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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23846–23855
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MHz rate and efficient synchronous heralding of single photons at telecom wavelengths

Enrico Pomarico, Bruno Sanguinetti, Thiago Guerreiro, Rob Thew, and Hugo Zbinden  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 23846-23855 (2012)
http://dx.doi.org/10.1364/OE.20.023846


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Abstract

We report on the realization of a synchronous source of heralded single photons at telecom wavelengths with MHz heralding rates and high heralding efficiency. This source is based on the generation of photon pairs at 810 and 1550 nm via Spontaneous Parametric Down Conversion (SPDC) in a 1 cm periodically poled lithium niobate (PPLN) crystal pumped by a 532 nm pulsed laser. As high rates are fundamental for multi-photon experiments, we show that single telecom photons can be announced at 4.4 MHz rate with 45% heralding efficiency. When we focus only on the optimization of the coupling of the heralded photon, the heralding efficiency can be increased up to 80%. Furthermore, we experimentally observe that group velocity mismatch inside long crystals pumped in a pulsed mode affects the spectrum of the emitted photons and their fibre coupling efficiency. The length of the crystal in this source has been chosen as a trade off between high brightness and high coupling efficiency.

© 2012 OSA

1. Introduction

In recent years, the generation of single photon Fock states has seen a significant increase in interest, not only from a fundamental perspective, but also for their key role in many quantum information applications [1

1. S. A. Castelletto and R. E. Scholten, “Heralded single photon sources: a route towards quantum communication technology and photon standards,” Eur. Phys. J. Appl. Phys. 41, 181–194 (2008). [CrossRef]

, 2

2. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: single-photon sources and detectors,” Rev. Scient. Instrum. 82, 071101 (2011). [CrossRef]

], such as linear-optics quantum computing [3

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nat. 409, 46–52 (2001). [CrossRef]

] and single-photon detectors calibration [4

4. S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” Journ. of Mod. Opt. 56, 1045–1052 (2009). [CrossRef]

]. In the context of quantum communication [5

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

], heralded single photon (HSP) sources could be adopted for a wide range of tasks, like device independent Quantum Key Distribution (QKD) [6

6. N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010). [CrossRef] [PubMed]

] or distribution of entangled photons at a distance via quantum repeaters [7

7. N. Sangouard, C. Simon, J. Minar, H. Zbinden, H. de Riedmatten, and N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76, 050301 (2007). [CrossRef]

, 8

8. N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011). [CrossRef]

].

The idea of a HSP source was introduced for the first time in 1986, when Hong and Mandel [9

9. C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986). [CrossRef] [PubMed]

] showed that a localized one-photon Fock state can be achieved by exploiting the temporal correlation of the photon pairs generated by Spontaneous Parametric Down Conversion (SPDC): one photon can be heralded by the detection of its twin. Due to the probabilistic nature of SPDC, single photons cannot be generated on demand. However, upon detection of one of the twin photons at a heralding rate RH, one can define the heralding efficiency ηH, i.e. the probability of finding a photon in a single mode fibre given the trigger signal. Thus far, significant theoretical and experimental efforts have been made to efficiently couple into fibre single photons generated via SPDC in bulk [10

10. C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001). [CrossRef]

12

12. R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010). [CrossRef]

] or periodically poled crystals [13

13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

, 14

14. P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Phys. Rev. Lett. 105, 253601 (2011). [CrossRef] [PubMed]

], and in nonlinear waveguides [15

15. P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett. 103, 233901 (2009). [CrossRef]

].

In the last two decades, a variety of HSP sources based on SPDC has been realized in an asynchronous configuration, via a CW pump [16

16. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New Journ. of Phys. 6, 163 (2004). [CrossRef]

19

19. M. Tengner and D. Ljunggren, “Characterization of an asynchronous source of heralded single photons generated at a wavelength of 1550 nm”, arXiv:0706.2985v1 (2007).

] and synchronously with a pulsed pump [20

20. A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient conditional preparation of high-fidelity single photon states for fibre-optic quantum networks,” Phys. Rev. Lett. 93, 093601 (2004). [CrossRef]

25

25. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008). [CrossRef] [PubMed]

]. Recently, promising all-fibre synchronous HSP sources based on Four Wave Mixing (FWM) have also been reported [26

26. A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Expr. 17, 6156–6165 (2009). [CrossRef]

29

29. C. Söller, O. Cohen, B. J. Smith, I. A. Walmsley, and C. Silberhorn, “High-performance single-photon generation with commercial-grade optical fibre,” Phys. Rev. A 83, 031806 (2011). [CrossRef]

]. However, only some of these HSP sources are suited to quantum communication applications, where it is necessary to herald with high probability, and rate, the presence of photons at telecom wavelengths into a single mode fibre. The majority of the HSP sources at telecom wavelengths based on SPDC operate in an asynchronous way [16

16. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New Journ. of Phys. 6, 163 (2004). [CrossRef]

19

19. M. Tengner and D. Ljunggren, “Characterization of an asynchronous source of heralded single photons generated at a wavelength of 1550 nm”, arXiv:0706.2985v1 (2007).

