For fiber-based polarization entangled photon pairs generated by four-wave mixing nonlinear effect, a common method to process coincidence counts and reconstruct density matrix of original quantum states is maximum likelihood estimation. Pump power is an essential parameter to investigate throughout the process of entanglement generation, correlation detection and quantum state tomography. Defined as the optical power of input laser pulses that enter dispersion-shifted fiber and generate entangled pairs, pump power directly affects single counts rates for both signal and idler. As noise rate changes accordingly, coincidence to accidental counts ratio does not necessarily increase with more detected counts. We derive relation between pump power and entangled correlation. Because different power is associated with different order of susceptibility, we also study its effect on entangled photon generation rate. Transmission rate through fibers, filters, polarizing beam splitters and other optical components as well as the detection efficiency at each avalanche photodiode are taken into consideration because they contribute to the reliability of photon counting statistics. System error such as measuring basis error is studied whether it is amplified, suppressed or remain invariant with pump power modification. Many parameters’ relations with pump power cannot be simply described as a one-line equation. Therefore, we explain those relations in detail and propose a method of finding a suitable pump power within given circumstances that would serve reconstructing the most accurate quantum state.
For fiber-based polarization entangled photon pairs generated by four-wave mixing nonlinear effect, a common method to process coincidence counts and reconstruct density matrix of original quantum states is maximum likelihood estimation. Pump power is an essential parameter to investigate throughout the process of entanglement generation, correlation detection and quantum state tomography. Defined as the optical power of input laser pulses that enter dispersion-shifted fiber and generate entangled pairs, pump power directly affects single counts rates for both signal and idler. As noise rate changes accordingly, coincidence to accidental counts ratio does not necessarily increase with more detected counts. We derive relation between pump power and entangled correlation. Because different power is associated with different order of susceptibility, we also study its effect on entangled photon generation rate. Transmission rate through fibers, filters, polarizing beam splitters and other optical components as well as the detection efficiency at each avalanche photodiode are taken into consideration because they contribute to the reliability of photon counting statistics. System error such as measuring basis error is studied whether it is amplified, suppressed or remain invariant with pump power modification. Many parameters’ relations with pump power cannot be simply described as a one-line equation. Therefore, we explain those relations in detail and propose a method of finding a suitable pump power within given circumstances that would serve reconstructing the most accurate quantum state.
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.
Quantum correlations, where two or more parties exhibit strong correlations in a particular degree of freedom are important resources for fundamental science [1], such as the exploration of non-locality and entanglement, as well as non-classical technologies including quantum computation, quantum key distribution and quantum metrology. One typical way to generate correlated photon pairs is to use the spontaneous four-wave mixing process, with demonstrations on various platforms [2]. So far, single-photon stimulated four-wave mixing (FWM) has been demonstrated in optical fibers [3]. Here we show induced correlation by single photon seeded FWM through exploiting the orthogonal polarization modes in an integrated ring resonator [4]. We allow two different four-wave mixing processes to occur simultaneously with the same signal frequency mode but different idler frequency modes (see Fig.1(a)). The single-photon induced FWM process, named here seeded FWM, was created through the link of type-0 SFWM and type-2 SFWM. In the type-0 process, two excitation photons from the same field are converted into two new photons, signal and idler, with the same polarization as the pump field. While in the type-2 FWM, two annihilated photons, each one from a different polarized pump field, namely TE and TM, generate an orthogonal-polarized photon pair. More importantly, spatial and temporal overlapping of two processes and their sharing of one common resonance lead to correlation between the other two signal photons, one from each process. For example, an idler photon created in type-0 FWM seeds the type-2 FWM process or vice versa, i.e. the TM idler photon in Fig. 1, induces correlation between the signal TM and TE photons. This is proven by the observation of a clear coincidence peak for both signal photons in Fig.1(b). Furthermore, we confirmed our observation via power-dependent correlation measurements (see Fig.1 (c)). We summarized the true coincidence count (C) and its coincidence to accidental ratio (CAR) when only the TE pump power is increased while maintaining the TM mode pump power (black squares), and both pump powers are increased with a constant ratio (blue dots). We found that the seeded FWM scales with the square of both pump powers (C ∝ PjePtm) and that the CAR reach its maxima of 1.5 at the available pump power, indicating thermal statistics. Our findings are relevant to the fundamental understanding of spontaneous parametric effects as well as single-photon induced processes and single photon cloning.
