Abstract

Quantum frequency conversion (QFC) of photonic signals preserves quantum information while simultaneously changing the signal wavelength. A common application of QFC is to translate the wavelength of a signal compatible with the current fiber-optic infrastructure to a shorter wavelength more compatible with high-quality single-photon detectors and optical memories. Recent work has investigated the use of QFC to manipulate and measure specific temporal modes (TMs) through tailoring the pump pulses. Such a scheme holds promise for multidimensional quantum state manipulation that is both low loss and re-programmable on a fast time scale. We demonstrate the first QFC temporal mode sorting system in a four-dimensional Hilbert space, achieving a conversion efficiency and mode separability as high as 92% and 0.84, respectively. A 20-GHz pulse train is projected onto 6 different TMs, including superposition states, and mode separability with weak coherent signals is verified via photon counting. Such ultrafast high-dimensional photonic signals could enable long-distance quantum communication at high rates.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (2)

2014 (6)

J. M. Donohue, J. Lavoie, and K. J. Resch, “Ultrafast time-division demultiplexing of polarization-entangled photons,” Phys. Rev. Lett. 113, 163602 (2014).
[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, 1–5 (2014).

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

P. Shadbolt, J. C. F. Mathews, A. Laing, and J. L. O’Brien, “Testing foundations of quantum mechanics with photons,” Nat. Phys. 10, 278–286 (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, 1–8 (2014).

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).

2013 (3)

2012 (4)

L. Ma, O. Slattery, and X. Tang, “Single photon frequency up-conversion and its applications,” Phys. Rep. 521, 69–94 (2012).
[Crossref]

T. Ralph and R. Mann, “Relativistic quantum information,” Class. Quantum Grav. 29, 220301 (2012).

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

J. S. Pelc, G.-L. Shentu, Q. Zhang, M. M. Fejer, and J.-W. Pan, “Up-conversion of optical signals with multi-longitudinal-mode pump lasers,” Phys. Rev. A 86, 033827 (2012).

2011 (5)

2010 (2)

2009 (2)

2008 (1)

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77, 033815 (2008).
[Crossref]

2006 (2)

R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, and H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).

R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, and H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform generation and characterization using spectral line-by-line control,” J. Lightwave Technol. 24, 2487–2494 (2006).

2004 (2)

2002 (2)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

1999 (1)

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A 59, 4249–4254 (1999).
[Crossref]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

J. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,” IEEE Trans. Autom. Control 37, 332–341 (1992).
[Crossref]

1990 (1)

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2010).

Aleksic, S.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Andriolli, N.

Anisimova, E.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

Apostolopoulos, D.

Avramopoulos, H.

Barbosa, G. A.

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175–179.

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref]

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175–179.

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, 1–17 (2015).
[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, 1–5 (2014).

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, 13770–13778 (2011).
[Crossref]

B. Brecht, A. Eckstein, and C. Silberhorn, “Experimental implementation of a quantum pulse gate for multi-mode quantum networks,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2013), paper QTu1C.2.

Brunner, N.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Cavalcanti, D.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref]

Christ, A.

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, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 1–4 (2011).
[Crossref]

Cirac, J. I.

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A 59, 4249–4254 (1999).
[Crossref]

Corzo, N. V.

Cova, S.

R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, and H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).

Dong, H.

H. Pan, E. Wu, H. Dong, and H. Zeng, “Single-photon frequency up-conversion with multimode pumping,” Phys. Rev. A 77, 033815 (2008).
[Crossref]

Donohue, J. M.

J. M. Donohue, J. Lavoie, and K. J. Resch, “Ultrafast time-division demultiplexing of polarization-entangled photons,” Phys. Rev. Lett. 113, 163602 (2014).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

Eckstein, A.

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, 1–5 (2014).

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 1–4 (2011).
[Crossref]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19, 13770–13778 (2011).
[Crossref]

B. Brecht, A. Eckstein, and C. Silberhorn, “Experimental implementation of a quantum pulse gate for multi-mode quantum networks,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2013), paper QTu1C.2.

Ekert, A. K.

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A 59, 4249–4254 (1999).
[Crossref]

Erasme, D.

Fejer, M. M.

Fontaine, N.

N. Fontaine, R. Scott, D. Geisler, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and measurement to increase the flexibility, fidelity and bandwidth of optical networks,” in Communication Systems, Networks Digital Signal Processing (CSNDSP) (2012), pp. 1–4.

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and detection in InP photonic integrated circuits for Tb/s optical communications,” Opt. Commun. 284, 3693–3705 (2011).
[Crossref]

Fujimura, M.

Geisler, D.