]. To the best of our knowledge, the only HSP sources based on pulsed SPDC are reported in [23

23. A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa, and M. Matsui, “Heralded single photon source at 1550 nm from pulsed parametric down conversion,” Journ. of Mod. Opt. 54, 467–471 (2007). [CrossRef]

, 24

24. F. Bussières, J. A. Slater, N. Godbout, and W. Tittel, “Fast and simple characterization of a photon pair source,” Opt. Expr. 16, 17060–17069 (2008). [CrossRef]

], but suffer from poor heralding efficiencies.

Nonetheless, the pulsed pumping regime is more advantageous than the CW one in some quantum communication applications. For example, in QKD the pulsed mode can make the synchronization of multiple communicating parties easier with respect to the CW mode. Some other challenging multi-photon quantum information experiments can take advantage of the pulsed pumping configuration. In particular, our study is motivated by the requirements of a recent proposal to use Sum Frequency Generation (SFG) between single photons belonging to two distinct entangled photon pairs in order to faithfully herald entanglement at a distance [30

30. N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew, and H. Zbinden, “Faithful entanglement swapping based on sum-frequency generation,” Phys. Rev. Lett. 106, 120403 (2011). [CrossRef] [PubMed]

]. The pulsed pumping configuration, with respect to the CW one, allows one to synchronize the arrival of the two single photons in the nonlinear crystal performing the SFG. For this experiment to be feasible, despite the low efficiency of the nonlinear interaction between single photons, high repetition rates and efficient coupling are required.

However, the coupling efficiency of pulsed SPDC sources is usually limited by the group velocity mismatch between the generated photons and the pump pulses inside the nonlinear crystal. Indeed, because of the dispersive properties of the crystal, the SPDC generated photons can acquire a temporal delay with respect to the pump, which can be larger than the pump pulses’ coherence time. Under these conditions, the coherence of the photons emitted from different longitudinal positions within the crystal is lost, resulting in a spatial multimode emission and in a reduction of the fibre coupling. These effects can be limited by reducing the length of the crystal, which, in turn, causes a decrease of the source brightness.

In this paper, we choose the length of the crystal in order achieve a trade off between high brightness and high coupling efficiency. Indeed, we experimentally demonstrate the realization of a synchronous HSP source at telecom wavelengths, based on pulsed SPDC in a 1 cm bulk PPLN crystal, with which telecom photons can be heralded at 4.4 MHz rate with 45% heralding efficiency. To the best of our knowledge, this is the most efficient high rate HSP source based on pulsed SPDC ever reported. We measure a 80% efficiency of announcing a telecom photon, when we concentrate only on the coupling of the heralded photon. Furthermore, by testing a 4 cm crystal in a pulsed and CW pumping configuration, we experimentally investigate how the group velocity mismatch in longer crystals affect the spectrum and the coupling efficiency of the emitted photons.

2. The source

A 430 MHz passively mode-locked laser (Time-bandwidth GE-100-VAN-HP-SHG-430) producing pulses of 8 ps at 532 nm, pumps a 1 cm Type 0 (e,e,e) PPLN bulk crystal (Covesion SFG2) with a 7.10μm poling period which gives the phasematching conditions necessary to produce photon pairs at 810 nm and 1550 nm via SPCD at a temperature of 180 C. This crystal has a clear aperture of 0.5 mm×0.5 mm and is anti-reflection coated on both sides for the pump, signal and idler wavelengths (see Fig. 1). The pump laser is coupled into a polarization maintaining fibre to select a single spatial mode and focused on the crystal with an aspheric lens (Geltech 352110) with focal length f=6.24 mm, which yields a 40μm waist within the crystal.

Fig. 1 Setup of the source. DM: dichroic mirror; IF: interference filter.

The generated signal (810 nm) and idler (1550 nm) photons are separated by a dichroic mirror and collimated using f=150 mm achromatic lenses (Thorlabs AC254-150-B/C). The pump light is removed using equilateral prisms (Schott F2 glass) at the Brewster angle. The photons are then coupled into fibres using aspheric lenses (Geltech 352220-B for the idler with f=11 mm and Geltech 350260-C for the signal with f=15.36 mm). Injecting light backwards through the fibres allows one to check for the correct alignment, for the size of the waists in the crystal and for the transmission in the optical path. On the 810 nm arm, we use an interference filter centered at 810 nm, with a 10 nm bandwidth and 55% transmission, to further remove the pump light.

