Spontaneous Four-wave Mixing Research Articles

No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources.

Generation of heralded single photons has recently been demonstrated using spontaneous four-wave mixing in integrated microresonators. While the results of coincidence measurements on the generated photon pairs from these systems show promise for their utility in heralding applications, such measurements do not reveal all of the effects of photon losses within the resonator. These effects, which include a significant degradation of the heralding efficiency, depend strongly on the relative strengths of the coupling of the ring modes to loss modes and channel modes. We show that the common choice of critical coupling neither optimizes the rate of successfully heralded photons nor coincidences and derives the coupling conditions needed to do so. Optimizing these rates has a considerable negative effect on the heralding efficiency.

Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing.

By investigating the intensity correlation function, we study the spectral/temporal mode properties of twin beams generated by the pulse-pumped high gain spontaneous four wave mixing (SFWM) in optical fiber from both the theoretical and experimental aspects. The results show that the temporal property depends not only on the phase matching condition and the filters applied in the signal and idler fields, but also on the gain of SFWM. When the gain of SFWM is low, the spectral/temporal mode properties of the twin beams are determined by the phase matching condition and optical filtering and are usually of multi-mode nature, which leads to a value larger than 1 but distinctly smaller than 2 for the normalized intensity correlation function of individual signal/idler beam. However, when the gain of SFWM is very high, we demonstrate the normalized intensity correlation function of individual signal/idler beam approaches to 2, which is a signature of single temporal mode. This is so even if the frequencies of signal and idler fields are highly correlated so that the twin beams have multiple modes in low gain regime. We find that the reason for this behavior is the dominance of the fundamental mode over other higher order modes at high gain. Our investigation is useful for constructing high quality multi-mode squeezed and entangled states by using pulse-pumped spontaneous parametric down-conversion and SFWM.

Experimental research on generating and splitting degenerate correlated photon pairs in Sagnac fiber loop

Degenerate correlated photon pairs (DCPPs) have been widely used in quantum information science,especially in the areas of quantum computation,quantum state control and precision measurement,which are typically generated in a (2) nonlinear crystal through the spontaneous parametric down-conversion.However,such a source is not compatible with optical fiber as large coupling losses occur when the pairs are launched into it,which restricts its direct application to quantum information processing system.More recently,DCPP generation from spontaneous four-wave mixing in (3) optical fiber has aroused strong interest,due to its advantages of compatibility with existing fiber networks and free of alignment.The process of generating DCPP in fiber can be described as follows:two pump photons at different frequencies p1 and p2 scatter through the (3) nonlinearity to create a pair of identical photons at the mean frequency c,such that p1+p2=2c.Because the collinear tensor component xxxx(3) in a Kerr nonlinear medium is 3 times as large as the tensor component xyxy(3),the co-polarized four-wave mixing is preferred,which means the two pump photons and new-born twin photons are both co-polarized.Therefore,it is very challenging to deterministically separate the fiber-based DCPP,since the twin photons share the same properties in all degrees of freedom:frequency,polarization and spatial.Sagnac fiber loop (SFL),composed of a piece of nonlinear fiber and 50/50 coupler,is presented as the splitter for DCPP based on the reversed Hong-Ou-Mandel quantum interference of counter-propagating DCPPs.The SFL can be configured as a total reflector,total transmitter or equally transmissive and reflective state,which sets the differential phases of counter-propagating DCPPs meeting at 50/50 coupler to be ,0 and -,respectively.In order to satisfy the differential phase requirement for completely splitting the DCPP,the SFL is always set to be equally transmissive and reflective state,however,the polarization-mode matching of counter-propagating DCPPs is not easily achieved due to the disturbance of fiber birefringence.According to the Jones matrix derivation of DCPP propagating in the SFL,the polarization mode of counter-propagating DCPPs when interference at 50/50 coupler is automatically matched,if the SFL is set as a total reflector or total transmitter.In experimental scheme,utilizing the SFL as a total reflector,the 1.1 nm bandwidth and 1544.53 nm central wavelength DCPPs are generated by two pulsed light beams pumping the 300 m dispersion-shifted fiber in the SFL.Using the two pieces of single mode fiber connecting the 300 m dispersion-shifted fiber and 50/50 coupler,whose length difference is fixed at 3.3 m,the differential phase of counter-propagating DCPPs highly dependent on the dispersion properties of single mode fiber is managed at 2 for fully distributing DCPPs into which degrades the fidelity of DCPP source.The measured ratio of coincidence to accidental-coincidence of DCPPs from one port is approximately 1.8:1,which indicates that the coincidence counts mainly originate from accidental coincidence counts and extra coincidence counts from photon bunching and there are not any DCPPs outputting from one port.Meanwhile,the ratio of best measured coincidence to accidental-coincidence of DCPPs from two ports reaches 47:1,when the average power of two pumps is fixed at 0.026 mW.The experimental results demonstrate that the high purity and fully spatial separation DCPPs are successfully prepared in optical fibers,which is a very useful tool for realizing various quantum information systems.How the spatial state of outputting DCPPs depends on the length difference between single-mode fiber and detuning wavelength is also discussed in detail.

