1. Introduction

Classical communication based on RSA encryption is inherently insecure to attacks from a future quantum computer. Secure communication can be provided through the use of quantum key distribution (QKD) [1]. QKD can be used to generate symmetric secret keys and distribute them between two users via a quantum mechanical link. QKD has the advantage that the secret key can be distributed with absolute certainty that it was not intercepted. Typically photons are used, as their quantum properties remain intact over the large distances required for useful communication. Fiber optics provides the ideal channel for transmitting QKD photons and building a secure key. If a photon is intercepted in flight by a malicious third party and the result is re-sent in the measured basis then the eavesdropper can be readily detected and communication ceased [2–4]. The information-theoretic security and eavesdropper detection makes QKD a promising route to future-proof global information security. Typically quantum signals are sent in a dark fiber [5] or in free-space [6–8] for QKD demonstrations; however one would like to carry both quantum and classical signals in fiber simultaneously to make use of the full global fiber optic infrastructure. Previously, quantum and classical signals have been transmitted in the same single-mode fiber by way of wavelength division multiplexing [9,10] or polarization multiplexing, or a combination of the two [11].

In this paper, quantum and classical signals are transmitted through a fiber supporting more than one spatial mode, showing excellent isolation between modes of up to 35 dB and the high fidelity reconstruction and collection of launched modes. Multimode fibers (MMF) are the dominant type used in short-reach communication links such as Local Area Networks (LAN) and modern datacenters and it is demonstrated here that this additional spatial degree of freedom can be used to provide increased isolation between the quantum and classical channels. Mode division multiplexing is being actively investigated for increasing the capacity of classical communications networks [12,13]. The larger effective area of the modes in an MMF also leads to lower nonlinearities, one of the motivations behind the use of mode division multiplexing (MDM) in classical telecommunications. In particular, the presence of spontaneous Raman scattering (SpRS) has previously [5,14] been put forward as a major limitation of transmitting single-photon and classical channels simultaneously. If the classical signal is transmitted on a higher-order mode then SpRS is reduced, not only due to the larger effective area of the mode, but any SpRS that does occur is also less likely to be captured by the fundamental mode on which the single-photon channel is propagating [15]. Previous experiments of encoding single-photons onto spatial modes have been either in free-space [16,17] or in hollow-core fiber [18] and recovery of a single-photon in the presence of mixing between the spatial modes has never previously been demonstrated. In this experiment, standard step-index fiber is used and the mixing between the spatial and polarization modes of the fiber which occurs during propagation is undone to recover the original single-photon at the receiver.

2. Experiment

2.1 Experimental overview

The spatial light modulator (SLM) based mode multiplexing system (MMUX) [19] of Fig. 1, in combination with a polarization controller (PC) has the ability to couple light from each of its input single-mode fibers (SMFs) independently into arbitrary spatial and polarization modes of the few-mode fiber (FMF). In the reverse direction, this system can be used to detect an arbitrary spatial and polarization mode at the other end of the FMF as a mode demultiplexer. The fiber in this case is a 2 m length of step-index fiber which supports a total of six spatial and polarization modes, which in the weak-guidance approximation [20] correspond to the degenerate horizontally and vertically polarized fundamental Gaussian modes (0H, 0V) and the degenerate positive and negative topological charge orbital angular momentum (OAM) modes in both polarizations ( + 1H, + 1V, −1H, −1V).

 

Fig. 1 Wavelength, polarization and spatial mode multiplexing system for single-photon and classical signals. ECL: external cavity laser; SPS: single-photon source; AWG: arrayed waveguide grating; BPF: band-pass filter; PC: polarization controller; MMUX: mode-multiplexer; FMF: few-mode fiber; CWDM: coarse wavelength division multiplexer; PM: power meter; POL: polarizer; SSPD: superconducting single-photon detector.

Download Full Size | PDF

2.2 Spatial light modulator mode multiplexing system

Figure 2(a) illustrates the mode multiplexing/demultiplexing system that is used at either side of the fiber to transmit/receive arbitrary mode/polarization states [19]. The SLM is shown as if it were a transmissive device for clarity, but in reality it is reflective and the optics on either side of the SLM in Fig. 2(a) are positioned on-top of one another, rather than in the same plane. The multiplexer consists of an array of input/output single-mode fibers, each representing an independent channel to be launched into the fiber. The beams from the fiber array enter polarisation diversity optics which creates two beams representing orthogonal polarisations, but which are both aligned to the polarisation axis required by the liquid crystals of the SLM. The two beams reflect off the left and right side of the SLM respectively, allowing each polarisation to be addressed independently by the device. The two polarisations are then recombined and focused into the FMF.