Spontaneous four-wave mixing (SFWM) in optical fibers is an important way to generate correlated/entangled photon pairs. When the pulsed pump light passes through the optical fiber, two kinds of SFWM will take place simultaneously. One is scalar scattering processes, in which two annihilated pump photons and generated photon pair are all polarized along the same fiber polarization axis. The other is vector scattering processes, in which two annihilated pump photons are polarized along different fiber polarization axes, either to the two photons of the generated pair. If the fiber has large group birefringence, the intensity of vector scattering processes will be suppressed at the phase matching frequencies of the scalar scattering processes. On the other hand, the walk-off effect of the pump pulse components polarized along the two fiber polarization axes also suppresses the vector scattering processes. Hence, by proper pump polarization and signal/idle frequency selection, photon pairs can be generated only by the two independent scalar scattering processes in optical fibers with birefringence, which provide a simple way to realize polarization entangled photon pair generation. In this paper, related experiments based on the high nonlinearity microstructure fiber (HN-MSF) with group birefringence and polarization maintained dispersion shifted fiber (PM-DSF) are introduced, showing their potential on developing practical quantum light sources.
By simultaneously measuring individual and coincidence counts of two single photon detectors connected to a fiber-based entangled photon source and fitting the results with a theoretical model of the photon generation rates, we determine the average number of polarization-entangled photon pairs generated by four-wave mixing and the average number of noise photons generated by Raman scattering and self-phase modulation of the pump as a function of power. In contrast to previous efforts to characterize fiber-based entangled photon sources, this method does not require additional coherence-based measurements to distinguish SPM photons from FWM and Raman-scattered photons.
We present a general quantum theory capable of describing photon statistics under the combined effects of four-wave mixing and Raman scattering inside optical fibers. Our theory is vectorial in nature and includes all polarization effects. Our analysis shows that spontaneous Raman scattering degrades the pair correlation in all cases but the extent of degradation depends on the pumping configuration employed. In a single-pump configuration, photon pairs can be created with polarization either parallel or orthogonal to the pump. Our results show that the orthogonal configuration can improve the extent of quantum correlation considerably over a broad bandwidth. In the case of a dual-pump configuration, we show that imbalance of two pump powers can be used to improve the quality of photon pairs. We show that orthogonally polarized pumps can generate photon pairs automatically in a polarization-entangled state. In particular, orthogonal pumping with circular polarizations produces such an entangled state with relatively high quality. We also quantify the quality of polarization entanglement as well as energy-time entanglement constructed using correlated photon pairs.
Single photon sources are a key element for quantum computing, quantum key distribution (QKD) and quantum communications. In particular, producing single photons at telecommunications wavelengths is valuable for QKD protocols and would enable realizing the quantum internet. The preferred method for their generation has long been spontaneous down conversion in bulk crystals, which suffers from connection loss to fiber networks. In-fiber spontaneous four-wave mixing provides a viable alternative as a photon pair source due to being compatible with existing fiber networks. We present an all-fiber photon pair source based on degenerate four-wave mixing in a 400 m Highly-Nonlinear fiber, with signal and idler wavelengths generated at 1552.5 nm and 1557 nm respectively. The source consists of CW pump laser operating at 1554.75 nm, which is slightly detuned from the zero group velocity dispersion wavelength into the normal dispersion regime. After pair generation in the highly-nonlinear fiber, three arrayed waveguide gratings are employed to spatially separate signal and idler, and provides a 120 dB pump power reduction. Firstly the source is modelled and experimentally characterized in the well known classical regime of stimulated four-wave mixing. The effect of fiber cooling on spontaneous Raman scattering is modelled and characterized, and a 30% reduction in spontaneous emission is found when cooling the fiber to -77°C. In the low power regime the coincidence to accidental count ratio is simulated and measured. An increase in the coincidence to accidental count ratio is observed when cooling the fiber.