Wavelength-multiplexed quantum networks with ultrafast frequency combs

Journal name:
Nature Photonics
Volume:
8,
Pages:
109–112
Year published:
DOI:
doi:10.1038/nphoton.2013.340
Received
Accepted
Published online

Abstract

Highly entangled quantum networks (cluster states) lie at the heart of recent approaches to quantum computing1, 2. Yet the current approach for constructing optical quantum networks does so one node at a time3, 4, 5, which lacks scalability. Here, we demonstrate the single-step fabrication of a multimode quantum resource from the parametric downconversion of femtosecond-frequency combs. Ultrafast pulse shaping6 is employed to characterize the comb's spectral entanglement7, 8. Each of the 511 possible bipartitions among ten spectral regions is shown to be entangled; furthermore, an eigenmode decomposition reveals that eight independent quantum channels9 (qumodes) are subsumed within the comb. This multicolour entanglement imports the classical concept of wavelength-division multiplexing to the quantum domain by playing upon frequency entanglement to enhance the capacity of quantum-information processing. The quantum frequency comb is easily addressable, robust with respect to decoherence and scalable, which renders it a unique tool for quantum information.

At a glance

Figures

  1. Experimental layout for the creation and characterization of multimode frequency combs.
    Figure 1: Experimental layout for the creation and characterization of multimode frequency combs.

    A titanium–sapphire oscillator produces a 76 MHz train of ~140 fs pulses centred at 795 nm. Its second harmonic synchronously pumps a below-threshold OPO, which consists of a 2 mm bismuth borate (BIBO) crystal contained within a ~4 m ring cavity. The cavity output is analysed with homodyne detection, in which the spectral composition of the LO is manipulated with a 512 element programmable two-dimensional liquid-crystal modulator capable of independent amplitude and phase modulation28. The spectrum of the LO is divided into ten discrete bands of equal energy (enumerated on the figure), and the amplitude and phase of each band can be addressed individually. By varying the relative phase between the shaped LO and the SPOPO output, the and quadrature noises of the quantum state projected onto the LO mode are measured. SHG, second-harmonic generation.

  2. Assessment of Duan inseparability criteria with ultrafast pulse shaping.
    Figure 2: Assessment of Duan inseparability criteria with ultrafast pulse shaping.

    a, Phase-independent excess noise of ~3.4 dB is present in both the high (blue) and low (red) frequency bands. b, The amplitude of the frequency band sum exhibits about −3.2 dB of squeezing. c, The pulse shaper writes a π-phase shift between the spectral wings, and the phase of the difference also shows a squeezing level of about −3.3 dB. Hence the Duan entanglement criterion is verified readily.

  3. Frequency correlations of the quantum comb.
    Figure 3: Frequency correlations of the quantum comb.

    a, Noise correlation matrix, defined as , for the x quadrature. b, EPR (red) and PPT (blue) inseparability criteria for all 511 bipartite combinations of the ten spectral bands, ordered according to increasing EPR values. The black dotted line is taken to be the entanglement boundary for both tests. All 511 bipartitions possess a PPT value below the boundary, which indicates complete non-separability for the state. Additionally, 115 bipartitions satisfy the more stringent criterion for EPR entanglement.

  4. Amplitude spectra and corresponding squeezing values and quadratures for the leading six experimental supermodes retrieved from the covariance matrix.
    Figure 4: Amplitude spectra and corresponding squeezing values and quadratures for the leading six experimental supermodes retrieved from the covariance matrix.

    The black trace is the approximate theoretical Hermite–Gauss form for the supermodes, where the appropriate spectral width is determined from the SPOPO above-threshold spectrum.

