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Quantum communication networks require single photon frequency converters, whether to shift photons between wavelength channels, to shift photons to the operating wavelength of a quantum memory, or to shift photons of different wavelengths to be of the same wavelength, to enable a quantum interference. Here, we demonstrate frequency conversion of laser pulses attenuated to the single photon regime in an integrated silicon-on-insulator device using four-wave mixing Bragg scattering, with conversion efficiencies of up to 12%, or 32% after correcting for nonlinear loss created by the pump lasers. The frequency shift can be conveniently chosen by tuning of the pump frequencies. We demonstrate that such frequency conversion enables interference between photons at different frequencies.
© 2016 Optical Society of America
1. Introduction
In quantum information, there are several applications for a single photon frequency converter. Single photon sources emitting visible wavelengths need to be shifted to telecom wavelengths for long distance transmission, and telecom photons can be shifted to visible for more convenient detection [1,2]. Quantum memories, required to synchronize single photons in time, are often based on atomic transitions and compatible only with specific frequencies, so it is vital to be able to shift a photon to the operating wavelength of a memory [3]. Many quantum optics experiments rely on Hong-Ou-Mandel (HOM) interference between photons of the same frequency [4], such as quantum teleportation [5], entanglement swapping [6], and in two-photon logic gates for quantum computation [7]. In particular, quantum communication over extended distances relies on quantum repeater schemes combining multiple photon sources, memories, and HOM interferences, so frequency conversion is essential to interfacing these separate components, and should ideally take place in an integrated device so that the converter is compatible with other photonic-chip-based components. It is also generally desirable to multiplex many frequency channels in quantum communications and optical quantum computing, and route photons between channels [8].
Frequency conversion of single photons can be realized using second-order (χ(2)) nonlinear processes such as sum and difference frequency generation [9], or a third-order (χ(3)) nonlinear process called four-wave mixing Bragg scattering (FWMBS). The frequency shift via a χ(2) nonlinear process is equal to the frequency of the pump laser, and tends to be very large, so the focus has been on shifting between visible and telecommunication wavelengths. In FWMBS the shift is equal to the difference Δ between the frequencies of two pumps, which allows more flexibility when small shifts are required. In addition, as FWMBS relies on a χ(3) nonlinearity, this allows frequency conversion in a wide range of materials, because all materials exhibit some χ(3) response, whereas those with a χ(2) response are more limited. In particular, frequency conversion in silicon is a goal because it opens up CMOS compatibility and integration into more complex devices.
FWMBS has been demonstrated in optical fibers [10–12], although either low conversion efficiencies or noise introduced by spontaneous Raman scattering of the pump have been problematic, until recently when Raman noise has been reduced in a liquid nitrogen cooled fiber [13]. Recently FWMBS has been demonstrated in silicon nitride waveguides [14–16], for conversion between 980 nm and 1550 nm, and for small separations around 980 nm, though not for small separations around 1550 nm. In this work, we demonstrate FWMBS in a silicon device in the single photon regime, converting pulses containing an average of one photon between telecom wavelengths. A silicon frequency converter has the potential for integration into more complex photonic and electronic circuits, where it could be one component in a quantum relay device or a single photon router. As crystalline silicon has a very narrow Raman peak at a separation of 15.6THz from the pump, Raman background is easily avoided, and so silicon has the advantage of being effectively Raman noise free at room temperature. We demonstrate single photon regime interference between two input frequencies, allowing the detection of a photon in a coherent superposition of the two frequencies.
2. Experiment
The principle of FWMBS is shown in Fig. 1(a). In other four-wave mixing processes, such as parametric amplification or phase conjugation, energy is transferred from a pump laser to the signal, and spontaneous four-wave mixing can occur, introducing excess noise photons. In FWMBS the process cannot occur spontaneously in the absence of a signal photon. This feature makes FWMBS intrinsically noiseless [17]. While noiseless frequency conversion has applications in classical communications, it is critical in quantum optics, because for single photon or few photon signals even a small amount of noise can be fatal to the encoded information, or can destroy quantum coherence.
Fig. 1 (a) Four-wave mixing Bragg scattering. Two pump frequencies ωp1 and ωp2 in a nonlinear medium coherently convert the signal at ωin to ωout (b) Experimental setup. A spectral pulse shaper (SPS) selects out two pump frequencies and an input signal from a broadband laser pulse. The pump pulses are amplified in an erbium doped fiber amplifier (EDFA) and then a bandpass filter (BPF) removes spontaneous emission. Pump and signal are recombined in a silicon nanowire where FWMBS takes place. The output is measured on an optical spectrum analyzer (OSA) or with an arrayed waveguide grating (AWG) and single photon detectors (SPDs).
