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arXiv:1205.3049 · New Journal of Physics

Quantum theory of all-optical switching in nonlinear Sagnac interferometers

Y. P. Huang, Prem Kumar

Published May 25, 2012• 8 citations
arXivHTMLPDF

Abstract

Recently, our group has demonstrated an ultrafast, low-loss, fiber-loop switch based on a nonlinear Sagnac-interferometer design, using which entangled photons were shown to be routed without any measurable degradation in their entanglement fidelity [Hall {\it et al.}, Phys. Rev. Lett. {\bf 106}, 053901 (2011)]. Such a device represents an enabling technology for a rich variety of networked quantum applications. In this paper we develop a comprehensive quantum theory for such switches in general, i.e., those based on nonlinear Sagnac interferometers, where the in-coupling of quantum noise is carefully modeled. Applying to the fiber-loop switch, the theory shows good agreement with the experimental results without using any fitting parameter. This theory can serve as an important guiding tool for configuring switches of this kind for future quantum networking applications.

DOI
10.1088/1367-2630/14/5/053038

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This work was supported by the Department of Defense Multidisciplinary University Research Initiative program administered by the Army Research Office under Grants DAAD19-00-1-0177 and DAAD19-00-1-0469, and by the U.S. Office of Naval Research under Grant N00014-91-J-1268.

