crossref]

2014 (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

2013 (8)

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental boson sampling,” Nat. Photonics 7, 540–544 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, and M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7, 1001–1005 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

2012 (2)

X.-H. Bao, A. Reingruber, P. Dietrich, J. Rui, A. Dück, T. Strassel, L. Li, N.-L. Liu, B. Zhao, and J.-W. Pan, “Efficient and long-lived quantum memory with cold atoms inside a ring cavity,” Nat. Phys. 8, 517–521 (2012).
[Crossref]

Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, “Topological states and adiabatic pumping in quasicrystals,” Phys. Rev. Lett. 109, 106402 (2012).
[Crossref]

2011 (1)

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7, 907–912 (2011).
[Crossref]

2010 (1)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

2009 (3)

N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, “Observation of optical Shockley-like surface states in photonic superlattices,” Opt. Lett. 34, 1633–1635 (2009).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102, 253904 (2009).
[Crossref]

2008 (2)

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100, 170506 (2008).
[Crossref]

C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, “Non-abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
[Crossref]

2007 (2)

S. Chen, Y.-A. Chen, B. Zhao, Z.-S. Yuan, J. Schmiedmayer, and J.-W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[Crossref]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express 15, 1579–1587 (2007).
[Crossref]

2004 (1)

J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, “Realization of quantum error correction,” Nature 432, 602–605 (2004).
[Crossref]

1996 (1)

1980 (1)

S. Aubry and G. André, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1980).

1974 (1)

J. F. Clauser, “Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect,” Phys. Rev. D 9, 853–860 (1974).
[Crossref]

1955 (1)

P. G. Harper, “Single band motion of conduction electrons in a uniform magnetic field,” Proc. Phys. Soc. London Sect. A 68, 874–878 (1955).
[Crossref]

Aaronson, S.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

Amo, A.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, H. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91, 015006 (2019).
[Crossref]

André, G.

S. Aubry and G. André, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1980).

Armando, P. L.

Aubry, S.

S. Aubry and G. André, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Isr. Phys. Soc. 3, 133–164 (1980).

Bao, X.-H.

X.-H. Bao, A. Reingruber, P. Dietrich, J. Rui, A. Dück, T. Strassel, L. Li, N.-L. Liu, B. Zhao, and J.-W. Pan, “Efficient and long-lived quantum memory with cold atoms inside a ring cavity,” Nat. Phys. 8, 517–521 (2012).
[Crossref]

Barbieri, M.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Barrett, M. D.

J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, “Realization of quantum error correction,” Nature 432, 602–605 (2004).
[Crossref]

Bell, B.

A. Blanco-Redondo, B. Bell, D. Oren, B. J. Eggleton, and M. Segev, “Topological protection of biphoton states,” Science 362, 568–571 (2018).
[Crossref]

Blakestad, R. B.

J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, “Realization of quantum error correction,” Nature 432, 602–605 (2004).
[Crossref]

Blanco-Redondo, A.

A. Blanco-Redondo, B. Bell, D. Oren, B. J. Eggleton, and M. Segev, “Topological protection of biphoton states,” Science 362, 568–571 (2018).
[Crossref]

Britton, J.

J. Chiaverini, D. Leibfried, T. Schaetz, M. D. Barrett, R. B. Blakestad, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, and D. J. Wineland, “Realization of quantum error correction,” Nature 432, 602–605 (2004).
[Crossref]

Brod, D. J.

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102, 253904 (2009).
[Crossref]

Broome, M. A.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

Bryant, G.

Carusotto, I.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, H. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91, 015006 (2019).
[Crossref]

Chaboyer, Z.

Z. Chaboyer, T. Meany, L. G. Helt, M. J. Withford, and M. J. Steel, “Tunable quantum interference in a 3D integrated circuit,” Sci. Rep. 5, 9601 (2015).
[Crossref]

Chapman, R. J.

J. L. Tambasco, G. Corrielli, R. J. Chapman, A. Crespi, O. Zilberberg, R. Osellame, and A. Peruzzo, “Quantum interference of topological states of light,” Sci. Adv. 4, eaat3187 (2018).
[Crossref]

Chen, J. Y.

H. Tang, X. F. Lin, Z. Feng, J. Y. Chen, J. Gao, X. Y. Xu, Y. Wang, L. F. Qiao, A. L. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref]

Chen, K. P.

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13, 611–617 (2017).
[Crossref]

Chen, S.

S. Chen, Y.-A. Chen, B. Zhao, Z.-S. Yuan, J. Schmiedmayer, and J.-W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[Crossref]

Chen, Y.