The experimental setup shown in Fig. 1(b) consists of a broadband mode-locked fiber laser extending from 1538 nm to 1565 nm, with 40 MHz repetition rate. It is filtered into two pump pulses, of equal power, and an input signal, using a spectral pulse shaper (SPS: Finisar Waveshaper). The SPS is able to independently control the transmission and phase-shift as a function of frequency. The pump pulses are amplified by an erbium doped fiber amplifier and then bandpass filters are used to remove spontaneous emission. A tunable fiber delay line is used in the signal channel to synchronize it with the pump pulses at a 99:1 coupler, re-combining the pumps and signal while attenuating the signal by 20 dB. This leaves the signal weak but far above the single photon regime, allowing classical characterization. The common output is coupled to the chip, which consists of a 2 cm silicon-on-insulator (SOI) nanowire with grating couplers at input and output, with a 450 × 220 nm cross-section, fabricated using ePIXfab at IMEC with 193 nm deep UV lithography. FWMBS scattering driven by the pump pulses occurs on the chip, and then for classical characterization the output is sent to an optical spectrum analyzer (OSA). For single photon regime measurements the frequencies are separated out by an arrayed waveguide grating (AWG) with 100 GHz channel spacing, followed by bandpass filters for additional pump light suppression, then sent to superconducting nanowire single photon detectors (SPDs, 10% efficiency). The extra attenuation to reach the single photon regime was applied using the SPS, and the average number of photons in the signal was 1 per pulse at the start of the chip, based on the total output counts at zero pump power, and extrapolating from the known losses and detection efficiencies.
The signal wavelength was set to 1538.9 nm and the longer wavelength pump was set to 1563.6 nm. Spontaneous four-wave mixing of the pumps is suppressed by phase mismatch. The shorter pump wavelength was varied to give pump frequency separations of 100, 200, 300, and 400 GHz. The current limitation in going to wider separations is that stimulated four-wave mixing between the pumps will create new pump frequencies, and will start to contaminate the signal with background photons, but this could be avoided by moving the pumps to longer wavelengths. The bandwidth of each pump was kept at 12.5 GHz and the signal bandwidth was 25 GHz. When pulsed pumps are used, it is preferable to have the signal shorter in time, and hence larger in bandwidth, otherwise components of the signal at different times will experience different pump fields and hence will be converted at different efficiencies [18].
Figure 2(a) shows output spectra measured on the OSA for the different pump separations, with the total average pump power immediately before the chip fixed at 2.8 mW. It can be seen that significant amounts of input signal are both red-shifted and blue-shifted by an amount equal to the pump separation Δ, and that, for the smaller separations, secondary and even tertiary side peaks are generated. This is because multiple FWMBS processes can occur efficiently, so the input is shifted in either direction and with sufficient pump power it can be shifted multiple times. In contrast, FWMBS in fiber involves much longer interaction lengths, so the phase-matching of the process becomes more critical, and it is unlikely that multiple processes will be phase-matched simultaneously. In a short waveguide, the phase-matching can only have a small effect: the phase mismatch due to dispersion can be approximately described by δβ = β2 Δ (ωin-ωp1) for up-shifting and δβ = β2 Δ (ωin-ωp2) for down-shifting, with the group-velocity dispersion β2 expected to be 3.7x10−24s2/m for the waveguide at wavelengths around 1550nm, based on a numerical simulation of the waveguide mode. Over a length of 2cm and for the frequency separations used here, this can only reduce the efficiency of FWMBS by a fraction sinc2(δβL/2) ≈ 4x10−5 of its phase-matched efficiency. There is also a nonlinear term in the phase mismatch proportional to the difference in pump powers, γ(P1-P2): if one of the pump beams is several times stronger than the other then this could become significant, but this is not the case here. Even in this case, since the phase mismatch due to dispersion is negligible, the nonlinear phase mismatch will affect up- and down- shifting processes equally, so this could not be used to suppress spurious processes. Hence the efficiency with which the input can be shifted to a desired output frequency is limited by the spurious scattering processes to other frequencies [19]. Increasing the length of the waveguide could improve this, but only if the dispersion is correct to phase-match the desired process, and if propagation loss in the waveguide is sufficiently low, as shown in section 3.
Fig. 2 (a) Measured spectra for pump separations of 400 GHz to 100 GHz, with the total pump power fixed at 2.8 mW. (b) Total loss of the chip, including grating couplers and linear propagation loss, varying with total average pump power due to nonlinear loss. The peak power before the chip in each pump frequency is approximately 500 times the total average power, and the peak power after coupling to the chip is reduced a further 5dB. (c) SPD count rates, with background subtracted, in blue- and red-shifted channels (blue squares and red triangles respectively). Blue and red lines show background level in blue- and red-shifted channels (d) Normalized count rates as a fraction of input counts, with nonlinear loss factored out. Black circles: input wavelength; blue squares: blue-shifted peak; red triangles: red-shifted peak At higher powers the three channels do not sum to 1, due to spurious processes converting photons to other channels.
