Spontaneous Four-wave Mixing Process Research Articles

Hybrid correlation and squeezing with Rabi oscillation in the diamond nitrogen-vacancy center at room temperature

For the first time, the energy level structure of the nitrogen-vacancy center in diamond is introduced in conjunction with a spontaneous parametric four-wave mixing (SP-FWM) process and fluorescence (FL) generation in heteronuclear-like (V-type level) systems. The obtained output signals are characterized by their decaying components and differentiated by Rabi oscillation, while their lifetimes are modulated by changing the power of the laser field. Two- and three-mode correlation and squeezing among the SP-FWM and FL composite signals are investigated theoretically and experimentally. By selecting different time delayed positions and changing the power of the laser field, competition between the SP-FWM and FL composite signals is demonstrated; this can also control the two-stage line shape of hybrid correlation and the magnitude of squeezing. Such results may find potential applications in optical transistors and optical hybrid communications.

Correlated-photon-pair emission from a cw-pumped Fabry-Perot microcavity

We study a dispersion-compensated high-finesse optical Fabry-Perot microcavity under high-intensity cw pumping. The Kerr non-linearity in the optical coatings causes a spontaneous four-wave mixing process, which leads to the emission of time-correlated photon pairs. The photon frequencies are shifted by $\pm 1$ free spectral range relative to the pump frequency. This setup allows for constructing a photon-pair source with precisely adjustable frequency difference between the emitted photons, which may have applications in quantum communication.

Temporal interference with frequency-controllable long photons from independent cold atomic sources

The interference of single photons from independent sources is an essential tool in quantum information processing. However, the interfering of photons with long temporal states in a time-resolved manner has rarely been studied. This is because without transmitting spectral filters or coupling to a cavity mode single photons generated in traditional nonlinear crystals suffer from a short temporal profile below 1 ns. With spectral correlation maintained in the biphotons generated from spontaneous four-wave mixing process in cold atom clouds, here we demonstrate the temporal interference of two frequency-tunable long photons from two independent cold atomic sources. We observe and analyze the interference of frequency-mismatched photons, where the phenomenon of the quantum beat at megahertz separation is displayed. Our paper provides more details for the quantum beat of two independent narrow-band single photons, which may find potential application in frequency-encoded photonic qubits in quantum information processing.

Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble

We report on heralded-single-photon superradiant beating in the spontaneous four-wave mixing process of Doppler-broadened ladder-type $^{87}\mathrm{Rb}$ atoms. When Doppler-broadened atoms contribute to two-photon coherence, the detection probability amplitudes of the heralded single photons are coherently superposed despite inhomogeneous broadened atomic media. Single-photon superradiant beating is observed, which constitutes evidence for the coherent superposition of two-photon amplitudes from different velocity classes in the Doppler-broadened atomic ensemble. We present a theoretical model in which the single-photon superradiant beating originates from the interference between wavelength-separated two-photon amplitudes via the reabsorption filtering effect.

Spectral tunability of two-photon states generated by spontaneous four-wave mixing: fibre tapering, temperature variation and longitudinal stress

We explore three different mechanisms designed to controllably tune the joint spectrum of photon pairs produced by the spontaneous four-wave mixing (SFWM) process in optical fibres. The first of these is fibre tapering, which exploits the modified optical dispersion resulting from reducing the core radius. We have presented a theory of SFWM for tapered fibres, as well as experimental results for the SFWM coincidence spectra as a function of the reduction in core radius due to tapering. The other two techniques that we have explored are temperature variation and application of longitudinal stress. While the maximum spectral shift observed with these two techniques is smaller than for fibre tapering, they are considerably simpler to implement and have the important advantage that they are based on the use of a single, suitably controlled, fibre specimen.

Benefit of birefringence for the direct generation of polarization-entangled photon pairs.

Generating polarization-entangled photon pairs on chip is generally complicated by the birefringence of waveguides. In this work, we propose a technique that uses waveguide birefringence and lends itself to simple device designs. The technique relies on two orthogonal spontaneous four-wave mixing processes. We employ the full quantum optics theory and dispersion analysis, and show that the technique can produce highly entangled states, with concurrence as high as 0.976 and covering the entire C-band.