 

Fig. 2 (a) Spatial light modulator based arbitrary mode/polarization multiplexing system. (b) Example transmit phase mask. (c) Example receive phase mask.

Download Full Size | PDF

Examples of the phase masks programmed onto the surface of the SLM are shown in Figs. 2(b) and 2(c) for the transmitter and receiver respectively. The masks are the wavefronts of the interference between the modes for each channel incident on the SLM at the angles corresponding with the assigned input/output single mode fiber for that channel. Hence when the mask is illuminated by a beam incident on the SLM at the correct angle, it excites the desired mode in the FMF. As shown in Fig. 2(b), at the transmitter the two channels are orthogonally polarized and as such there is no interference and the masks for each of the channels are completely separate. On the left, for the horizontal polarization, the mask is effectively a blazed grating (with aberration correction) which simply redirects the Gaussian beam from the input fiber directly onto the core of the FMF. On the right, for the vertical polarization, the blazed grating has a different period corresponding with the angle of the other input fiber, but it also contains a fork dislocation at the centre which converts the input Gaussian beam into an OAM mode. For the receiver side, the phase pattern of the mask is more complicated as the two channels are no longer orthogonally polarized, nor does their polarization necessarily align with the polarization axis of the SLM system. Hence the masks consist of the interference between the two modal superpositions that arrive at the receiver due to each of the two modes launched at the transmitter.

2.3 Heralded single-photon source

Single-photon measurements were performed using a silicon photonic crystal waveguide single-photon source [21,22] (SPS) of Fig. 1. The source setup is shown schematically in Fig. 3(a).A wavelength-tunable pulsed pump laser set to 1556 nm was coupled to the photonic crystal waveguide using polymer access waveguides and inverse tapers, resulting in a 5 dB per facet loss. Two photons from the pump pulse were annihilated to create signal and idler photons of higher and lower energy through the process of spontaneous four-wave mixing (SFWM), as shown in Fig. 3(b). The photonic crystal was dispersion engineered by shifting the two rows of holes closest to the waveguide creating a slow light region over 15 nm wide [23]. This region had a slow-down factor S ≈10, defined as the ratio of the group index inside the waveguide over the group index of bulk silicon. The nonlinearity of the waveguide is enhanced by S², thereby enhancing the SFWM efficiency by S⁴. The generated photons were separated using an arrayed waveguide grating (AWG) before passing through 0.5 nm bandpass filters (BPF). The idler photon at 1561 nm was then detected using a superconducting single-photon detector (SSPD) and heralds the presence of the signal photon at 1551 nm which can then be forwarded to the MMUX system.

 

Fig. 3 A schematic of spontaneous four-wave mixing. (a) a pulse enters the photonic crystal waveguide and is slowed, causing an increase in peak power and interaction time in the waveguide. Two photons from the pump are annihilated to create signal and idler photons of higher and lower energy, as described by the arrows in (b). The photons and residual pump then exit the waveguide.

Download Full Size | PDF

3. Results and analysis

3.1 Propagation matrix

A photon launched into a particular mode |a⟩ at one end of the fiber, will arrive at the other in some corresponding mode |b⟩. In the approximation of a lossless fiber, |b⟩ = U |a⟩ where U is the propagation matrix, an N × N unitary matrix which in this instance is of N = 6. The propagation matrix U was measured classically [13] with the resulting amplitude and phase shown in Figs. 4(a) and 4(b) respectively. U is measured using the same basis set of modes {|a_i⟩} at either end, which are illustrated for clarity along the x and y axes. Even over short distances mode coupling is likely to occur, at least between the degenerate modes, meaning U is unlikely to be the identity. This can be seen in Fig. 4(a) where even over a length of only two metres, the OAM state is not maintained and arrives as a superposition of modes. However the modal coupling is almost entirely within a degenerate mode-group, with the two LP_0,1 states and four OAM states remaining mostly independent of each other to form the 2x2 and 4x4 sub-matrices visible in Fig. 4(a). Hence when the MMUX1 at one end of the fiber is programmed to launch |a_i⟩, the MMUX2 at the other end of the fiber must be programmed to detect |b_i⟩ in order to extract the launched channel. The heralded photons at 1551 nm were coupled into the FMF using MMUX1 and assigned to a polarized mode |a_i⟩. After propagation the photon was detected using another SSPD after being demultiplexed by MMUX2 from mode |b_j⟩ to measure all 6 × 6 values of ⟨b_j|a_i⟩ with the results shown in Fig. 2(c). As would be expected, significant photon counts are only registered for measurements of ⟨b_i|a_i⟩ confirming the orthogonality of the modes, where the diagonal elements contained at least 700 coincidences collected for 120 s and were then normalized. This is consistent with the classically measured matrix |UU*|, shown in Fig. 4(d) where the overlap between elements in each column of the matrix was always less than −22dB.

