Frequency downconversion for a quantum networkYu Ding and Z. Y. Ou*

Department of Physics, Indiana University–Purdue University Indianapolis,402 N. Blackford Street, Indianapolis, Indiana 46202, USA

*Corresponding author: zou@iupui.edu

Received February 2, 2010; revised June 20, 2010; accepted June 28, 2010;posted July 13, 2010 (Doc. ID 123732); published July 26, 2010

By using a parametric downconversion process with a strong signal field injection, we demonstrate coherent fre-quency downconversion from a pump photon to an idler photon. Contrary to a commonmisunderstanding, we showthat the process can be free of quantum noise. With an interference experiment, we demonstrate that the coherenceis preserved in the conversion process. This may lead to a high-fidelity quantum state transfer from a high-frequencyphoton to a low-frequency photon and connects a missing link in a quantum network. With this scheme of coherentfrequency downconversion of photons, we propose a method of single-photon WDM. © 2010 Optical Society ofAmericaOCIS codes: 270.0270, 190.0190, 190.4410, 270.5565.

Photons are generally believed to be good quantum infor-mation carriers for transmission and are dubbed the term“flying qubits,” whereas atoms are best for storing andprocessing the quantum information. Therefore, a quan-tum network usually consists of nodes made of atomsand connected by photons [1]. In the network, quantuminformation is constantly transferred between photonsand atoms and transmitted between atoms via photons.Because quantum information is sensitive to losses, mini-mum losses are required in the network. However, in cur-rent technology, atoms interact best with photons ofwavelength around 0:8 μm [1,2], whereas optical commu-nication system has low losses at 1:6 μm [3]. So there is amismatch between the atomic transition wavelength andthe optical transmission wavelength. Thus it is necessaryto convert photons from one wavelength to another inorder to set up the quantum network.Quantum information transfer between atoms and

photons has been realized [4] in a near-resonance Ramansystem based on the electromagnetically induced trans-parency effect [5–10]. For the photonic state transfer be-tween different wavelengths, a frequency upconversionprocess was realized many years ago [11–16], basedon sum-frequency generation, but none was reportedfor frequency downconversion (to our knowledge). Thisis so because current research focus is on upconvertingphotons at optical communication wavelength (∼1:6 μm)to shorter wavelength (∼0:8 μm) for photon counting inquantum cryptography [16]—detectors at 1:6 μm are justfar more noisy than those at 0:8 μm. Moreover, the noisebehavior in parametric dowconversion process [17] leadsto the belief that it is impossible to have high-fidelityquantum state transfer in a frequency downconversionprocess [12]. Therefore frequency downconversionseems to be the missing link in a quantum network.Frequency conversion was also achieved in four-wavemixing via Bragg scattering in fiber [18,19]. However, be-cause phonons are involved, the frequency shift is rela-tively small.In this Letter, we study a parametric downconversion

scheme for photon frequency downconversion and quan-tum information transfer. We will demonstrate thatcontrary to some misunderstanding about parametricdownconversion, noise-free photon frequency downcon-

version is achievable in this process. We implement aproof-of-principle experiment and show that quantumcoherence is preserved in the process.

The parametric frequency downconversion process isusually described by the Hamiltonian [20–23]:

HPA ¼ iℏηApa†s a

†i − iℏη�asaiA�

p; ð1Þ

where Ap is the strong pump field and usually is treatedas a classical field. s; i stand for “signal” and “idler” fieldsfor historic reason. This leads to the evolution equationfor parametric amplifier:

aðoutÞs ¼ Gas þ ga†i ; aðoutÞi ¼ Gai þ ga†s ; ð2Þ

where G≡ cosh jηApjτ is the amplitude gain andg≡ −ejφp sinh jηApjτ. The appearance of the a† terms inEq. (2) leads to spontaneous quantum noise and the be-lief that frequency downconversion is noisy and cannotpreserve quantum coherence [12,17].

On the other hand, there is another regime of operationinwhichwe inject a strong signal field. This regime is oftenignoredbecauseofgainsaturation: theamplificationof thestrong signal field requires more energy from the pumpfield, which eventually will be depleted. In this regimeof operation, the spontaneous emission for frequencydownconversion isnegligible, andwemayachieveanoise-less frequency downconversion of photons. We will showthis more rigorously in the following.

