Nondegenerate Four-wave Mixing Process Research Articles

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Wavefront shaping with nonlinear four-wave mixing

Wavefront manipulations have enabled wide applications across many interdisciplinary fields ranging from optics and microwaves to acoustics. However, the realizations of such functional surfaces heavily rely on micro/nanofabrication to define the structured surfaces, which are fixed and only work within a limited spectrum. To address these issues, previous attempts combining tunable materials like liquid crystal or phase-change ones onto the metasurfaces have permitted extra tunability and working spectra, however, these additional layers bring in inevitable loss and complicate the fabrication. Here we demonstrate a fabrication-free tunable flat slab using a nonlinear four-wave mixing process. By wavefront-shaping the pump onto the flat slab, we can successfully tune the effective nonlinear refraction angle of the emitting FWM beams according to the phase-matching condition. In this manner, a focusing and a defocusing nonlinear of FWM beam through the flat slab have been demonstrated with a converging and a diverging pump wavefronts, respectively. Furthermore, a beam steering scheme over a 20° angle has been realized through a non-degenerate four-wave mixing process by introducing a second pump. These features open up a door to manipulating light propagation in an all-optical manner, paving the way to more functional and tunable flat slab devices in the applications of imaging and all-optical information.

Two-pump parametric amplification in the presence of fiber dispersion fluctuations: a comparative study.

Fiber optical parametric amplifiers (FOPAs) operating based on four-wave mixing (FWM) are versatile devices with increasing applications in optical communication systems. In this paper, the effects of dispersion fluctuations on the performance of bandwidth, ripple, parametric gain, and saturation power of a two-pump FOPA based on four-wave and six-wave models are studied and compared. Coupled-amplitude equations representing the non-degenerate FWM process in optical fiber are solved numerically to compute the parametric gain over the communication wavelengths. The behaviors of the performance parameters are critically analyzed and compared with different types of fluctuation strengths (or amplitudes) specified by the combinations of correlation length (Lc) and fluctuation amplitude (σ). Based on the results, it was found that the flat gain bandwidth for the four-wave model remains unchanged and is insensitive to the strengths of fluctuations. The gain ripples, however, get higher as the fluctuation strengths increase. On the other hand, the flat gain bandwidths of the six-wave model are hardly identified due to the tremendous and continuous ripples within the pump wavelengths. In addition, the minimum parametric gain values for both four-wave and six-wave models reduce as the fluctuation strengths increase. Also, the lowest value of parametric gain leads to the highest saturation power and vice versa. The dispersion fluctuations affect the FWM process's efficiency and deteriorate the overall amplifier performance, particularly for the six-wave model. The numerical analysis obtained via the six-wave model is especially useful since this model closely matches with practical circumstances.

Quantum beam splitter for orbital angular momentum of light: quantum correlation by four-wave mixing operated in a nonamplifying regime.

Nondegenerate four-wave mixing (FWM) process based on a double-Λ scheme in hot alkali metal vapor is a versatile tool in quantum state engineering, quantum imaging, and quantum precision measurements. In this Letter, we investigate the generation of quantum correlated twin beams which carry nonzero orbital angular momentums (OAMs) based on the FWM process in hot cesium vapor. The amplified probe beam and the newly generated conjugate beam in the FWM process have the same and opposite topological charge as the seed beam, respectively. We also explore the FWM process operated in a nonamplifying regime where quantum correlated twin beams carrying OAMs can still be generated. In this regime, the FWM process plays the role of quantum beam splitter for the OAM of light; that is, a device that can split a coherent light beam carrying OAM into quantum-correlated twin beams carrying OAMs. More generally, our setup can be used as a quantum beam splitter of images.

Generation of 87Rb resonant bright two-mode squeezed light with four-wave mixing.

Squeezed states of light have found their way into a number of applications in quantum-enhanced metrology due to their reduced noise properties. In order to extend such an enhancement to metrology experiments based on atomic ensembles, an efficient light-atom interaction is required. Thus, there is a particular interest in generating narrow-band squeezed light that is on atomic resonance. This will make it possible not only to enhance the sensitivity of atomic based sensors, but also to deterministically transfer quantum correlations between two distant atomic ensembles. We generate bright two-mode squeezed states of light, or twin beams, with a non-degenerate four-wave mixing (FWM) process in hot 85Rb in a double-lambda configuration. Given the proximity of the energy levels in the D1 line of 85Rb and 87Rb, we are able to operate the FWM in 85Rb in a regime that generates two-mode squeezed states in which both modes are simultaneously on resonance with transitions in the D1 line of 87Rb, one mode with the F = 2 to F' = 2 transition and the other one with the F = 1 to F' = 1 transition. For this configuration, we obtain an intensity difference squeezing level of 3.5 dB. Moreover, the intensity difference squeezing increases to -5.4 dB and -5.0 dB when only one of the modes of the squeezed state is resonant with the D1 F = 2 to F' =-2 or F = 1 to F' = 1 transition of 87Rb, respectively.