The heralding photon at 810 nm is detected by a free running Silicon Avalanche PhotoDiode (Si-APD) (Laser Components ‘Count’) with η810 =50% efficiency at 810 nm, 5 Hz dark counts and 110 ns dead time. The telecom photon is detected by an InGaAs APD (ID201, IDQuantique) in gated mode with η1550 =10% efficiency and 10 μs dead time in order to reduce after-pulsing. We measured the dark count probability of this detector at 10 kHz triggering rate to be 8·10−6 per ns.

Note that we assume a 10% relative uncertainty in the calibration of the detectors efficiency, which produces a similar error in the coupling efficiencies reported in this paper. In order to characterize the source, we measure via a Time to Digital Converter (TDC) (Agilent Acqiris TC890) the coincidences between the detections of the InGaAs and the Si detectors as a function of their time difference.

In order to study effects due to the group velocity mismatch in the presence of a pulsed pump, we also test a 4 cm PPLN bulk crystal. In this case, an aspheric lens (Geltech 350280-C) with f=18.40 mm is used for fibre coupling the telecom photon and the distance between the optical elements is set in order to provide the optimal beam waists inside the longer crystal. For further characterization of the source, a CW laser at 532 nm (Laser Quantum Torus) is also used.

2.1. Photon coupling optimization

The coupling efficiency of a single photon (or photon pair) source is a critical parameter, especially in multi-photon experiments where the probability of success decreases with the photon losses to the power of the number of photons involved in the experiment. In [13

13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

] it is theoretically shown that by properly focusing the pump onto a bulk crystal, one can attain SPDC photon emission very close to the single mode of optical fibres, independently of the crystal length. For a monochromatic pump with a specific waist, it is possible to calculate the density matrix of the emitted SPDC two-photon state, which is constrained by phase-matching conditions, in terms of angular and frequency distribution, as described in [13

13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

]. Due to the high dimensionality of the problem, the calculation can be numerically intensive but gives access to the full information about the state, including spatial and spectral correlations. In our case, we use this information for optimizing the pump focusing in order to maximize the fibre coupling.

We calculate with this model that with a beam waist inside the 1 cm crystal of 40 μm for the pump and of 30 μm for the idler and signal beams collected by the corresponding fibres, the photons generated by SPDC in the crystal are emitted with a spatial distribution which has a 96% overlap with a single gaussian mode. Beam waists of 80μm, 60μm, 60μm for the pump, signal and idler respectively are calculated for the 4 cm crystal.

Although there are optimal beam waists, the overlap between the pump and the generated photons can be better than 90% over nearly one order of magnitude in waist size, provided that the collecting optics is chosen accordingly. In order to accurately plan the beam paths and to avoid optics or alignments which could introduce aberrations, we simulated the beams propagation using the optical modeling software “Code V”. All alignment takes advantage of CCD cameras to ensure that the beam profile is of the desired size, to guarantee overlap between the different modes and to avoid the aberrations which can arise if the lenses are not exactly on axis, or if the prism is not at the Brewster-angle.

3. Characterization of a HSP source

Different parameters can be adopted for characterizing a HSP source. Here, we focus on the heralding efficiency and on the conditional autocorrelation function.

3.1. Heralding efficiency

The heralding efficiency ηH is the probability of finding the signal photon (1550 nm) in the single mode fibre once the idler (810 nm) is detected. In our case, ηH is equivalent to the overall transmission of the telecom photon, from the nonlinear crystal to the InGaAs detector. A first and simple way to estimate ηH is to measure the coincidences with the TDC between the InGaAs and the Si-APD detections, with the InGaAs detector triggered by the signal provided by the Si-APD. Indeed, in this situation the overall transmission of the telecom photon is given by:
t1550=ηH=CS810η1550,
(1)
where C is the coincidence count rate and S810 the singles on the Si-APD. Accidental coincidences and dark counts of the Si-APD are subtracted from the value of C and S810 respectively. It is desirable to perform the measurement of t1550 at a low pumping regime, in order to make the emission of multiple photon pairs negligible.

The transmission of the photon at 810 nm, can also provide other useful information about the source. It can be estimated by measuring the coincidences with the InGaAs APD in gated mode but not triggered by the Si detector. Indeed, in this situation the transmission of the idler photon is given by
t810=CS1550η810.
(2)
where C′ are the net coincidence counts in this configuration and S1550 the singles on the InGaAs-APD. Even in this case, we subtract accidental coincidences from the value of C′. We subtract from S1550 a value of dark counts corresponding to a triggering rate equal to the value of S1550 itself. Notice that Eq. (1) and (2) are valid in a regime where the detectors are not in a saturated condition.