Intracavity Spontaneous Parametric Down-Conversion in Bragg Reflection Waveguide Edge Emitting Diode**Supported by the National Key Basic Research Program of China under Grant Nos 2013CB933304 and 2014CB643904, the National Natural Science Foundation of China under Grant Nos 61435012 and 61274125, and the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant No XDB01010200.

A four-wavelength Bragg reflection waveguide edge emitting diode based on intracavity spontaneous parametric down-conversion and four-wave mixing (FWM) processes is made. The structure and its tuning characteristic are designed by the aid of FDTD mode solution. The laser structure is grown by molecular beam epitaxy and processed to laser diode through the semiconductor manufacturing technology. Fourier transform infrared spectroscopy is applied to record wavelength information. Pump around 1.071 μm, signal around 1.77 μm, idler around 2.71 μm and FWM signal around 1.35 μm are observed at an injection current of 560 mA. The influences of temperature, carrier density and pump wavelength on tuning characteristic are shown numerically and experimentally.

Two-color hyper-entangled photon pairs generation in a cold 85Rb atomic ensemble.

Hyper-entangled photon pairs are very promising in the quantum information field for enhancing the channel capacity in communication and improving compatibility for networks. Here we report on the experimental generation of a hyper-entangled photon pair at a wavelength of 795 nm and 1475 nm via the spontaneous four-wave mixing process in a cold 85Rb atomic ensemble. The photons in each pair generated are entangled in both the time-frequency and polarization degrees of freedom. Such hyper-entangled photon pairs with special wavelength have potential applications in high-dimensional quantum communication and quantum physics.

Photon-pair generation in lossy coupled-resonator optical waveguides via spontaneous four-wave mixing

We theoretically model pair generation and evolution via the nonlinear process of spontaneous four-wave mixing in a coupled-resonator optical waveguide in a photonic crystal slab. Using the adjoint master equation for a system of lossy coupled cavities, we calculate a symmetrized second-order coherence function to determine pair detection probability. We find that the scattering loss can have as large an effect on pair generation as waveguide dispersion. In particular, the wave-vector dependence of the loss can shift the frequency of the maximum detection probability and therefore cannot, in general, be ignored or treated via a simple overall loss factor.

Switching Correlation and Noise Level in Pr(3+):YSO Crystal via Dressing Nonlinear Phase.

We propose and experimentally demonstrate that the intensity noise correlation and the noise level of intensity-difference and intensity-sum in Stokes and anti-Stokes channel can be well controlled by the relative nonlinear phase in spontaneous parametric four-wave mixing process. By modulating the relative nonlinear phase, including self-phase modulation and cross-phase modulation, switching the correlation into anti-correlation and the relative intensity noise level between the intensity-difference and intensity-sum are realized. We also show that the variation tendencies of the relative intensity noise level and the corresponding intensity fluctuations correlation are in accordance with each other.

Generation of photon pairs through parametric processes in nonlinear waveguides with the account of losses

We present an analytical description of the process of spontaneous four-wave mixing in a cubic nonlinear fiber with linear losses. We consider the generation of photon pairs in the fiber when in the input of fiber is fed the pumping wave and single signal photon. The focus of attention is on three cases: when the signal photon propagates in the fiber without generating of biphotons; when the photon pair is generated; and when the photon is lost in the fiber. We also consider the cascade processes, but do not give them an analytical description because of their smallness. Description of the biphotons generation process we provide using the Schrodinger-type equation, and take into account the losses in the fiber through the introduction of the virtual beam splitters. We demonstrate the effectiveness of the generation of photon pairs through parametric processes.