When the pump field is depleted, we can no longer usethe evolution equations in Eq. (2). We need to start with aHamiltonian for three-wave mixing:

H3W ¼ iℏηapa†s a†i − iℏη�asaia†p: ð3Þ

Here the pump field is also treated quantum mechani-cally. If the signal field is very strong, as in our case here,we can treat it as a classical field and replace it with aconstant As. The pump field and the idler field are quan-tum fields. So the Hamiltonian in Eq. (3) becomes

HFC ¼ iℏηapa†iA�s − iℏη�Asaia

†p: ð4Þ

August 1, 2010 / Vol. 35, No. 15 / OPTICS LETTERS 2591

0146-9592/10/152591-03$15.00/0 © 2010 Optical Society of America

The evolution of the pump and the idler fields is exactlythat for a beam splitter [24] and is given by [20,21]

aðoutÞp ¼ ap cos jηAsjτ þ ejφs ai sin jηAsjτ;aðoutÞi ¼ ai cos jηAsjτ − e−jφs ap sin jηAsjτ; ð5Þ

where ejφs ¼ η�As=jηAsj and τ is the interaction time.When jηAsjτ ¼ π=2, we have aðoutÞp ¼ ejφs ai and aðoutÞi ¼−e−jφs ap. So we may achieve quantum field conversionbetween ai and ap with unit conversion efficiency. Note

that both the frequency downconversion of ap → aðoutÞi

and upconversion of ai → aðoutÞp coexist, and whicheverhappens all depends on what the input field is.In the nonideal case when jηAsjτ < π=2, Eq. (5) is sim-

ply a beam splitter equation, which mixes the two inputstogether coherently. The transmissivity is simplyt≡ cos jηAsjτ, and the reflectance r ≡ sin jηAsjτ.Next, we describe a proof-of-principle demonstration

experiment for photon frequency downconversion. Theexperimental sketch is shown in Fig. 1. The source oflight in our experiment is a femtosecond Ti:sapphire la-ser with a modest power (300 mW) and a repetition rateof 80 MHz. The signal field is directly from the laser witha wavelength of 850 nm. The pump field is from the at-tenuation of the frequency doubling of the laser. Whenthe two pulses are overlapping at a nonlinear crystal(LiIO3) in a noncollinear fashion with a proper anglefor phase matching (Fig. 1), a field with frequency differ-ence (ωi ¼ ωp − ωs) is generated at another direction. Inthe first experiment, we check the linearity of the de-tected idler field as a function of the attenuation factoron the incoming pump field, as predicted from Eq. (5).The result is shown in Fig. 2 in logarithmic scale. It

can be seen that in a range of 2 orders of magnitude,the detected signal follows well the linear dependence.The last point at the low end is due to the limit of thedetector sensitivity. By a direct measurement of inputpower at the pump and output power of the idler, we es-timate the photon conversion efficiency is about 1%. Thelow efficiency is a result of an inefficient nonlinear crys-tal that we pulled out of shelf for the proof-of-principleexperiment. More efficient nonlinear materials like per-iodically poled lithium niobate can significantly improvethe conversion efficiency.

According to Eq. (5), the output-input relation is thatfor a beam splitter, which preserves the phase coher-ence. Thus we check next the phase preservation inthe conversion from the pump field to the idler field. Herewe use the original laser as a reference and beat the gen-erated idler field with a small portion split from the laser(dashed line in Fig. 1). Since the downconversion pro-cess that we are using is a degenerate one withωs ¼ ωi ¼ ωp=2, the generated idler field has the samefrequency as that of the laser. Therefore we should beable to observe the interference effect. Figure 3 showsa trace of the detected combined field at detector D.The phase scan is on the pump field and is achievedby applying a ramp voltage on a piezoelectric transducer(PZT in Fig. 1). The sinusoidal change in the detected sig-nal shows the interference effect between the generatedidler field and the laser field but with a phase dependencefrom the pump field. This clearly demonstrates the coher-ent photon conversion from the pump field to the id-ler field.

The frequency downconversion scheme can be used tocreate a superposition of multiple-frequency componentsfrom an input of single photon of one frequency compo-nent, equivalent to the WDM technique widely used inclassical optical fiber communication. Such a techniquecombines multiple-wavelength components from differ-ent lasers into one field. The source so created has dif-ferent channels that are independent of each other. Sodifferent information can be simultaneously transmittedover a single fiber, thus increasing the channel capacityof the fiber. In quantum communication, we may apply

Fig. 1. Schematics for the demonstration of frequency down-conversion. X2, frequency doubling; DM, dichroic mirror; PZT,piezoelectric transducer; ATT, attenuator; D, photodetector.