Plasmonic Mirrorless Optical Parametric Oscillator

We analyze a nondegenerate four-wave mixing process on a metal–dielectric interface in which the signal and idler waves are counter-propagating surface plasmons and the process is pumped by a free ...

Compact sub-kilohertz low-frequency quantum light source based on four-wave mixing in cesium vapor.

Using a nondegenerate four-wave mixing (FWM) process based on a double-Λ scheme in hot cesium vapor, we demonstrate a compact diode-laser-pumped quantum light source for the generation of quantum correlated twin beams with a maximum squeezing of 6.5dB. The squeezing is observed at a Fourier frequency in the audio band down to 0.7kHz which, to the best of our knowledge, is the first observation of sub-kilohertz intensity-difference squeezing in an atomic system so far. A phase-matching condition is also investigated in our system, which confirms the spatial-multi-mode characteristics of the FWM process. Our compact low-frequency squeezed light source may find applications in quantum imaging, quantum metrology, and the transfer of optical squeezing onto a matter wave.

Principle and noise performance of optical phase arithmetic devices using four wave mixing

The existing theoretical equations cannot provide an excellent guidance for developing four-wave mixing (FWM)-based optical logic devices, though the experiments have been done in several researches. The optimization of noise figure performances of such devices should be further investigated. In the paper, the universal analytic expressions for the amplitude and phase of the idler in degenerate or non-degenerate FWM process under pump depletion are derived in detail from the nonlinear coupled-mode equations for guiding optical waves propagation in highly nonlinear fiber. The universal analytic expressions are obtained by the first-and the third-kind of elliptic integrals. By using equivalent infinitesimal to calculate the limit of phase sensitive amplification, we find out the initial phase relationship between the idler and the input guided wave for phase-independent amplification, which is crucially important for explaining the operating principles of the FWM-based adder and subtracter. As an example, the configuration of non-degenerate FWM-based hybrid arithmetic device with three logic functions of A+B-C, A+C-B, and B+C-A for QPSK signals is presented, and then the noise transfer characteristics in terms of signal-to-noise ratio (SNR) and error vector magnitude (EVM) are taken into account by adjusting the fiber length, input wavelength, and optical power. The calculation results show as follows. 1) This kind of arithmetic device has a noise figure of about 1.1 dB and an input SNR of more than 24 dB is necessary for the symbol error rate of 10-3 without forward error correction, corresponding to an output EVM of 23.2%. 2) The length of highly nonlinear fiber used in the hybrid arithmetic device may be taken flexibly, provided that the variation of FWM conversion efficiency is controlled in a range of 1 dB relative to the maximum, with an EVM fluctuation of less than for the idlers. 3) The hybrid arithmetic device has an operating optical bandwidth of about 16 nm for the SNR degradation of 1.3 dB. 4) The output EVM increases with the increase of input power, and the allowable input power should be no more than 100 mW for an input SNR of 28 dB, noting that the larger the input SNR, the higher the allowable input power is.

Generating quantum correlated twin beams by four-wave mixing in hot cesium vapor

Using a nondegenerate four-wave mixing process based on a double-$\Lambda$ scheme in hot cesium vapor, we generate quantum correlated twin beams with a maximum intensity-difference squeezing of 6.5 dB. The substantially improved squeezing can be mainly attributed to very good frequency and phase-difference stability between the pump and probe beams in our experiment. Intensity-difference squeezing can be observed within a wide experimental parameter range, which guarantees its robust generation. Since this scheme produces multi-spatial-mode twin beams at the Cs $D_{1}$ line, it is of interest for experiments involving quantum imaging and coherent interfaces between atomic and solid-state systems.

Generation of frequency degenerate twin beams in Rb85 vapor.

We demonstrate a new phase-matching geometry for four-wave mixing processes in hot Rb85 vapor, in which all four fields propagate in different directions but two of them are degenerate in frequency. When used as a parametric amplifier with an injected seed, two types of quantum mechanically correlated twin-beam states, either frequency degenerate or nondegenerate, can be generated. The quantum noise reduction in the intensity difference is almost 7dB for the nondegenerate type and nearly 5dB for the degenerate type. The spatial nondegeneracy of the four waves allows a variety of configurations of parametric processes, leading to flexible control for both phase insensitive and sensitive parametric amplification. The spatially nondegenerate but frequency degenerate four-wave mixing process will find wide applications in quantum metrology, quantum communication, and quantum information of continuous variables.

