Harnessing high-dimensional hyperentanglement through a biphoton frequency comb

Journal name:
Nature Photonics
Volume:
9,
Pages:
536–542
Year published:
DOI:
doi:10.1038/nphoton.2015.110
Received
Accepted
Published online

Abstract

Quantum entanglement is a fundamental resource for secure information processing and communications, and hyperentanglement or high-dimensional entanglement has been separately proposed for its high data capacity and error resilience. The continuous-variable nature of the energy–time entanglement makes it an ideal candidate for efficient high-dimensional coding with minimal limitations. Here, we demonstrate the first simultaneous high-dimensional hyperentanglement using a biphoton frequency comb to harness the full potential in both the energy and time domain. Long-postulated Hong–Ou–Mandel quantum revival is exhibited, with up to 19 time-bins and 96.5% visibilities. We further witness the high-dimensional energy–time entanglement through Franson revivals, observed periodically at integer time-bins, with 97.8% visibility. This qudit state is observed to simultaneously violate the generalized Bell inequality by up to 10.95 standard deviations while observing recurrent Clauser–Horne–Shimony–Holt S-parameters up to 2.76. Our biphoton frequency comb provides a platform for photon-efficient quantum communications towards the ultimate channel capacity through energy–time–polarization high-dimensional encoding.

At a glance

Figures

  1. Generation and quantum revival observations of the high-dimensional biphoton frequency comb.
    Figure 1: Generation and quantum revival observations of the high-dimensional biphoton frequency comb.

    a, Illustrative experimental scheme. FFPC, fibre Fabry–Pérot cavity; FBG, fibre Bragg grating; FPC, fibre polarization controller; LPF, long-pass filter; PBS, polarizing beamsplitter; P, polarizer; S.C., single counts; C.C., coincidence counts. b, Coincidence counting rate as a function of relative delay, ΔT, between the two arms of the HOM interferometer. The HOM revival is observed in the two-photon interference, with dips at 19 time-bins in this case. The visibility change across the different relative delays arises from the single FFPC bandwidth, Δω. The red solid line is the theoretical prediction from the phase-matching bandwidth. Left inset: zoom-in coincidence around zero relative delay between the two arms. The dip width was fit to be 3.86 ± 0.30 ps, which matches well with the 245 GHz phase-matching bandwidth. The measured visibility of the dip is observed at 87.2 ± 1.5, or 96.5% after subtracting the accidental coincidence counts. Right inset: measured bin visibility versus HOM delay, compared with theoretical predictions (Supplementary Section I).

  2. Quantum frequency correlation measurement of the biphoton frequency comb.
    Figure 2: Quantum frequency correlation measurement of the biphoton frequency comb.

    a, Experimental schematic for the frequency correlation measurement. Signal and idler photons are sent to two narrowband filters for the frequency bin correlation measurement with coincidence counting. Each filter consists of a FBG and a circulator. The FBGs have a matched FWHM bandwidth of 100 pm and are thermally tuned for scans from the −4th to +4th frequency bins from the centre. b, Measured frequency correlation of the BFC. The relative coincidence counting rate is recorded while the signal and idler filters are set at different frequency-bin numbers.

  3. Franson interference of the high-dimensional biphoton frequency comb.
    Figure 3: Franson interference of the high-dimensional biphoton frequency comb.

    a, Schematic map and concept of Franson interference of the BFC. The BFC is prepared with high-dimensional correlation features of mode-locked behaviour with a repetition period of T. Franson-type interference between the long–long (L–L) and short–short (S–S) events can therefore be observed when ΔT=NT, where N is an integer. b, Experimental Franson interference set-up. Faraday mirrors (FRMs) are used to compensate the stress-induced birefringence of the single-mode fibre interferometers. A compact optical delay line was used in the longer path of arm2 to achieve different imbalances ΔT (= ΔT2 − ΔT1). Both arms are double-temperature stabilized, first on the custom aluminium plate mountings and second by the sealed enclosures (light blue thick lines).