 

Fig. 4 Classically measured (a) amplitude of the propagation matrix U (b) Phase of the propagation matrix U. (c) Single-photon measurement of UU* and (d) Numerical evaluation of the amplitude of UU* using (a) and (b).

Download Full Size | PDF

3.2 Mode multiplexed single-photon and classical channels

A classical information channel was simulated using a 1531 nm external cavity laser (ECL) which passed through a 0.5 nm BPF to reduce spectral noise before passing into MMUX₁ where it was assigned to a vertically polarized higher-order OAM mode, as shown in Fig. 1. The heralded single-photon channel again originated from the SPS and was coupled into the other port of MMUX₁ and assigned to the horizontally polarized fundamental mode of the fiber. At the other end of the FMF, MMUX₂ demultiplexed the two spatial channels to two separate output fibers. The leakage of the classical channel into the single-photon channel output fiber immediately after MMUX₂ was measured to be approximately −35 dB. This isolation is provided by the spatial and polarization filtering the MMUX₂ system provides and is the isolation between the channels as measured at the point after MMUX₂ but before the CWDM of Fig. 1. The single-photon channel then passed through a coarse-wavelength division demultiplexer (CWDM) and a 0.5 nm BPF before passing through a PC and a polarizer (POL) which is aligned with the polarization axis of the SSPD via one final PC. The loss from the SMF inputs of the transmit MMUX₁ to the SMF outputs of the receive MMUX₂ where measured to be 9.5 dB, with approximately 6 dB of that due to the reflectivity of the two SLMs with the remaining 3.5 dB due to coupling and other MMUX component losses such as lenses, beam-splitters and waveplates. The receiver wavelength and polarization components gave an additional 5.6 dB loss.

The coincidence-to-accidental ratio (CAR) was measured for several classical channel received powers, shown in Fig. 5 as black circles, from −10 dBm, sufficient for error-free operation using direct-detection schemes even without pre-amplification, down to −40 dBm, likely be too little power for error-free operation even using coherent techniques. With the ECL turned off, a CAR of 31.9 ± 1.6 was measured, given by the dotted black line of Fig. 5. At −10 dBm of received power the CAR drops slightly to 29.2 ± 1.4, with a fit to the data suggesting a minor drop as the classical power was increased (red line). However the trend is weak and the CAR remains consistent from no ECL power all the way up to −10dBm to within experimental error. A test was also performed where the classical and single-photon channels were launched onto the same spatial and polarization mode (fundamental mode, horizontally polarized). In this case the CAR approached zero and became immeasurable. The extracted heralded photon rate, shown as blue squares, remains constant and comparable to the case with the ECL turned off, shown as a blue dashed line.

 

Fig. 5 The extracted heralded single-photon rate (blue squares) did not vary significantly as the power was increased in the classical channel and was close to the rate when no power is present (blue dashed line). The measured CAR (black circles) and trend (red line) show values comparable to the classical channel off (black dotted line). Errors are from Poissonian statistics.

Download Full Size | PDF

To further prove the usefulness of this scheme it must be scaled up to longer fiber lengths of the order of a few kilometers to be compatible with short-range communication and datacenters. Similar MMUX techniques have been demonstrated over kilometers of fiber [19] where the tracking of mode evolution is possible in real-time and can be corrected using the deMMUX SLM. It will also be important in the future to demonstrate the building of a secure key via QKD through this system, with measurements of key rates and quantum bit error rates as the classical channel power is increased.

4. Conclusion

We have shown that classical and single-photon channels can be successfully multiplexed onto different spatial modes of the same few-mode fiber. This demonstrates that the orthogonality between the modes of a fiber can be used to isolate multiple channels for simultaneous quantum and classical communication, enabling quantum communications in multimode fibers which is especially suited to use in datacenters and short-haul local networks.