In the waveguide used, the coupling loss to fiber at the signal wavelength was about 5 dB for each grating coupler, which could be avoided using low-loss inversed tapers [20]. The couplers are currently the largest source of loss, and improving this would enable frequency conversion of heralded single photon sources from existing photon pair sources. The propagation loss was 2 dB/cm when the pump power was close to zero. This could be avoided by using a shorter waveguide (a correspondingly higher pump power would be required, not possible here due to technical limitations), or lower loss silicon waveguide geometries have been demonstrated. However, when the pump power was increased, the signal experienced increased loss due to cross two photon absorption with the pump [21], as shown from a classical measurement in Fig. 2(b). This is the only significant source of loss which is intrinsic to the material, and so cannot be avoided. The measured variation of loss with pump power was used to normalize out loss when calculating conversion efficiencies. After the chip, the loss from the AWG was about 2dB, and the single photon detector efficiency was 10%.
Figure 2(c) shows the count rates in the first red- and blue-shifted peaks as a function of pump power for a single photon regime input signal, with a 200 GHz pump separation. Comparing these count rates to that in the input channel with the pumps off (265kHz), maximum conversion efficiencies are extracted of 12% in the red direction and 11% in the blue. This occurs at a power of 1.6mW, beyond which the counts decrease due to increased nonlinear loss and photons coupling into the secondary peaks seen in Fig. 2(a). The input channel is depleted to 4% of its original count rate, or 13% if the increase of nonlinear loss with pump power is factored out. If the other counts are corrected for nonlinear loss, as shown in Fig. 2(d), maximum conversion efficiencies of 32% and 31% are extracted in red and blue directions respectively. These loss-corrected conversion efficiencies are the relevant ones to realizing a frequency beamsplitter as proposed in [8] – here, it is not possible to realize a 50:50 splitter between two channels, due to the spurious processes coupling photons into other channels, but we show below a method by which we can still demonstrate a high-contrast interference fringe. A background level of noise photons [Fig. 2(d)] has been subtracted from the counts, which is due to Raman scattering of the pump in the fibers before and after the chip, and spontaneous four-wave mixing of the pumps. This becomes more significant at higher pump powers, so in the following measurements the total pump power was fixed at 1 mW, where the background was about 10 dB smaller than the level of converted signal photons. It is expected that the weak coherent inputs could be replaced with heralded single photons and the conversion efficiencies would be unaffected, since the wavelength and bandwidth of the inputs are comparable to those generated by existing silicon-based telecom pair-photon sources [22], though the signal to noise ratio would clearly depend on the brightness of the source.
3. Simulations
A split-step fourier simulation was used to model the experiment [23]. We assume this approach is able to describe both the classical and single photon regime experiments [24], with the complex amplitude of a weak classical field or the wavefunction of a photon undergoing the same evolution along the waveguide. The simulation is based on the nonlinear Schrödinger equations for the combined pump and combined signal amplitudes:
With Ap the pump amplitude and As the signal amplitude. The linear loss coefficient α was chosen to give 2dB/cm loss, as seen experimentally. The nonlinear phase-shift and nonlinear loss coefficients γ and αTPA were 250/W/m and 100/W/m, fairly typical values for a silicon nanowire, which fit the power dependence of the experiment. The group-velocity dispersion and third order dispersion were obtained from a separate simulation of the nanowire structure, with β2 = 3.7x10−24s2/m and β3 = 10−38s3/m. Figure 3(a) shows the results as a function of total pump power. The simulation is in good agreement with the experimental results, with a maximum corrected conversion efficiency of 33%.Fig. 3 (a) Simulated count rates as pump power is varied. Black line: depleted input signal; Blue: blue-shifted signal; Red: red-shifted signal; Purple: double blue-shifted; Brown: double red-shifted. (b) Simulated results for a hypothetical improved 10cm waveguide.
Improving this conversion efficiency requires dispersion engineering of the waveguide, combined with a longer length and a low propagation loss. This allows a desired Bragg scattering process to be phase-matched, and sufficient phase mis-match to suppress other processes. In particular the third-order dispersion should be increased compared to the group-velocity dispersion, to maximize the blue-shifted signal. Figure 3(b) shows the simulation results when the third-order dispersion is increased by a factor of 1000, with a length of 10 cm, and the linear loss reduced to 0.5 dB/cm (the nonlinear loss coefficient is unchanged, as it is a material parameter). Conversion efficiencies >60% are possible, and a 50:50 beamsplitter can be realized between two neighboring frequency channels. A more favourable ratio of group-velocity dispersion to third-order dispersion could be found by increasing the width of the waveguide, and this is also expected to decrease propagation losses. Separate numerical simulation shows that a zero-dispersion wavelength exists at 1550nm for a 700x220nm waveguide, which would allow phase-matching of the desired process. Losses as low as 0.3dB/cm have been seen in etchless silicon waveguides [25], so 0.5dB/cm is realistic.