  4. Measured Franson interference around different relative delays of arm2.
    Figure 4: Measured Franson interference around different relative delays of arm2.

    af, Franson interferences at time-bins #0 (ΔT = 0), #1 (ΔT = 66.7 ps), #2 (ΔT = 133.4 ps), #3 (ΔT = 200.1 ps), #4 (ΔT = 266.9 ps) and #5 (ΔT = 333.6 ps), respectively. Also included in a′ is the interference measured away from the above time-bins at ΔT = 30 ps, with no observable interference fringes. The data points in each panel (of the different relative Franson delays) include the measured error bars across each data set, arising from Poisson statistics, experimental drift and measurement noise. The error bars from repeated coincidence measurements are much smaller than the observed coincidence rates in our measurement and set-up. In each panel, the red line denotes the numerical modelling of the Franson interference on the high-dimensional quantum state. g, Theoretical fringe envelope of Franson interference for the high-dimensional biphoton frequency comb, with superimposed experimental observations. The marked labels (af,a′) correspond to the actual delay points from which the above measurements were taken. h, Witnessed visibility of high-dimensional Franson interference fringes as a function of ΔT. The experimental (and theoretical) witnessed visibilities for the kth-order peaks are 97.8 (100), 93.3 (96.0), 83.0 (86.8), 74.1 (75.6), 59.0 (64.0) and 45.4% (53.3%), respectively.

  5. High-dimensional hyperentanglement on polarization and energy–time basis.
    Figure 5: High-dimensional hyperentanglement on polarization and energy–time basis.

    a, Set-up for the high-dimensional two degree-of-freedom entanglement measurement. The state is generated by mixing the signal and idler photons at the 50:50 fibre beamsplitter with orthogonal polarizations. Perfect temporal overlap between signal and idler photons is ensured by the HOM interference, as already discussed. High-dimensional hyperentanglement is measured with polarization analysis using polarizers P1 and P2, cascaded with a Franson interferometer. λ/2, half waveplate; λ/4, quarter waveplate; λ, multi-order full waveplate. b,c, Measured two-photon interference fringes when P1 is set at 45 and 90 degrees, respectively. The period variance of the fringe on the temporal domain arises because of a slow pump laser drift. d, Measured Bell inequality violation at different time-bins and P1 angles. pol, polarization basis; e–t, energy–time basis.