Noise correlations controlled by dressed suppression and enhancement

The intensity noise correlations between anti-Stokes and Stokes fields, generated from spontaneous parametric four-wave mixing (SP-FWM) process have been investigated in a ladder-type three-level system of sodium atomic vapor. By introduction of an external dressing field, the strengthened (weakened) correlations are obtained under enhancement (suppression) condition of SP-FWM. Besides, sharp correlations have been obtained as attributed to a pair of non-classical beams generated from amplified spontaneous emission.

Fiber-based photon-pair source capable of hybrid entanglement in frequency and transverse mode, controllably scalable to higher dimensions.

We have designed and implemented a photon-pair source, based on the spontaneous four wave mixing (SFWM) process in a few-mode fiber, in a geometry which permits multiple, simultaneous SFWM processes, each associated with a distinct combination of transverse modes for the four participating waves. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorable, and ii) the spectral separation between neighboring processes is greater than the marginal spectral width of each process. Consequently, there is a direct correspondence between the joint amplitude of each process and each of the Schmidt mode pairs of the overall two-photon state. Our approach permits hybrid entanglement in discrete frequency and in transverse mode, whereby control of the number of supported fiber transverse modes allows scalability to higher dimensions while spectral filtering may be used for straightforward Schmidt mode discrimination.

Broadband photon pair generation in green fluorescent proteins through spontaneous four-wave mixing.

Recent studies in quantum biology suggest that quantum mechanics help us to explore quantum processes in biological system. Here, we demonstrate generation of photon pairs through spontaneous four-wave mixing process in naturally occurring fluorescent proteins. We develop a general empirical method for analyzing the relative strength of nonlinear optical interaction processes in five different organic fluorophores. Our results indicate that the generation of photon pairs in green fluorescent proteins is subject to less background noises than in other fluorophores, leading to a coincidence-to-accidental ratio ~145. As such proteins can be genetically engineered and fused to many biological cells, our experiment enables a new platform for quantum information processing in a biological environment such as biomimetic quantum networks and quantum sensors.

A compact, integrated silicon device for the generation of spectrally filtered, pair-correlated photons

The third-order nonlinearity of silicon gives rise to a spontaneous four-wave mixing process in which correlated photon pairs are generated. Sources based on this effect can be used for quantum computation and cryptography, and can in principle be integrated with standard CMOS fabrication technology and components. However, one of the major challenges is the on-chip demultiplexing of the photons, and in particular the filtering of the pump power, which is many orders of magnitude larger than that of the signal and idler photons. Here, we propose a photonic crystal coupled-cavity system designed so that the coupling of the pump mode to the output channel is strictly zero due to symmetry. We further analyze this effect in the presence of fabrication disorder and find that, even then, a pump suppression of close to 40 dB can be achieved in state-of-the-art systems. Due to the small mode volumes and high quality factors, our system is also expected to have a generation efficiency much higher than in standard micro-ring systems. Those two considerations make a strong case for the integration of our proposed design in future on-chip quantum technologies.

Photon-pair generation by intermodal spontaneous four-wave mixing in birefringent, weakly guiding optical fibers

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 "bow-tie" 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 which are present in the source, and ii) the characterization of the fiber used.

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.

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.

Dressed four-wave mixing second-order Talbot effect

We theoretically demonstrate second-order Talbot effect (SOTE) based on entangled photon pairs. The photon pairs are generated from the spontaneous parametric four-wave mixing (SPFWM) process in a cold atomic medium and can be taken as the imaging light in order to realize coincidence recording. A strong standing wave is used to create the electromagnetically induced grating in the entangled photon pairs channels. By changing the frequency detuning of the standing wave or the other optical fields participating in the process, we can manipulate the contrast of the second-order Talbot image. We use the second-order correlation function and the dressed-state picture to explain the SOTE occurring in the SPFWM process. Moreover, we demonstrate the scheme for SOTE based on the spatially correlated twin beams generated from the SPFWM process with injection. This scheme provides a convenient detection proposal for the SOTE at the cost of the image contrast. Compared to the previous self-imaging schemes, the present schemes have the characteristic of controllable image contrast and of nonlocal imaging, and thus, they might broaden their applications in imaging techniques and find applications in quantum lithography.