Once the overall transmission of the two photons is determined, together with the knowledge of the detectors’ efficiency, one can calculate the number of photon pairs generated per pulse p. This quantity can be also measured by adopting an alternative method [31

31. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002). [CrossRef]

]: the detection of the twin SPDC photons produces the appearance of a coincidence peak in the distribution of the coincidences measured by the TDC with respect to the time delay between the idler and the signal photon. However, for a pulsed source, because of inefficient detection, side peaks, corresponding to coincidences between not correlated photons, are also present. The value of p can also be determined by measuring the ratio between the counts in one side peak and the counts in the main peak.

3.2. Conditional autocorrelation function

The conditional autocorrelation function ga|b(2)(0) of the state of the heralded photon a, given a detection of the heralding photon b, is often adopted as a figure of merit for evaluating the single photon emission of a HSP source. In our case, the photons a and b are the idler at 1550 nm and the signal at 810 nm respectively. For a SPDC source, the ga|b(2)(0) can be calculated exactly using Eq. (24) in [34

34. P. Sekatski, N. Sangouard, F. Bussières, C. Clausen, N. Gisin, and H. Zbinden, “Detector imperfections in photon-pair source characterization,” J. Phys. B: At. Mol. Opt. Phys. 45, 124016 (2011). [CrossRef]

], that can be written in the case of low values of p (p << 1) and no detector noise as
ga|b(2)(0)=fN(2ηb)p+O(p2),
(3)
where fN=1+1N is a factor depending on N, i.e. the number of modes characterizing the state of the heralded photon, and ηb is the overall detection efficiency of the triggering (heralding) photon b, which in our case can be expressed as ηb = t810η810. The factor fN has a value of 2 in the single mode case (N = 1), while it is equal to 1 in the fully multimode configuration. Notice that fN drops quickly to 1 for increasing N.

The ga|b(2)(0) also depends, to a first approximation, on the detection and coupling efficiency of the heralding photon ηb. In particular, ga|b(2)(0) increases for lower values of ηb. In [34

34. P. Sekatski, N. Sangouard, F. Bussières, C. Clausen, N. Gisin, and H. Zbinden, “Detector imperfections in photon-pair source characterization,” J. Phys. B: At. Mol. Opt. Phys. 45, 124016 (2011). [CrossRef]

] the authors take into account a non unit efficiency and non photon number resolving detector.

From Eq. (3), we see that ga|b(2)(0) is proportional, to a first approximation, to the pair generation probability of the source p. Since p represents the main factor on which ga|b(2)(0) depends, it is sufficient to measure p in order to have a good estimation of the autocorrelation function ga|b(2)(0). The autocorrelation function ga|b(2)(0) goes to zero for low values of p. However, for practical applications, a tradeoff between a low ga|b(2)(0) and a high photon generation rate must be found. A pulsed laser with high repetition rate, such as the one used in our experiment, allows one to have high production rates even at relatively low p [32

32. M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Reducing multi-photon rates in pulsed down-conversion by temporal multiplexing,” Opt. Expr. 19, 22698–22708 (2011). [CrossRef]

].

4. Experimental results

4.1. High heralding rate

We first show that with our source one can herald single telecom photons efficiently even at high heralding rates. High heralding rates are allowed by the high repetition rate (430 MHz) of our pump laser. Moreover, they can be achieved with high detection and fibre coupling efficiency of the heralding photon at 810 nm. Therefore, we optimize the fibre coupling of both photons by maximizing the coincidence rate.

We initially characterize the source at low pump power, in order to avoid the saturation of the detectors and to measure more accurately the overall transmission of the photons. At an average pump power of 45 μW, we measure 49 kHz of counts of the Si-APD and 2.2 kHz of coincidences with the InGaAs detector triggered by the Si-APD. Using Eq. (1), we calculate a overall coupling, or heralding efficiency, of the telecom photon of 45%. We measure a 80% transmission through the optical elements on the telecom arm of the source. On the 810 nm arm, we measure instead a overall coupling of 39%. Notice that the lower coupling efficiency at 810 nm is partly due to the presence of additional filtering losses in the 810 nm arm, and to the fact that the collecting single mode fibre, unlike the 1550 nm one, is not anti-reflection coated. With the values mentioned above, we estimate to have generated a number of photon pairs per pulse of p = 6 · 10−4. This value is confirmed by the alternative measurement method described in 3.1. At this point, we increase the average pump power to 7.5 mW, corresponding to p = 0.1, and we measure 4.4 MHz rate on the Si-APD. At 0.1 photons per pulse the expected number of coupled 810 nm photons per second is 16.8 × 106. At these high rates the deadtime of the detector (110±10 ns) has a strong influence on its effective efficiency, reducing it from 50% to 29% [36