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Recently, our group has demonstrated an ultrafast, low-loss, fiber-loop switch based on a nonlinear Sagnac-interferometer design, using which entangled photons were shown to be routed without any measurable degradation in their entanglement fidelity [Hall {\it et al.}, Phys. Rev. Lett. {\bf 106}, 053901 (2011)]. Such a device represents an enabling technology for a rich variety of networked quantum applications. In this paper we develop a comprehensive quantum theory for such switches in general, i.e., those based on nonlinear Sagnac interferometers, where the in-coupling of quantum noise is carefully modeled. Applying to the fiber-loop switch, the theory shows good agreement with the experimental results without using any fitting parameter. This theory can serve as an important guiding tool for configuring switches of this kind for future quantum networking applications.
An essential component of future quantum networks is an optical switch capable of dynamically routing single photons. Here we implement such a switch, based on a fiber-optical Sagnac interferometer design. The routing is implemented with a pair of fast electro-optical telecom phase modulators placed inside the Sagnac loop, such that each modulator acts on an orthogonal polarization component of the single photons, in order to yield polarization-independent capability that is crucial for several applications. We obtain an average extinction ratio of more than 19 dB between both outputs of the switch. Our experiment is built exclusively with commercial off-the-shelf components, thus allowing direct compatibility with current optical communication systems.
Future quantum optical networks will require the ability to route entangled photons at high speeds, with minimal loss and added in-band noise, and---most importantly---without disturbing the photons' quantum state. Here we present an all-optical switch which fulfills these requirements and characterize its performance at the single photon level. It exhibits a 200-ps switching window, 120:1 contrast, 1.5-dB loss, and induces no measurable degradation in the switched photons' entangled-state fidelity (< 0.002). As a proof-of-principle demonstration of its capability, we use the switch to demultiplex a single quantum channel from a dual-channel, time-division-multiplexed entangled photon stream. Furthermore, because this type of switch couples the temporal and spatial degrees of freedom, it provides an important new tool with which to encode multiple-qubit quantum states on a single photon.
Q uantum entanglement refers to the nonclassical dependency of physically separated quantum systems. It is an essential resource that must be freely available for implementing many of the novel functions of quantum information processing, such as database searching, clock synchronization, teleportation, computing and cryptography.1 The efficient generation and transmission of quantum entanglement is therefore of prime importance. With the ubiquitous standard optical fiber serving as the transmission medium and the widespread availability of efficient active and passive fiber devices, technological synergy between the generation and propagation components of the overall quantum network can be achieved by deploying sources of entanglement that rely on the nonlinearity of the fiber itself. Such fiber-based sources of quantum entanglement would also have the advantage of modal purity over their crystal counterparts,2,3 which is very important for realizing complex networks that involve many quantum operations. In our quest to develop fiber-based devices for quantum information processing, we have recently demonstrated an allfiber source of quantum-correlated photon pairs.4 The operating physical mechanism in this source is nondegenerate fourphoton mixing, wherein two pump photons scatter through the Kerr nonlinearity of the fiber to create simultaneous signal and idler photons. Our experiment is conducted near the zero-dispersion wavelength of standard dispersion-shifted fiber, where such scattering is enhanced owing to phase matching of the photon wave functions. It must be pointed out here that in a conventional wavelength-divisionmultiplexed classical optical communication line, one strives to suppress the fourphoton or four-wave mixing process, which otherwise causes cross talk between the wavelength channels and sets limits on the total data capacity of the communication line. In our experiment, the four-photon mixing takes place in a nonlinear-fiber Sagnac interferometer (NFSI), which we previously used to generate quantum-correlated twin beams in the fiber.5 The pump is a mode-locked train of ~3-ps-long pulses. The pulsed operation serves two important purposes: the NFSI amplifier can be operated at low average powers and the production of the signal/ idler fluorescence photons is confined to well-defined temporal windows, allowing use of a gated detection scheme to increase the signal-to-noise ratio. To measure the nonclassical (i.e., quantum) correlations between the signal and the idler photons, one must effectively suppress the pump photons from reaching the detectors. Since a typical pump pulse contains ~108 photons and we are interested in detecting ~0.01 signal (idler) photons/pulse, a pump-to-signal (idler) rejection ratio in excess of 100 dB is required. We achieved this specification by sending the fluorescence photons through a free-space double-grating spectral filter that separates the signal and idler photons from each other and from the pump photons not rejected by the NFSI. To demonstrate the quantum nature of the four-photon scattering at the single photon level, we assembled a photonFigure 1.C oincidence rates as a function of the single-photon rates in two different cases: signalidler fluorescence produced by a pump pulse (diamonds) and signal-idler fluorescence produced by two consecutive pump pulses (triangles). T he line represents the calculated accidental counts. T he inset shows a plot of the detected idler photons as a function of the injected pump photons (hollow circles). A second-order polynomial is shown to fit the experimental data. T he contributions of the dark counts, linear scattering and quadratic scattering are plotted separately as well. counting apparatus for detecting the signal and idler photons in coincidence. This apparatus is based on commercial InGaAs avalanche photodiodes operating in the gated Geiger mode.4 In the inset in Fig. 1, we show the number of scattered photons, NS, versus the number of pump photons, NP, injected into the NFSI. We fit the experimental data with a second-order polynomial fit, including the number of dark counts during the gate interval, ND. The fit clearly shows that the quadratic scattering ( ∝NP) in the fiber can dominate over the residual linear scattering ( ∝NP) of the pump, owing to imperfect filtering. The main body of Fig. 1 shows the coincidence-counting results. The diamonds represent the rate of coincidence counts versus the rate of the signal (idler) photons generated during the same pump pulse. The triangles represent the measured coincidence rate versus the signalphoton count rate when the signal is delayed with respect to the idler by one pulse period. For two independent photon sources, each with a count rate RS <<1, the accidental coincidence rate RC is given by RC = RS 2, regardless of the photon statistics of the sources. This quadratic relation is plotted as the solid line in Fig. 1, which fits the delayed-coincidence data (triangles) very well. These measurements show that while the fluorescence photons produced by the adjacent pump pulses are independent, those coming from the same pump pulse show a strong correlation, which is a signature of their non-classical behavior. This work was supported by the Department of Defense Multidisciplinary University Research Initiative program administered by the Army Research Office under Grants DAAD19-00-1-0177 and DAAD19-00-1-0469, and by the U.S. Office of Naval Research under Grant N00014-91-J-1268.
A Sagnac loop structure can help overcome the major difficulty in the practical implementation of a twin field quantum key distribution (TFQKD) network, namely, the need to stabilize the phase of a quantum state over many kilometers of fiber. Unfortunately, Rayleigh backscattering noise limits the signal-to-noise ratio for Sagnac systems containing long fibers and lossy photonic devices. Here, we solve this problem by sending optical pulses in long on-off bursts and using time post-selection on measurements taken with free-run single-photon avalanche detectors. We also investigate the impact of the residual phase noise uncompensated by the Sagnac structure and find that the variance of the phase noise scales as loop length to the third power, verifying an existing calculation in the literature. We measure the interference visibility in Sagnac loops of varying length without active phase stabilization and achieve > 97% visibility in 200 km ultra-low-loss fiber, which is, to our knowledge, the longest fiber Sagnac interferometer demonstrated. Our results suggest that a Sagnac system is feasible for long-distance TFQKD networks, an important step towards the practical implementation of metropolitan quantum networks.
A fully fibered source of entangled photon pairs based on a nonlinear Sagnac interferometer is reported. Operating at telecom wavelengths, the source relies exclusively on standard fiber-optic components and periodically poled lithium niobate (PPLN) waveguides, resulting in a compact, robust, and field-deployable architecture. The generation stage supports both polarization and energy-time entanglement without modification, enabling versatile operation depending on the targeted application. Broadband spontaneous parametric down-conversion allows dense wavelength-division multiplexing over the telecom C and L bands. High normalized brightness (10.3 kpairs/s/nm/mW2^22) is achieved on a standard 100 GHz ITU channel pair, together with high entanglement quality. Polarization and energy-time encodings are characterized through state tomography and two-photon interference measurements, yielding fidelities, purities, and visibilities exceeding 96 % over multiple wavelength channels. The stability and reproducibility of the source are further evaluated through long-duration operation in a network environment. These results demonstrate that the proposed Sagnac source constitutes a practical and scalable building block for future plug-and-play quantum communication and quantum networking platforms.