References

  1. Menicucci, N. C. et al. Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett. 97, 110501 (2006).
  2. Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621669 (2012).
  3. Yukawa, M., Ukai, R., van Loock, P. & Furusawa, A. Experimental generation of four-mode continuous-variable cluster states. Phys. Rev. A 78, 012301 (2008).
  4. Aoki, T. et al. Quantum error correction beyond qubits. Nature Phys. 5, 541546 (2009).
  5. Su, X. et al. Experimental preparation of eight-partite cluster state for photonic qumodes. Opt. Lett. 37, 51785180 (2012).
  6. Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 19291960 (2000).
  7. Van Loock, P. & Furusawa, A. Detecting genuine multipartite continuous-variable entanglement. Phys. Rev. A 67, 052315 (2003).
  8. Polycarpou, C., Cassemiro, K., Venturi, G., Zavatta, A. & Bellini, M. Adaptive detection of arbitrarily shaped ultrashort quantum light states. Phys. Rev. Lett. 109, 053602 (2012).
  9. Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513577 (2005).
  10. Menicucci, N. C., Flammia, S. T. & Pfister, O. One-way quantum computing in the optical frequency comb. Phys. Rev. Lett. 101, 130501 (2008).
  11. Ukai, R. et al. Demonstration of unconditional one-way quantum computations for continuous variables. Phys. Rev. Lett. 106, 240504 (2011).
  12. Pysher, M., Miwa, Y., Shahrokhshahi, R., Bloomer, R. & Pfister, O. Parallel generation of quadripartite cluster entanglement in the optical frequency comb. Phys. Rev. Lett. 107, 030505 (2011).
  13. Pinel, O. et al. Generation and characterization of multimode quantum frequency combs. Phys. Rev. Lett. 108, 083601 (2012).
  14. Grice, W. P., U'Ren, A. B. & Walmsley, I. A. Eliminating frequency and space–time correlations in multiphoton states. Phys. Rev. A 64, 063815 (2001).
  15. Mosley, P. J. et al. Heralded generation of ultrafast single photons in pure quantum states. Phys. Rev. Lett. 100, 133601 (2008).
  16. Patera, G., Treps, N., Fabre, C. & de Valcarcel, G. J. Quantum theory of synchronously pumped type I optical parametric oscillators: characterization of the squeezed supermodes. Eur. Phys. J. D 56, 123140 (2010).
  17. Hyllus, P. & Eisert, J. Optimal entanglement witnesses for continuous-variable systems. New J. Phys. 8, 51 (2006).
  18. Duan, L-M., Giedke, G., Cirac, J. I. & Zoller, P. Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84, 27222725 (2000).
  19. Bowen, W. P., Schnabel, R., Lam, P. K. & Ralph, T. C. Experimental investigation of criteria for continuous variable entanglement. Phys. Rev. Lett. 90, 043601 (2003).
  20. Simon, R. Peres–Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 27262729 (2000).
  21. Treps, N., Delaubert, V., Maître, A., Courty, J. M. & Fabre, C. Quantum noise in multipixel image processing. Phys. Rev. A 71, 013820 (2005).
  22. Opatrný, T., Korolkova, N. & Leuchs, G. Mode structure and photon number correlations in squeezed quantum pulses. Phys. Rev. A 66, 053813 (2002).
  23. Braunstein, S. L. Squeezing as an irreducible resource. Phys. Rev. A 71, 055801 (2005).
  24. Ferrini, G., Gazeau, J. P., Coudreau, T., Fabre, C. & Treps, N. Compact gaussian quantum computation by multi-pixel homodyne detection. New J. Phys. 15, 093015 (2013).
  25. Armstrong, S. et al. Programmable multimode quantum networks. Nature Commun. 3, 1026 (2012).
  26. Yokoyama, S. et al. Ultra-large-scale continuous-variable cluster states multiplexed in the time domain. Nature Photon. 7, 982986 (2013).
  27. Lamine, B., Fabre, C. & Treps, N. Quantum improvement of time transfer between remote clocks. Phys. Rev. Lett. 101, 123601 (2008).
  28. Vaughan, J., Hornung, T., Feurer, T. & Nelson, K. Diffraction-based femtosecond pulse shaping with a two-dimensional spatial light modulator. Opt. Lett. 30, 323325 (2005).

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Affiliations

  1. Laboratoire Kastler Brossel, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France

    • Jonathan Roslund,
    • Renné Medeiros de Araújo,
    • Shifeng Jiang,
    • Claude Fabre &
    • Nicolas Treps

Contributions

C.F. and N.T. developed and supervised the project. All authors designed the experiments. S.J. designed the optical cavity. J.R. and R.M.A. constructed the apparatus and performed the experiments. All authors contributed to the authorship of the manuscript.

Competing financial interests

The authors declare no competing financial interests.

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