36. T. Lunghi, E. Pomarico, C. Barreiro, D. Stucki, B. Sanguinetti, and H. Zbinden, “Advantages of gated silicon single photon detectors,” arXiv:1208.4205

]. We would therefore expect a 4.8 MHz heralding rate instead of the measured 4.4 MHz. This small discrepancy is not due to multi-photon terms which remain negligible even at these rates, but rather to the uncertainty in the measurement of the dead time of the detector.

By using the Eq. (3) in the multimode case, we calculate in this regime for the conditional autocorrelation function ga|b(2)(0) a value of 0.18. This confirms that with our source it is possible to herald single telecom photons even at high heralding rates.

4.2. High heralding efficiency

We now show that very high heralding efficiencies of the telecom photon can also be achieved with our source. Changing the position of the two lenses along the propagation axis of each photon it is possible to mode-match the fiber mode to the mode of the generated photons. Doing so we can choose whether to optimize for heralding efficiency of the 1550 nm photon or for pair coupling efficiency (maximizing the coincidence rate). This arises from the fact that it is possible to align the 810 nm collection optics to match the mode most correlated to the actually collected 1550 nm photons. This effect is predicted in [13

13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

]. We measure the heralding efficiency at rates which are high enough to reduce the effect of dark counts but low enough to avoid detector saturation. At an average pump power of 68 μW, we measure 94 kHz of counts of the Si-APD and 7.5 kHz of coincidences with the InGaAs detector triggered by the Si-APD. Using Eq. (1), we calculate a 80% heralding efficiency of the telecom photon. The photon at 810 nm has an overall transmission of 5%. With the values mentioned above, we calculate p = 0.009.

Using Eq. (3), we find a value for the autocorrelation function ga|b(2)(0) of 0.018. In this regime, corresponding to low values of p and 100 kHz heralding rate, the heralded state corresponds of a single telecom photon of good quality, in the sense that it has a negligible multi-photon component.

4.3. Group velocity mismatch in longer crystals

In order to investigate the coupling efficiency with longer crystals, we test a 4 cm PPLN crystal. With an average pump power of 54 μW, we measure 54 kHz of counts of the Si-APD and 2.6 kHz of coincidences with the InGaAs detector triggered by the Si-APD. The overall transmission of the telecom photon is 48%. We measure an overall transmission of the photon at 800 nm of 24.5%. With these values we calculate a number of photon pairs per pulse p of 0.001. The difference in coupling efficiency between the 1 cm and 4 cm crystal can be attributed in part to the difficulty of aligning the 4 cm crystal which has a 0.5 mm × 0.5 mm clear aperture and in part, as we shall see below, to the fact that the group velocity mismatch between the pump and the photons is more critical in the longer crystal: the photons are not emitted coherently over the all length of the crystal, and therefore they are not in a single spatial mode.

Fig. 2 a) Measured spectrum of the heralded photons in the pulsed and CW pumping configuration for a PPLN bulk crystal of 4 cm of length. The calculated spectrum is also reported. b) Measured spectrum for a PPLN bulk crystal of 1 cm of length in the pulsed regime compared with the theoretical curve.

Let us give a simple, yet illustrative estimation of the effect of the group velocity mismatch in the pulsed pumping mode. The group velocity mismatch per unit length [s/m] is given by the difference of temporal delays of the telecom photon and of the pump pulses
τ=1vg5321vg1550=ng532cng1550c,
(4)
where vg532(1550) and ng532(1550) are the group velocities and group indices of the fields at 532 and 1550 nm, and c is the speed of the light in the vacuum. By considering the PPLN dispersion properties [35

35. D.H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction ne in congruent lithium niobate,” Opt. Lett. 22, 1553–1555, 1997.

], we found, with ng532=2.4746 and ng1550=2.1762 at 180 °C, a τ1550 = 9.994 ps per cm. In a similar way, with ng810=2.2697, we find a delay of τ810 = 6.830 ps per cm for the photon at 810 nm, with a mean delay of 8.412 ps per cm. The group velocity mismatch reduces the effective interaction length between the pump and the down-converted components to a value at which the group delay is close to the coherence time of the pump pulses, which is around 8 ps. Therefore, the group velocity mismatch turns out to be less critical in a PPLN crystal of 1 cm pumped by our laser. Indeed, in the right part of Fig. 2, we report the spectrum of the telecom photons produced by the 1 cm crystal and with the pulsed pump. In this case, the spectrum is in better agreement with the one calculated without considering the group velocity mismatch.