Y. Wang, J. Gao, X. L. Pang, Z. Q. Jiao, H. Tang, Y. Chen, L. F. Qiao, Z. W. Gao, J. P. Dou, A. L. Yang, and X. M. Jin, “Parity-induced thermalization gap in disordered ring lattices,” Phys. Rev. Lett. 122, 013903 (2019).
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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Band structure and the schematic diagram of the topological system. (a) The photons will be confined in the boundary of the lattice when the photons are injected from the boundary with ϕ = 0.2 , which is the result of (b), i.e., the gaps between bands are crossed by two topologically nontrivial boundary modes (represented with the yellow and dark gray lines for the E > 0 and E < 0 cases, respectively) in band structure. (c) The photons injected from the middle site tend to evolve into different sites for the bulk state. The parameters are adopted as t = 0.5 , λ = 0.5 , b = ( 5 + 1 ) / 2 .
Fig. 2.
Fig. 2. Experimental setup. Pair-like correlated photons with a wavelength of 810.4 nm are simultaneously generated from PPKTP crystal; both photons are prepared to horizontal polarization after a half-wave plate (HWP) and a polarizing beam splitter (PBS) with 25% probability as shown in the inset i, and then they are injected into the lattice. Two photons out of a certain site, spatially selected by an iris, are detected by APDs after being split by a fiber beam splitter. A counter (not shown in the setup) is used to record the coincidence of the photon pairs. The single-photon counts and coincidence together can give the cross-correlation. By inserting a polarizer (Pol), also shown in the inset ii, the signal photon and the idler photon can be chosen individually with the same probability of 25%, and then their auto-correlation can be measured separately. The detection can be switched into a single-photon sensitive ICCD for the measurement on photon outgoing distribution. QWP, quarter-wave plate; LPF, long-pass filter.
Fig. 3.
Fig. 3. Experimental results of the photon probability distribution and the coincidence counts (labeled in right) over 300 s. (a) The measured probability distribution of outgoing photons from the boundary state (represented with the red histogram) obtained from ICCD and the measured coincidence counts over 300 s at the output of the lattice (represented with black dots) obtained from APDs. There are only seven sites around the boundary state, and eight sites in the bulk state have observable probabilities. The values of coincidences for the other sites are too low to be detected in a reasonable amount of time. (b) and (c) Accumulated part images of photon probability distribution over 1500 s of (b) the boundary state and (c) the bulk state. The color bar normalizes the distribution with the maximal value of each sample. (d) The measured results for the outgoing photons from the bulk state. The measured coincidence counts are much smaller than that in the boundary state. The hollow histograms present the simulated results.
Fig. 4.
Fig. 4. Measured cross-correlation g ( 2 ) of the outgoing photons. The value of g s i ( 2 ) for the leftmost site ( n = 1 , protected site) up to 10.70 ± 0.25 approaches to that of the input state. Both the sites near by the leftmost site and the sites in the bulk state are not topologically protected by the boundary state; all of them have comparably much smaller g s i ( 2 ) as well as very large variances. Site 21, 30, 31, 32, 36, 38, and 39 are measured in the bulk state.
Fig. 5.
Fig. 5. Measured cross-correlation g ( 2 ) of the outgoing photons with distinguishable wavelength. (a) The spectra of two frequency-correlated distinguishable photons. The wavelengths of horizontal and vertical photons become different after tuning the temperature of PPKTP crystal. (b) The measured cross-correlation of the distinguishable photons. The value of g s i ( 2 ) for the leftmost site ( n = 1 ) up to 24.08 ± 1.90 approaches to that of the input state g s i ( 2 ) = 30.00 ± 0.30 . The sites near by the leftmost site for the topologically nontrivial boundary state and the sites in the bulk state all have comparably much smaller g s i ( 2 ) . Site 21, 30, 31, 32, and 36 are measured in the bulk state.
Fig. 6.
Fig. 6. Measured coincidence count of the outgoing indistinguishable photons. (a) The joint spectrum and (b) the Hong–Ou–Mandel dip imply that two indistinguishable photons at wavelength of 810 nm are well obtained. The inset in (a) is the joint spectrum before being reshaped by bandpass coherent filters. The white curve is the measured spectrum transmission rate of the filters. The coincidence count at zero delay is twice larger than that at larger delay for both the protected site in (c) the boundary state and (d) the unprotected site in the bulk state, while the count of the bulk state is one-ninth of that of the boundary state. Site 31 is measured in the bulk state.

Tables (1)

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Table 1. Measured Cross-Correlation, Auto-Correlation, and Violation of the Cauchy–Schwarz Inequality a

Equations (2)

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H = n t ( 1 + λ cos ( 2 π b n + ϕ ) ) a ^ n a ^ n + 1 + H.c. ,
( g s i ( 2 ) ) 2 g s s ( 2 ) · g i i ( 2 ) ,

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