Squeezed-twin-beam generation in strongly absorbing media

In this Letter we experimentally demonstrate the generation of squeezed, bright twin beams which arise due to competing gain and absorption, in a medium that is overall transparent. To accomplish this, we make use of a non-degenerate four-wave mixing process in warm potassium vapor, such that one of the twin beams experiences strong on-resonant absorption. At room temperature and above, due to Doppler broadening and smaller frequency detunings compared to other schemes, the ground state hyperfine splittings used in the present double-$\Lambda$ setup are completely overlapped. We show that despite the resulting significant asymmetric absorption of the twin beams, quantum correlations may still be generated. Our results also demonstrate that the simplified model of gain, followed by loss, is insufficient to describe the amount of quantum correlation resulting from the process.

A theory for non-degenerate four-wave mixing in doped graphene

We present a theoretical study of the nonlinear optical (NLO) response of doped graphene to two coherent laser beams, of frequencies ω1 and ω2, resulting in the generation of radiation at frequency ωσ=2ω1−ω2. The two main ingredients of the developed theory are the interplay of interband and intraband electron motion, induced by the incident light waves, and the finite lifetime of excited electronic states, caused by electron scattering. Adopting a tight-binding approximation for the π-electronic band structure of graphene and the Genkin-Mednis formalism of the nonlinear conductivity theory of semiconductors, we calculate the third-order NLO susceptibility χ(3)(−ωσ;ω1,ω1,−ω2) responsible for the non-degenerate four-wave mixing process under consideration. Our calculations show the resonant enhancement of the |χ(3)| (up to a value of 2.8×10−7esu) when the frequencies ω1 and ω2 of the input beams are mat"ched to provide a resonance for the output photon energy ℏωσ with an effective optical gap of 2EF in the π-electronic band structure of doped graphene (EF is the Fermi energy of charge carriers in the graphene, tunable by an external gate voltage). The results obtained may be of practical interest for generating mid-infrared radiation from doped graphene pumped with two near-infrared laser beams.

Graphene-assisted multiple-input high-base optical computing.

We propose graphene-assisted multiple-input high-base optical computing. We fabricate a nonlinear optical device based on a fiber pigtail cross-section coated with a single-layer graphene grown by chemical vapor deposition (CVD) method. An approach to implementing modulo 4 operations of three-input hybrid addition and subtraction of quaternary base numbers in the optical domain using multiple non-degenerate four-wave mixing (FWM) processes in graphene coated optical fiber device and (differential) quadrature phase-shift keying ((D)QPSK) signals is presented. We demonstrate 10-Gbaud modulo 4 operations of three-input quaternary hybrid addition and subtraction (A + B − C, A + C − B, B + C − A) in the experiment. The measured optical signal-to-noise ratio (OSNR) penalties for modulo 4 operations of three-input quaternary hybrid addition and subtraction (A + B − C, A + C − B, B + C − A) are measured to be less than 7 dB at a bit-error rate (BER) of 2 × 10−3. The BER performance as a function of the relative time offset between three signals (signal offset) is also evaluated showing favorable performance.

Highly Nondegenerate Four-Wave Mixing in Single-Mode Fabry–Pérot Laser Diode Subject to Dual-Mode Injection

In this paper, highly nondegenerate four-wave mixing (NDFWM) resulting from external dual-mode injection (pump-probe structure) in the single-mode Fabry-Perot laser diode (SMFP-LD) is proposed and experimentally demonstrated. To cause the effective NDFWM process, both pump and probe beams with enough power levels should, respectively, be close to various resonance modes in the active region, whose detuning frequency can be discontinuously varied from more than 100 GHz to up to 800 GHz. Normalized conversion efficiency (NCE) and optical signal-to-noise ratio (OSNR) of newly generated conjugate signals are strongly dependent on external injection power, wavelength detuning, and detuning frequency. In addition, the NDFWM process exhibits injection probe power-related hysteresis behaviors, whereas the input power and wavelength for pump beam are, respectively, fixed at some special constants.

Optical data exchange of differential quadrature phase-shift keying based on four-wave mixing using a semiconductor optical amplifier

We propose to use a semiconductor optical amplifier as the nonlinear medium to realize data exchange of two differential quadrature phase-shift keying (DQPSK) signals based on the nondegenerate four-wave mixing (FWM) process. This scheme exploits the parametric depletion effect of the FWM process, when proper pump power and wavelength result in almost negligible noise of the original signal for the converted signal after data exchange. Optical data exchange of two DQPSK signals at 10 Gbps is achieved with a power penalty of less than 4 dB at the bit-error rate of 10−9.