Taking into account these effects seems very important for optimizing the fibre coupling in a pulsed regime for SPDC sources. For this reason an extension of the theoretical model in [13

13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

], taking into consideration the spectral and temporal properties of the pump should be formulated.

5. Comparison with other HSP sources

In Table 1 the most relevant synchronous and asynchronous HSP sources based on SPDC and FWM at telecom wavelength are compared. Different parameters are considered:
  • the repetition rate of the pump laser (fpump);
  • the average pump power (Ppump);
  • the number of photon pairs generated per pulse (p) in the case of synchronous sources, or, alternatively, the number of pairs generated per ns for the asynchronous sources;
  • the spectral bandwidth of the heralded telecom photon (ΔλH);
  • the reported heralding rate (RH and rate Rp=0.1H in the case of p = 0.1);
  • the heralding efficiency (ηH);

Table 1. Comparison between HSP sources based on SPDC and FWM at telecom wavelengths. Synchronous (SYNCH) and asynchronous (ASYNCH) HSP sources are listed in the upper and lower block of the table respectively.

table-icon
View This Table

The results in Table 1 suggest that HSP sources based on SPDC have better heralding efficiencies when working in an asynchronous way. All asynchronous sources listed in Table 1 are based on periodically poled crystals, except for the source in [17

17. O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett. 30, 1539–1541 (2005). [CrossRef] [PubMed]

], made of a nonlinear waveguide. However, this source shows only a 37% coupling, confirming the fact that the waveguide technology still needs optimization in terms of internal losses and single mode operation.

Among the synchronous HSP sources at telecom wavelengths reported in the literature, only two, as far as we know, are based on SPDC [23

23. A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa, and M. Matsui, “Heralded single photon source at 1550 nm from pulsed parametric down conversion,” Journ. of Mod. Opt. 54, 467–471 (2007). [CrossRef]

, 24

24. F. Bussières, J. A. Slater, N. Godbout, and W. Tittel, “Fast and simple characterization of a photon pair source,” Opt. Expr. 16, 17060–17069 (2008). [CrossRef]

]. However, these sources show poor heralding efficiencies of 19% and 12% respectively. In the last few years, more efficient synchronous HSP sources have been obtained with fibre-based FWM, such as in [26

26. A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Expr. 17, 6156–6165 (2009). [CrossRef]

]. However, the source described in this paper, producing single telecom photons at MHz heralding rates with 45% heralding efficiency, turns out to be the fastest and the most efficient among the synchronous HSP sources in the telecom regime.

6. Conclusion

Acknowledgments

We would like to thank valuable discussions with Felix Bussières, Nicolas Sangouard, Pavel Sekatski and Nicolas Gisin. Financial support for this project has been provided by the Swiss National Science Foundation (SFNS) and by Q-Essence.

References and links

1.

S. A. Castelletto and R. E. Scholten, “Heralded single photon sources: a route towards quantum communication technology and photon standards,” Eur. Phys. J. Appl. Phys. 41, 181–194 (2008). [CrossRef]

2.

M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: single-photon sources and detectors,” Rev. Scient. Instrum. 82, 071101 (2011). [CrossRef]

3.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nat. 409, 46–52 (2001). [CrossRef]

4.

S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” Journ. of Mod. Opt. 56, 1045–1052 (2009). [CrossRef]

5.

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

6.

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010). [CrossRef] [PubMed]

7.

N. Sangouard, C. Simon, J. Minar, H. Zbinden, H. de Riedmatten, and N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A 76, 050301 (2007). [CrossRef]

8.

N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80 (2011). [CrossRef]

9.

C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58–60 (1986). [CrossRef] [PubMed]

10.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001). [CrossRef]

11.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fibre-coupling of entangled photons for quantum communication,” Opt. Comm. 227, 343–348 (2003). [CrossRef]

12.

R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010). [CrossRef]

13.

D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A 72, 062301 (2005). [CrossRef]

14.

P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Phys. Rev. Lett. 105, 253601 (2011). [CrossRef] [PubMed]

15.

P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett. 103, 233901 (2009). [CrossRef]

16.

S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New Journ. of Phys. 6, 163 (2004). [CrossRef]

17.

O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett. 30, 1539–1541 (2005). [CrossRef] [PubMed]

18.

S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Optimizing single-photon-source heralding efficiency and detection efficiency metrology at 1550 nm using periodically poled lithium niobate,” Metr. 43, S56–S60 (2006). [CrossRef]

19.

