In this work, we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.
In this work, we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.
We present a study of the spectral properties of photon pairs generated through the process of spontaneous four-wave mixing (SFWM) in single mode fiber. Our analysis assumes narrowband pumps, which are allowed to be frequency degenerate or nondegenerate. Based on this analysis, we derive conditions on the pump frequencies and on the fiber dispersion parameters which guarantee the generation of ultrabroadband photon pairs. Such photon pairs are characterized by (i) a very large degree of entanglement, and (ii) a very high degree of temporal synchronization between the signal and idler photons. Through a numerical exercise, we find that the use of photonic crystal fiber (PCF) facilitates the fulfilment of the conditions for ultrabroadband photon pair generation; in particular, the spectral region in which emission occurs can be adjusted to particular needs through an appropriate choice of the PCF parameters. In addition, we present a quantum interference effect, resulting from indistinguishable pathways to the same outcome, which can occur when pumping a SFWM source with multiple spectral lines.
We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four-wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact possible, each associated with a different combination of transverse modes for the four waves involved. We show that in the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized modes, the departure from circular symmetry due to the fiber birefringence translates into conservation rules, which retain elements from azimuthal and rectangular symmetries: both OAM and parity must be conserved for a process to be viable. We have implemented a SFWM source based on a bowtie birefringent fiber, and have measured for a collection of pump wavelengths the SFWM spectra of each of the signal and idler photons in coincidence with its partner photon. We have used this information, together with knowledge of the transverse modes into which the signal and idler photons are emitted, as input for a genetic algorithm, which accomplishes two tasks: (i) the identification of the particular SFWM processes that are present in the source, and (ii) the characterization of the fiber used.
Based on the dispersion property of a given photonic crystal fiber (PCF), we study how to directly generate photon pairs with minimized frequency correlation via pulse-pumped spontaneous four-wave mixing. After illustrating why the intensity correlation function g (2) of individual signal (idler) photons can be used to reliably characterize the frequency correlation of photon pairs, we numerically investigate the dependence of g (2) under various kinds of experimental conditions. The results show that to minimize the frequency correlation, the experimental parameters should be properly optimized by balancing the influences of the high-order dispersion and the intrinsic sinc oscillation of phase matching function, apart from the satisfaction of the specified phase matching condition and the usage of transform-limited pump pulses. To verify the calculated results, we conduct two series of experiments by regulating the pump to respectively satisfy the asymmetric and symmetric group velocity matching conditions in our 0.6 m-long PCF. In both cases, the measured values of g (2) are less than the calculated results due to the inhomogeneity of the PCF; however, the experimental results qualitatively agree with the numerical simulations. Our investigation is very useful in fiber-based quantum state engineering.
The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which, together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of frequency, transverse mode, and polarization degrees of freedom—the first linked to the latter two through fiber dispersion—leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon-pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counterpropagating pumps, as well as methods for characterizing photon pairs generated in optical fibers.
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.