Spectral features of spontaneous four-wave mixing in tapered nanofibers

Features of biphoton states generated via spontaneous four-wave mixing in tapered nanofibers are studied. The spectral amplitude of a biphoton field is calculated and the effect of interference of the biphoton field in such structures is discussed. The effect of nanofiber environment on the spectral amplitude of the biphoton field is investigated.

Generation of heralded single photons beyond 1100 nm by spontaneous four-wave mixing in a side-stressed femtosecond laser-written waveguide

We demonstrate a monolithically integrable heralded photon source in a femtosecond laser direct written glass waveguide. The generation of photon pairs with a wide wavelength separation requires a concomitant large birefringence in the normal dispersion regime. Here, by incorporation of side-stress tracks, we produce a waveguide with a birefringence of 1.64×10−4 and propagation loss as low as 0.21 dB/cm near 980 nm. We measure photon pairs with 300 nm wavelength separation at an internal generation rate exceeding 5.05×106/s. The second order correlations indicate that the generated photon pairs are in a strongly non-classical regime.

Effects of self- and cross-phase modulation on photon purity for four-wave-mixing photon pair sources

We consider the effect of self-phase modulation and cross-phase modulation on the joint spectral amplitude of photon pairs generated by spontaneous four-wave mixing. In particular, the purity of a heralded photon from a pair is considered, in the context of schemes that aim to maximise the purity and minimise correlation in the joint spectral amplitude using birefringent phase-matching and short pump pulses. We find that non-linear phase modulation effects will be detrimental, and will limit the quantum interference visibility that can be achieved at a given generation rate. An approximate expression for the joint spectral amplitude with phase modulation is found by considering the group velocity walk-off between each photon and the pump, but neglecting the group-velocity dispersion at each wavelength. The group-velocity dispersion can also be included with a numerical calculation, and it is shown that it only has a small effect on the purity for the realistic parameters considered.

Shaping the Biphoton Temporal Waveform with Spatial Light Modulation

We demonstrate a technique for shaping the temporal wave function of biphotons generated from spatially modulated spontaneous four-wave mixing in cold atoms. We show that the spatial profile of the pump field can be mapped onto the biphoton temporal wave function in the group delay regime. The spatial profile of the pump laser beam is shaped by using a spatial light modulator. This spatial-to-temporal mapping enables the generation of narrow-band biphotons with controllable temporal waveforms.

Numerical solution of Schrödinger equation for biphoton wave function in twisted waveguide arrays

We consider the generation of entangled biphoton states with orbital-angular-momentum in triangular quadratic waveguide arrays with twisted geometry. For this purpose, we derive the Shrodinger equation for biphoton wave function and equation for pump field profile. We describe numerically the process of biphoton generation through spontaneous four-wave mixing. We suggest that biphoton correlations can be controlled by the amount of twist and pump field profile.

Controllable lifetime of fourth-order fluorescence and spontaneous parametric four-wave mixing in Pr^3+:YSO

We report the measured dressed lifetimes of fourth-order fluorescence and spontaneous parametric four-wave mixing signals by the perturbation chain method in a two-level and heteronuclear-like molecule system of Pr3+:YSO both in theory and experiment. The lifetime of the fourth-order fluorescence depends on the nonlinear processes in the perturbation chain, and can be modulated by the dark state due to the dressing effect and the induced dipole–dipole interaction by changing the frequency detuning and power of the controlling field. Such results can find potential applications in all-optical communication and optical information processing on photonic chips.