A universal quantum information processor for scalable quantum communication and networks.

Entanglement provides an essential resource for quantum computation, quantum communication, and quantum networks. How to conveniently and efficiently realize the generation, distribution, storage, retrieval, and control of multipartite entanglement is the basic requirement for realistic quantum information processing. Here, we present a theoretical proposal to efficiently and conveniently achieve a universal quantum information processor (QIP) via atomic coherence in an atomic ensemble. The atomic coherence, produced through electromagnetically induced transparency (EIT) in the Λ-type configuration, acts as the QIP and has full functions of quantum beam splitter, quantum frequency converter, quantum entangler, and quantum repeater. By employing EIT-based nondegenerate four-wave mixing processes, the generation, exchange, distribution, and manipulation of light-light, atom-light, and atom-atom multipartite entanglement can be efficiently and flexibly achieved in a deterministic way with only coherent light fields. This method greatly facilitates the operations in quantum information processing, and holds promising applications in realistic scalable quantum communication and quantum networks.

Optical data exchange of m-QAM signals using a silicon-organic hybrid slot waveguide: proposal and simulation.

We present modulation-format-transparent data exchange for m-ary quadrature amplitude modulation (m-QAM) signals using a single silicon-organic hybrid slot waveguide which offers tight light confinement and enhanced nonlinearity. By exploiting the parametric depletion effect of non-degenerate four-wave mixing (ND-FWM) process in the slot waveguide, we simulate low-power (<10 mW) ultrahigh-speed optical data exchange of 640 Gbaud (2.56 Tbit/s) optical time-division multiplexed (OTDM) 16-QAM and 640 Gbaud (3.84 Tbit/s) OTDM 64-QAM signals and characterize the operation performance in terms of error vector magnitude (EVM) and bit-error rate (BER). The calculated signal-to-noise ratio (SNR) penalties of data exchange are negligible for 2.56 Tbit/s 16-QAM signals and less than 2 dB for 3.84 Tbit/s 64-QAM signals at a BER of 2e-3. For a given pump power of 9 mW, the operation performance dependence on the waveguide length is studied, showing an optimized waveguide length of ~17 mm. For a given waveguide length of 17 mm, the SNR penalty of data exchange, at a BER of 2e-3, is kept below 4 dB when varying input pump power from 8.4 to 9.8 mW for 2.56 Tbit/s 16-QAM and from 8.9 to 9.2 mW for 3.84 Tbit/s 64-QAM. In addition, data exchange running at low speed (e.g. 20 Gbaud) and data exchange taking into account waveguide propagation loss are also analyzed with favorable operation performance.

Generation of Airy beams by four-wave mixing in Rubidium vapor cell.

We report on an experimental generation of Airy beams by four-wave mixing (FWM) in atomic vapor cells. This is achieved by using a non-degenerate FWM process, which occurs with two Gaussian pump beams and one Airy signal beam in hot Rubidium vapor. After satisfying the phase matching condition, a FWM field with the profile of an Airy beam can be generated. In our experiment, the diffraction-free and self-healing behaviors of the generated FWM beam are examined. The results shown that the generated FWM beam is an Airy beam. The nonlinear generation process can be extended to other configurations in the atomic medium, which will be useful for manipulation and application of Airy beams in atomic systems.

Telecom-band degenerate-frequency photon pair generation in silicon microring cavities

In this Letter, telecom-band degenerate-frequency photon pairs are generated in a specific mode of a silicon microring cavity by the nondegenerate spontaneous four-wave mixing (SFWM) process, under two continuous-wave pumps at resonance wavelength of two different cavity modes. The ratio of coincidence to accidental coincidence is up to 100 under a time bin width of 5ns, showing their characteristics of quantum correlation. Their quantum interference in balanced and unbalanced Mach-Zehnder interferometers is investigated theoretically and experimentally, and the results show potential in quantum metrology and quantum information.

Measurement of intensity difference squeezing via non-degenerate four-wave mixing process in an atomic vapor

We report the measurement of the intensity difference squeezing via the non-degenerate four-wave mixing process in a rubidium atomic vapor medium. Two pairs of balanced detection systems are employed to measure the probe and the conjugate beams, respectively. It is convenient to get the quantum shot noise limit, the squeezed and the amplified noise power spectra. We also investigate the influence of the input extra quadrature amplitude noise of the probe beam. The influence of the extra noise can be minimized and the squeezing can be optimized under the proper parameter condition. We measure the −3.7-dB intensity difference squeezing when the probe beam has a 3-dB extra quadrature amplitude noise. This result is slightly smaller than −4.1 dB when the ideal coherent light (no extra noise) for the probe beam is used.