M. Tengner and D. Ljunggren, “Characterization of an asynchronous source of heralded single photons generated at a wavelength of 1550 nm”, arXiv:0706.2985v1 (2007).

20.

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient conditional preparation of high-fidelity single photon states for fibre-optic quantum networks,” Phys. Rev. Lett. 93, 093601 (2004). [CrossRef]

21.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Heralding single photons from pulsed parametric down-conversion,” Opt. Comm. 246, 545–550 (2005). [CrossRef]

22.

S. Castelletto, I. Degiovanni, V. Schettini, and A. Migdall, “Spatial and spectral mode selection of heralded single photons from pulsed parametric down-conversion,” Opt. Expr. 13, 6709–6722 (2005). [CrossRef]

23.

A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa, and M. Matsui, “Heralded single photon source at 1550 nm from pulsed parametric down conversion,” Journ. of Mod. Opt. 54, 467–471 (2007). [CrossRef]

24.

F. Bussières, J. A. Slater, N. Godbout, and W. Tittel, “Fast and simple characterization of a photon pair source,” Opt. Expr. 16, 17060–17069 (2008). [CrossRef]

25.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008). [CrossRef] [PubMed]

26.

A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Expr. 17, 6156–6165 (2009). [CrossRef]

27.

J. A. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fibre source of photon pairs at widely separated wavelengths,” Opt. Lett. 35, 499–501 (2010). [CrossRef] [PubMed]

28.

C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St. J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A 81, 031801 (R) (2010). [CrossRef]

29.

C. Söller, O. Cohen, B. J. Smith, I. A. Walmsley, and C. Silberhorn, “High-performance single-photon generation with commercial-grade optical fibre,” Phys. Rev. A 83, 031806 (2011). [CrossRef]

30.

N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew, and H. Zbinden, “Faithful entanglement swapping based on sum-frequency generation,” Phys. Rev. Lett. 106, 120403 (2011). [CrossRef] [PubMed]

31.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002). [CrossRef]

32.

M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Reducing multi-photon rates in pulsed down-conversion by temporal multiplexing,” Opt. Expr. 19, 22698–22708 (2011). [CrossRef]

33.

A. Soujaeff, T. Nishioka, T. Hasegawa, S. Takeuchi, T. Tsurumaru, K. Sasaki, and M. Matsui, “Quantum key distribution at 1550 nm using a pulse heralded single photon source,” Opt. Expr. 15, 726–734 (2007). [CrossRef]

34.

P. Sekatski, N. Sangouard, F. Bussières, C. Clausen, N. Gisin, and H. Zbinden, “Detector imperfections in photon-pair source characterization,” J. Phys. B: At. Mol. Opt. Phys. 45, 124016 (2011). [CrossRef]

35.

D.H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction ne in congruent lithium niobate,” Opt. Lett. 22, 1553–1555, 1997.

36.

T. Lunghi, E. Pomarico, C. Barreiro, D. Stucki, B. Sanguinetti, and H. Zbinden, “Advantages of gated silicon single photon detectors,” arXiv:1208.4205

OCIS Codes
(030.5260) Coherence and statistical optics : Photon counting
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(270.5290) Quantum optics : Photon statistics
(040.1345) Detectors : Avalanche photodiodes (APDs)
(270.5565) Quantum optics : Quantum communications

ToC Category:
Quantum Optics

History
Original Manuscript: July 3, 2012
Revised Manuscript: September 16, 2012
Manuscript Accepted: September 21, 2012
Published: October 2, 2012

Citation
Enrico Pomarico, Bruno Sanguinetti, Thiago Guerreiro, Rob Thew, and Hugo Zbinden, "MHz rate and efficient synchronous heralding of single photons at telecom wavelengths," Opt. Express 20, 23846-23855 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23846