Ultrafast optical transistor and router of multi-order fluorescence and spontaneous parametric four-wave mixing in Pr³⁺:YSO.

We study the realization of an optical transistor (switch and amplifier) and router in multi-order fluorescence (FL) and spontaneous parametric four-wave mixing (SP-FWM). We estimate that the switching speed is about 15 ns. The router action results from the Autler-Townes splitting in spectral or time domain. The switch and amplifier are realized by dressing suppression and enhancement in FL and SP-FWM. The optical transistor and router can be controlled by multi-parameters (i.e., power, detuning, or polarization).

Optimizing photon-pair generation electronically using a p-i-n diode incorporated in a silicon microring resonator

Silicon photonic microchips may be useful for compact, inexpensive, room-temperature optically pumped photon-pair sources, which unlike conventional photon-pair generators based on crystals or optical fibers, can be manufactured using CMOS-compatible processes on silicon wafers. It has been shown that photon pairs can be created in simple structures such as microring resonators at a rate of a few hundred kilohertz using less than a milliwatt of optical pump power, based on the process of spontaneous four-wave mixing. To create a practical photon-pair source, however, also requires some way of monitoring the device and aligning the pump wavelength when the temperature varies, since silicon resonators are highly sensitive to temperature. In fact, monitoring photodiodes are standard components in classical laser diodes, but the incorporation of germanium or InGaAs photodiodes would raise the cost and fabrication complexity. Here, we present a simple and effective all-electronic technique for finding the optimum operating point for the microring used to generate photon pairs, based on measuring the reverse-biased current in a silicon p-i-n junction diode fabricated across the waveguide that constitutes the silicon microring. We show that by monitoring the current, and using it to tune the pump laser wavelength, the photon-pair generation properties of the microring can be preserved over a temperature range of more than 30 °C.

Strongly driven nonlinear quantum optics in microring resonators

We present a detailed analysis of strongly driven spontaneous four-wave mixing in a lossy integrated microring resonator side-coupled to a channel waveguide. A nonperturbative, analytic solution within the undepleted pump approximation is developed for a cw pump input of arbitrary intensity. In the strongly driven regime self- and cross-phase modulation, as well as multi-pair generation, lead to a rich variety of power-dependent effects; the results are markedly different than in the low power limit. The photon pair generation rate, single photon spectrum, and joint spectral intensity (JSI) distribution are calculated. Splitting of the generated single photon spectrum into a doublet structure associated with both pump detuning and cross-phase modulation is predicted, as well as substantial narrowing of the generated signal and idler bandwidths associated with the onset of optical parametric oscillation at intermediate powers. Both the correlated and uncorrelated contributions to the JSI are calculated, and for sufficient powers the uncorrelated part of the JSI is found to form a quadruplet structure. The pump detuning is found to play a crucial role in all of these phenomena, and a critical detuning is identified which divides the system behaviour into distinct regimes, as well as an optimal detuning strategy which preserves many of the low-power characteristics of the generated photons for arbitrary input power.

Dressed spontaneous parametric the four-wave mixing process in Pr3+:YSO crystal

We investigate fluorescence (FL) and spontaneous parametric four-wave mixing (SP-FWM) signals in V-, Λ- and N-type energy level systems by changing the frequency detuning or power of the dressing field in Pr3+ doped Y2SiO5 at 77 K. The lifetime of the two kinds of signals has been calculated, and the desired experimental results have been obtained. We successfully control the intensity and lifetime of fluorescence and SP-FWM signals by changing the power or frequency detuning of the dressing field. The research has potential applications in optical switches and all optical communication.

Lifetime Polarization of Dressed Multiorder Fluorescence and Spontaneous Parametric Four-Wave Mixing in Pr <inline-formula> <tex-math notation="TeX">$^{3+}$</tex-math></inline-formula>:YSO

We investigate lifetime (induced dipole–dipole interaction) of spontaneous parametric four-wave mixing (SP-FWM) and multiorder fluorescence (FL) signals controlled by polarization dressing in a heteronuclear-like molecule system of Pr $^{3+} $ :YSO. The comparisons between a lifetime of SP-FWM and multiorder FL controlled by single dressing, double dressing, and triple dressing polarization have been investigated. It is observed that FLs have a stronger dressing effect than SP-FWM. The polarization dressing is more obvious in the intensity signal in the spectral domain than that in the time domain. Such results have potential applications in quantum communication such as optical information storage, routing, and processing on a photonic chip.