4. Interference between frequency channels
Here, we demonstrate the application of FWMBS to detecting photons in a superposition state of two frequencies. Recently, Ramsey inteferomtry of single photons was demonstrated using cascaded FWMBS to split photons into two frequencies, then recombine them after a variable delay [26]. In [26] the interference contrast was limited by the conversion efficiency of FWMBS, which is not the case here. Further, there the interference fringe was only stable because the same pumps were used to split the photons and recombine them, so this cannot be used to detect frequency superposition states generated by a remote source unless the FWMBS pump lasers are used to create the original superposition state, and then are transmitted along with the state. As we show below, otherwise the relative phase between the two pumps must be stabilized.
The SPS is configured to have two signal pass-bands, providing two input signals at ω1 and ω2. The quantum state can be expressed as the product of two coherent states:
When the coherent states are sufficiently weak and we consider single photon detections from the SPDs, the relevant part of the state contains one photon, which after renormalizing can be expressed as:Detecting this superposition state may be useful in quantum key distribution schemes which encode information in the photons’ frequency and arrival times [27, 28]. Here, we observe interference between two frequencies by setting, so that both frequencies are shifted to the center frequency ωout = (ω1 + ω2)/2 with approximately equal probability ε. With the average pump power 1mW, ε is approximately 20%. In our experiment, Δ was kept at 200 GHz, and ω2 was added at 400 GHz below ω1. The probability of detecting the photon at ωout is equal towhere θ is the relative phase between inputs and θp1 and θp2 are the phases of the two pump pulses. Note that this allows high contrast interference in a single channel, and hence a high quality measurement of a superposition state, even when the efficiency ε is low. This is because the two input channels are mixed equally in this central channel, so they can cancel completely. In the other channels, the input signals will not mix equally, so a lower contrast is expected. The pump pulses must be phase-stable with respect to each other for a stable interference fringe to be observed. Phase stability between the pump and the signal is not required. The frequency difference between the pumps cancels out the rapid oscillations in time of θ, and because the two pump pulses are emitted from the same source and follow the same path, θp1 ‒ θp2 is stable against small changes in path length. Figure 4(a) shows two experimental spectra measured on the OSA, demonstrating constructive and destructive interference of the peak at ωout. The SPS has been used to tune the phase of the input signal at ω2. Destructive interference almost completely removes the peak at ωout, while constructive interference enhances it considerably. A smaller variation is seen in the input peaks so that energy is conserved. Figure 4(b) shows an interference fringe in the single photon regime as the phase is varied between 0 and 2π. The raw visibility is 80%, calculated as (Maximum-Minimum)/(Maximum + Minimum) for this channel. After correction for the background level of detections created by the pump this visibility is increased to 86%. The corrected visibility is thought to be limited by imperfect overlap in time or spectrum between converted photons from the two input frequencies: although the spectra appeared well-overlapped on the OSA, the nonlinear process could leave differing frequency chirps on the up- and down-converted signals, or they could have experienced different dispersion, leading to imperfect interference.Fig. 4 (a) Measured spectra for input frequencies ω1 and ω2 interfering at ωout constructively (top) and destructively (bottom). (b) Single photon regime interference as the relative phase is varied. The red line shows the background of noise created by the pump.
5. Conclusion
In conclusion, we have demonstrated frequency conversion of single photon regime signals using FWMBS in an integrated silicon device. The frequency shift is flexible and easily tuned using the separation between two pump frequencies. Conversion efficiency to a particular frequency is limited by spurious Bragg scattering processes, which scatter the input to other undesired frequencies. These processes could be eliminated using a long dispersion engineered waveguide, so that only the desired process is phase-matched, although it would also be necessary to reduce the propagation losses. Even with low conversion efficiencies, it is possible to observe high contrast interference between disparate input frequencies, by converting both input frequencies with equal probability to a central frequency half-way between them. This enables the detection of coherent superpositions of frequencies, which is useful in quantum key distribution as a test of security when time-frequency entanglement of photon pairs is used.
Acknowledgments
This work was funded by Australian Research Council (ARC) Centre of Excellence CUDOS (CE110001018), ARC Laureate Fellowship (FL120100029), and ARC Discovery Early Career Researcher Award (DE120100226).
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