N. Fontaine, R. Scott, D. Geisler, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and measurement to increase the flexibility, fidelity and bandwidth of optical networks,” in Communication Systems, Networks Digital Signal Processing (CSNDSP) (2012), pp. 1–4.

Gisin, N.

R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, and H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref]

Harris, J. S.

Herbst, T.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

Huang, Y. P.

V. G. Velev, C. Langrock, P. Kumar, M. M. Fejer, and Y. P. Huang, “Selective manipulation of overlapping quantum modes,” in IEEE Photonics Society Summer Topical Meeting Series (2014), pp. 138–139.

Huang, Y.-P.

Huelga, S. F.

J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A 59, 4249–4254 (1999).
[Crossref]

Huo, Y.

Jelezko, F.

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

Jennewein, T.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

Jiang, X.

Jiang, Z.

Jin, G.

Kanter, G. S.

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref]

Klonidis, D.

Kofler, J.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

Köprülü, K. G.

Kowligy, A. S.

Krainer, L.

R. T. Thew, S. Tanzilli, L. Krainer, S. C. Zeller, A. Rochas, I. Rech, S. Cova, and H. Zbinden, and N. Gisin, “Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).

Kropatschek, S.

X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, and A. Zeilinger, “Quantum teleportation over 143 kilometres using active feed-forward,” Nature 489, 269–273 (2012).
[Crossref]

Kumar, P.

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Figures (6)

Fig. 1.
Fig. 1.

Mode-separable frequency conversion. The temporal modes S 1 - S 4 were computed by simulating the SPDC process. Together with S 5 and S 6 , superpositions of S 1 and S 2 , these input signal pulses are converted in a mode-separable manner by appropriately shaped pump pulses P 1 - P 6 inside the nonlinear medium. In our work, the 6 × 6 mode combinations are investigated as two 4 × 4 alphabets: S 1 - S 4 with P 1 - P 4 , and S 3 - S 6 with P 3 - P 6 . For an input signal S j and pump P k in a given alphabet, the signal ideally remains undepleted at the output (black dotted line) if j k . Otherwise, if j = k , its frequency gets converted (red dashed line). This provides a way to separate the different modes.

Fig. 2.
Fig. 2.

Detailed optical schematic. The figure shows the different interconnected setups involved in the optimal preparation of the pump and signal waveforms, various (intermediate) measurements to ensure the optimality, mode-separable frequency conversion, and the (final) power or photon counting measurements. Details of the individual components and operation of these setups are given in the main text. All solid blue/green lines denote fiber-optical paths, while the dotted and dashed lines denote free-space links. FPC, fiber polarization controller; PM/AM, phase/amplitude modulator; WS, waveshaper; PODL, programmable optical delay line; OSw, optical switch; OSA, optical spectrum analyzer; FB-ST, fiber stretcher; PD, photodiode; WDM, wavelength division (de-)multiplexer; VATT, variable attenuator; WG, waveguide; PwM, classical power meter; ATF, angle tuned filter; OSO, optical sampling oscilloscope; SPAD, single-photon avalanche diode.

Fig. 3.
Fig. 3.

Interference visibility versus delay and pump-phase optimization. (a) Interference patterns with S 3 as the reference signal on WS-B. The delay value on the PODL that yields the lowest S 4 - S 3 visibility sets the origin. After the interferometric rectification, the measurements show good matches between the theoretical (dashed) and experimental (solid) curves. (b) By means of optimizing the phase of the 17 comb lines of pump P 3 , we obtain around 20% increase in S 3 conversion, which is directly related to η 33 per Eq. (2).

Fig. 4.
Fig. 4.

Conversion efficiencies of signals S 1 - S 4 measured at various average pump powers and pump-signal delay. For all pump powers (indicated in boxes), the delay was varied in steps of 0.2 ps. The maximum separability was obtained at an average pump power ρ 1 fin = 25    mW and delay δ 11 fin = 33.4    ps , indicated by the shaded rectangle in (b). Error bars are included but may be too small to be observed.

Fig. 5.
Fig. 5.

Conversion efficiency results from the two 4 × 4 alphabets. For any given pump P k , the average pump power and relative delay between the pump and signal pulses in the experiment were the same across all four signals S j .

Fig. 6.
Fig. 6.

Experimental separability results with classical ( μ 1 ) and weak coherent ( μ < 1 ) signals S 1 - S 6 that were upconverted by pump waveforms P 1 - P 6 in a mode-separable manner. These results were obtained at a pump-signal delay δ k k fin and pump power ρ k fin . Separabilities evaluated using the simulation model are also shown.

Equations (2)

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σ k = η k k j = 1 N η k j ,
η = ρ sum λ sum ρ sig λ sig ,

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