References

  1. Dada, A. C., Leach, J., Buller, G. S., Padgett, M. J. & Andersson, E. Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nature Phys. 7, 677680 (2011).
  2. Barreiro, J. T., Wei, T. C. & Kwiat, P. G. Beating the channel capacity of linear photonic superdense coding. Nature Phys. 4, 282286 (2008).
  3. Menicucci, N. C., Flammia, S. T. & Pfister, O. One-way quantum computing in the optical frequency comb. Phys. Rev. Lett. 101, 130501 (2008).
  4. Krenn, M. et al. Generation and confirmation of a (100 × 100)-dimensional entangled quantum system. Proc. Natl Acad. Sci. USA 111, 62436247 (2014).
  5. Strobel, H. et al. Fisher information and entanglement of non-Gaussian spin states. Science 345, 424427 (2014).
  6. Howland, G. A. & Howell, J. C. Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera. Phys. Rev. X 3, 011013 (2013).
  7. Bao, W.-B. et al. Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nature Phys. 6, 331335 (2010).
  8. Sun, F. W. et al. Experimental demonstration of phase measurement precision beating standard quantum limit by projection measurement. Europhys. Lett. 82, 24001 (2008).
  9. Badziag, P., Brukner, C., Laskowski, W., Pterek, T. & Zukowski, M. Experimentally friendly geometrical criteria for entanglement. Phys. Rev. Lett. 100, 140403 (2008).
  10. Fickler, R. et al. Quantum entanglement of high angular momenta. Science 338, 640643 (2012).
  11. Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nature Commun. 5, 4502 (2014).
  12. Leach, J. et al. Quantum correlations in optical angle–orbital angular momentum variables. Science 329, 662665 (2010).
  13. Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 15001503 (2010).
  14. Edgar, M. P. et al. Imaging high-dimensional spatial entanglement with a camera. Nature Commun. 3, 984 (2012).
  15. Dixon, P. B., Howland, G. A., Schneeloch, J. & Howell, J. C. Quantum mutual information capacity for high-dimensional entangled states. Phys. Rev. Lett. 108, 143603 (2012).
  16. Franson, J. D. Bell inequality for position and time. Phys. Rev. Lett. 62, 22052208 (1989).
  17. Shalm, L. K. et al. Three-photon energy–time entanglement. Nature Phys. 9, 1922 (2013).
  18. Cuevas, A. et al. Long-distance distribution of genuine energy–time entanglement. Nature Commun. 4, 2871 (2013).
  19. Thew, R. T., Acin, A., Zbinden, H. & Gisin, N. Bell-type test of energy–time entangled qutrits. Phys. Rev. Lett. 93, 010503 (2004).
  20. Lloyd, S., Shapiro, J. H. & Wong, F. N. C. Quantum magic bullets by means of entanglement. J. Opt. Soc. Am. B 19, 312318 (2002).
  21. Ali-Khan, I., Broadbent, C. J. & Howell, J. C. Large-alphabet quantum key distribution using energy–time entangled bipartite states. Phys. Rev. Lett. 98, 060503 (2007).
  22. Zhong, T. et al. Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding. New J. Phys. 17, 022002 (2015).
  23. Takeda, S., Mizuta, T., Fuwa, M., van Loock, P. & Furusawa, A. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature 500, 315318 (2013).
  24. Jayakumar, H. et al. Time-bin entangled photons from a quantum dot. Nature Commun. 5, 4251 (2014).
  25. Marcikic, I. et al. Time-bin entangled qubits for quantum communication created by femtosecond pulses. Phys. Rev. A 66, 062308 (2002).
  26. De Riedmatten, H. et al. Tailoring photonic entanglement in high-dimensional Hilbert spaces. Phys. Rev. A 69, 050304(R) (2004).
  27. Roslund, J., de Araújo, R. M., Jiang, S., Fabre, C. & Treps, N. Wavelength-multiplexed quantum networks with ultrafast frequency combs. Nature Photon. 8, 109112 (2014).
  28. Pinel, O. et al. Generation and characterization of multimode quantum frequency combs. Phys. Rev. Lett. 108, 083601 (2012).
  29. Lu, Y. J., Campbell, R. L. & Ou, Z. Y. Mode-locked two-photon states. Phys. Rev. Lett. 91, 163602 (2003).
  30. Shapiro, J. H. Coincidence dips and revivals from a Type-II optical parametric amplifier. Technical Digest of Topical Conference on Nonlinear Optics, paper FC7-1, Maui, HI, 2002.
  31. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 20442046 (1987).
  32. Zhong, T., Wong, F. N. C., Roberts, T. D. & Battle, P. High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide. Opt. Express 17, 1201912030 (2009).
  33. Gisin, N. & Thew, R. Quantum communication. Nature Photon. 1, 165171 (2007).
  34. Restelli, A. & Bienfang, J. C. Avalanche discrimination and high-speed counting in periodically gated single-photon avalanche diodes. Proc. SPIE. 8375, 83750Z (2012).
  35. Yuan, Z. L., Kardynal, B. E., Sharpe, A. W. & Shields, A. J. High speed single photon detection in the near infrared. Appl. Phys. Lett. 91, 041114 (2007).

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Author information

Affiliations

  1. Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, California 90095, USA

    • Zhenda Xie &
    • Chee Wei Wong
  2. Optical Nanostructures Laboratory, Columbia University, New York, New York 10027, USA

    • Zhenda Xie,
    • Sajan Shrestha,
    • XinAn Xu,
    • Junlin Liang &
    • Chee Wei Wong
  3. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Tian Zhong,
    • Jeffrey H. Shapiro &
    • Franco N. C. Wong
  4. Department of Physics, Southeast University, Nanjing 211189, People's Republic of China

    • Yan-Xiao Gong
  5. Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    • Joshua C. Bienfang &
    • Alessandro Restelli

Contributions

Z.X., T.Z., S.S., X.X. and J.L. performed the measurements. J.C.B. and A.R. developed the 1.3 GHz detectors. T.Z., Y.X.G., F.N.C.W. and J.H.S. provided the theory and samples. All authors helped with manuscript preparation.

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The authors declare no competing financial interests.

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