Dressed intensity noise correlation and intensity-difference squeezing of spontaneous parametric four-wave mixing process in a Pr³⁺:YSO crystal.

We report dressed intensity noise correlation and intensity-difference squeezing based on spontaneous parametric four-wave mixing (SP-FWM) in Pr³⁺:Y₂SiO₅ crystal both experimentally and theoretically. We found such intensity noise correlation and intensity-difference squeezing can be controlled by using the dressing effect to manipulate the nonlinear optical coefficient of the SP-FWM process. By changing detuning and power of the optical field, we manipulate the nonlinear optical coefficient of the SP-FWM process, thus control the correlation and squeezing. The results show stronger correlation and squeezing with single dressing, while weaker near the resonant point due to destructive double dressing. Furthermore,we observed the dependence of correlation times on the power of dressing field, and explained by the combination of the dressing effect and induced dipole-dipole interaction. We also showed the fourth-order fluorescence signals accompanying with the SP-FWM process.

Enhancing the heralded single-photon rate from a silicon nanowire by time and wavelength division multiplexing pump pulses.

Heralded single photons produced on a silicon chip represent an integrated photon source solution for scalable photonic quantum technologies. The key limitation of such sources is their non-deterministic nature introduced by the stochastic spontaneous four-wave mixing (SFWM) process. Active spatial and temporal multiplexing can improve this by enhancing the single-photon rate without degrading the quantum signal-to-noise ratio. Here, taking advantage of the broad bandwidth of SFWM in a silicon nanowire, we experimentally demonstrate heralded single-photon generation from a silicon nanowire pumped by time and wavelength division multiplexed pulses. We show a 90±5% enhancement on the heralded photon rate at the cost of only 14±2% reduction to the signal-to-noise ratio, close to the performance found using only time division multiplexed pulses. As single-photon events are distributed to multiple wavelength channels, this new scheme overcomes the saturation limit of avalanche single-photon detectors and will improve the ultimate performance of such photon sources.

Frequency-induced phase-tunable polarization-entangled narrowband biphotons

Manipulating polarization entanglement of paired photons is always of great interest for understanding the quantum nature of photons and exploring their applications in quantum information processing and quantum communication. Narrowband biphotons with polarization entanglement are especially important for a quantum network based on efficient photon–atom interactions. In most demonstrated cases, the polarization-entangled states are manipulated through the birefringent effect. In this Letter, we produce narrowband polarization-entangled biphotons from spontaneous four-wave mixing in cold atoms and demonstrate a new method to tune the phase of the polarization entanglement by varying the frequency of one of the classical driving lasers. This is achieved through two-photon interference with a path-exchange symmetry. Our result represents a precision control of polarization entanglement from the frequency domain, and may have promising applications in quantum information and precision measurement.

Spontaneous four-wave mixing in lossy microring resonators

We develop a general Hamiltonian treatement of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.

Spontaneous four-wave mixing in liquid-core fibers: towards fibered Raman-free correlated photon sources

We experimentally demonstrate, for the first time to our knowledge, the generation of correlated photon pairs in a liquid-core photonic crystal fiber. Moreover, we show that, thanks to the specific Raman properties of liquids, the Raman noise (which is the main limitation of the performance of silica-core fiber-based correlated photon pair sources) is highly reduced. With a demonstrated coincident-to-accidental ratio equal to 63 and a pair generation efficiency of about 10−4 per pump pulse, this work contributes to the development of high-quality correlated photon pair sources for quantum communications.

Narrowband polarization entangled paired photons with controllable temporal length

Quantum networks strongly depend on the efficient interactions between flying photonic quantum bits and local long-lived atomic matter nodes. To achieve the efficient quantum interfaces between polarization-encoding photons and spin-encoding atoms, polarization-entangled paired photons with a bandwidth narrower than the natural linewidth of the atoms are highly required. In this paper, we review the generation of subnatural-linewidth polarization-entangled paired photons through spontaneous four-wave mixing with cold atoms, which is very suitable for the application of quantum networks.