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References

  1. S. A. Castelletto and R. E. Scholten, “Heralded single photon sources: a route towards quantum communication technology and photon standards,” Eur. Phys. J. Appl. Phys.41, 181–194 (2008). [CrossRef]
  2. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: single-photon sources and detectors,” Rev. Scient. Instrum.82, 071101 (2011). [CrossRef]
  3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nat.409, 46–52 (2001). [CrossRef]
  4. S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” Journ. of Mod. Opt.56, 1045–1052 (2009). [CrossRef]
  5. N. Gisin and R. Thew, “Quantum communication,” Nat. Phot.1, 165–171 (2007). [CrossRef]
  6. N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett.105, 070501 (2010). [CrossRef] [PubMed]
  7. N. Sangouard, C. Simon, J. Minar, H. Zbinden, H. de Riedmatten, and N. Gisin, “Long-distance entanglement distribution with single-photon sources,” Phys. Rev. A76, 050301 (2007). [CrossRef]
  8. N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys.83, 33–80 (2011). [CrossRef]
  9. C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett.56, 58–60 (1986). [CrossRef] [PubMed]
  10. C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A64, 023802 (2001). [CrossRef]
  11. F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fibre-coupling of entangled photons for quantum communication,” Opt. Comm.227, 343–348 (2003). [CrossRef]
  12. R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A81, 053805 (2010). [CrossRef]
  13. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibres,” Phys. Rev. A72, 062301 (2005). [CrossRef]
  14. P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission,” Phys. Rev. Lett.105, 253601 (2011). [CrossRef] [PubMed]
  15. P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett.103, 233901 (2009). [CrossRef]
  16. S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” New Journ. of Phys.6, 163 (2004). [CrossRef]
  17. O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett.30, 1539–1541 (2005). [CrossRef] [PubMed]
  18. S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Optimizing single-photon-source heralding efficiency and detection efficiency metrology at 1550 nm using periodically poled lithium niobate,” Metr.43, S56–S60 (2006). [CrossRef]
  19. M. Tengner and D. Ljunggren, “Characterization of an asynchronous source of heralded single photons generated at a wavelength of 1550 nm”, arXiv:0706.2985v1 (2007).
  20. A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient conditional preparation of high-fidelity single photon states for fibre-optic quantum networks,” Phys. Rev. Lett.93, 093601 (2004). [CrossRef]
  21. T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Heralding single photons from pulsed parametric down-conversion,” Opt. Comm.246, 545–550 (2005). [CrossRef]
  22. S. Castelletto, I. Degiovanni, V. Schettini, and A. Migdall, “Spatial and spectral mode selection of heralded single photons from pulsed parametric down-conversion,” Opt. Expr.13, 6709–6722 (2005). [CrossRef]
  23. A. Soujaeff, S. Takeuchi, K. Sasaki, T. Hasegawa, and M. Matsui, “Heralded single photon source at 1550 nm from pulsed parametric down conversion,” Journ. of Mod. Opt.54, 467–471 (2007). [CrossRef]
  24. F. Bussières, J. A. Slater, N. Godbout, and W. Tittel, “Fast and simple characterization of a photon pair source,” Opt. Expr.16, 17060–17069 (2008). [CrossRef]
  25. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008). [CrossRef] [PubMed]
  26. A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Expr.17, 6156–6165 (2009). [CrossRef]
  27. J. A. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fibre source of photon pairs at widely separated wavelengths,” Opt. Lett.35, 499–501 (2010). [CrossRef] [PubMed]
  28. C. Söller, B. Brecht, P. J. Mosley, L. Y. Zang, A. Podlipensky, N. Y. Joly, P. St. J. Russell, and C. Silberhorn, “Bridging visible and telecom wavelengths with a single-mode broadband photon pair source,” Phys. Rev. A81, 031801 (R) (2010). [CrossRef]
  29. C. Söller, O. Cohen, B. J. Smith, I. A. Walmsley, and C. Silberhorn, “High-performance single-photon generation with commercial-grade optical fibre,” Phys. Rev. A83, 031806 (2011). [CrossRef]
  30. N. Sangouard, B. Sanguinetti, N. Curtz, N. Gisin, R. Thew, and H. Zbinden, “Faithful entanglement swapping based on sum-frequency generation,” Phys. Rev. Lett.106, 120403 (2011). [CrossRef] [PubMed]
  31. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A66, 062308 (2002). [CrossRef]
  32. M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Reducing multi-photon rates in pulsed down-conversion by temporal multiplexing,” Opt. Expr.19, 22698–22708 (2011). [CrossRef]
  33. A. Soujaeff, T. Nishioka, T. Hasegawa, S. Takeuchi, T. Tsurumaru, K. Sasaki, and M. Matsui, “Quantum key distribution at 1550 nm using a pulse heralded single photon source,” Opt. Expr.15, 726–734 (2007). [CrossRef]
  34. P. Sekatski, N. Sangouard, F. Bussières, C. Clausen, N. Gisin, and H. Zbinden, “Detector imperfections in photon-pair source characterization,” J. Phys. B: At. Mol. Opt. Phys.45, 124016 (2011). [CrossRef]
  35. D.H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction ne in congruent lithium niobate,” Opt. Lett.22, 1553–1555, 1997.
  36. T. Lunghi, E. Pomarico, C. Barreiro, D. Stucki, B. Sanguinetti, and H. Zbinden, “Advantages of gated silicon single photon detectors,” arXiv:1208.4205

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