Fig. 2. Detected signal size of the idler field as a function of theattenuation factor of the pump field or the transmission coeffi-cient of the attenuator. The solid line is y ¼ ax with a ¼ 7 forbest fit.

Fig. 3. Upper trace, interference fringe between the generatedidler field and the original laser field. Lower trace, ramp signalð=100Þ from the high voltage applied to the PZT for phase scanof the pump field.

2592 OPTICS LETTERS / Vol. 35, No. 15 / August 1, 2010

the same multiplexing technique on quantum informationcarriers, namely, photons. However, since quantum infor-mation requires preservation of quantum superposition,different channels may not be independent of each other.Furthermore, in quantum key distribution (QKD) [25], asingle-photon source is preferred to defeat the photonsplitting attack. Thus, for multichannel QKD, we needa single-photon source with WDM. In the WDM-QKDsystem, we can use multiple single-photon sources withdifferent frequencies, just as in classical optical com-munication. However, single-photon sources are oftenfrom a single quantum system such as atom or ion, whichgives rise to a single frequency. Sometimes we may alsohave only one such kind of system because of limitedresources.Using the frequency downconversion scheme dis-

cussed earlier, we can create multiple-frequency compo-nents from only one single-frequency source andimplement the WDM technique on single photons. Theidea is to use a light source of many wavelengths asthe signal field to drive the three-wave mixing process(Fig. 4). Owing to energy conservation, ωp ¼ ωs þ ωi,the downconverted idler field will have different frequen-cies, ωi1;ωi2;ωi3;…, corresponding to the different fre-quencies of the signal field. The system will behavelike a multiple of beam splitters for the input pump field.If the input pump field is in a single-photon state j1ip, theoutput will be a superposition state of many frequencies,j1ip →

Pk ckj1ωk

i; realizing single-photon WDM. Thestrong signal field of multiple wavelengths can be froma mode-locked laser [26] where all frequency com-ponents are coherent to each other so that the photonso produced is in a superposition state of different fre-quencies. Such a WDM scheme for a quantum sourcepreserves quantum entanglement.

References

1. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys.Rev. Lett. 78, 3221 (1997).

2. A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J.Kimble, Phys. Rev. Lett. 98, 193601 (2007).

3. K. C. Kao and G. A. Hockham, Proc. IEEE 113, 1151 (1966).4. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W.

Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).5. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84,

5094 (2000).6. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and

M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).7. A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D.

Lukin, Phys. Rev. A 65, 031802(R) (2002).8. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, Nature 452,

67 (2008).9. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409,

490 (2001).10. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A.

Musser, B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett.88, 023602 (2001).

11. J. Huang and P. Kumar, Phys. Rev. Lett. 68, 2153 (1992).12. G. Giorgi, P. Mataloni, and F. De Martini, Phys. Rev. Lett.

90, 027902 (2003).13. A. P. VanDevender and P. G. Kwiat, J. Mod. Opt. 51,

1433 (2004).14. M. A. Albota and F. N. C. Wong, Opt. Lett. 29, 1449 (2004).15. R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, Opt.

Lett. 29, 1518 (2004).16. S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin,

and H. Zbinden, Nature 437, 116 (2005).17. C. M. Caves, Phys. Rev. D 26, 1817 (1982).18. C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer,

Opt. Express 13, 9131 (2005).19. A. H. Gnauck, R. M. Jopson, C. J. McKinstrie, J. C. Centanni,

and S. Radic, Opt. Express 14, 8989 (2006).20. W. H. Louisell, Coupled Mode and Parametric Electronics

(Wiley, 1960).21. W. H. Louisell, A. Yariv, and A. E. Siegman, Phys. Rev. A

124, 1646 (1961).22. Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984).23. R. W. Boyd, Nonlinear Optics (Academic, 1992).24. R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A

40, 1371 (1989).25. N. Gisin, G. G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod.

Phys. 74, 145 (2002).26. S. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).

Fig. 4. Single-photon WDM.

August 1, 2010 / Vol. 35, No. 15 / OPTICS LETTERS 2593