We demonstrate a new four-wave mixing (4WM) geometry based on structured light. By utilizing near-field diffraction through a narrow slit, the pump beam is asymmetrically structured to modify the phase matching condition, generating multi-mode output in both the spatial and frequency domains. We show that the frequency parameter enables selection of various spatial-mode outputs, including a twin-beam geometry which preserves relative intensity squeezing shared between the two beams. The results suggest that the engineering of atomic states via structured light may provide a pathway to a diverse set of quantum resources based on multi-mode squeezed light.
We report on four-wave mixing in a silicon microring resonator using a self-pumping scheme instead of an external laser. The ring resonator is inserted in an external-loop cavity with a fibered semiconductor amplifier as a source of gain. The silicon microring acts as a filter and we observe lasing in one of the microring's resonances. We study correlations between signal and idler generated beams using a Joint Spectral Density experiment.
We demonstrate experimental generation of spatially-entangled photon-pairs by spontaneous parametric down conversion (SPDC) using a partial spatially coherent pump beam. By varying the spatial coherence of the pump, we show its influence on the downconverted photon's spatial correlations and on their degree of entanglement, in excellent agreement with theory. We then exploit this property to produce pairs of photons with a specific degree of entanglement by tailoring of the pump coherence length. This work thus unravels the fundamental transfer of coherence occuring in SPDC processes, and prov…
We study the process of co-polarized spontaneous four-wave mixing in single-mode optical fibers, with an emphasis on an analysis of the conversion efficiency. We consider both the monochromatic-pumps and pulsed-pumps regimes, as well as both the degenerate-pumps and non-degenerate-pumps configurations. We present analytical expressions for the conversion efficiency, which are given in terms of double integrals. In the case of pulsed pumps we take these expressions to closed analytical form with the help of certain approximations. We present results of numerical simulations, and compare them to…
The advanced-wave picture is "... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ..." [A. V. Belinskii and D. N. Klyshko, JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture; an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case…
Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field, and have neglected its spatial structure. We present a simple model which allows to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically-tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2N+1-partite entanglement using 2N symmetrically-tilted plane pump waves. Another interesting feature is the possibility of entanglement loc…
In this article, we use quantum Langevin equations to provide a theoretical understanding of the non-classical behavior of Kerr optical frequency combs when pumped below and above threshold. In the configuration where the system is under threshold, the pump field is the unique oscillating mode inside the resonator, and triggers the phenomenon of spontaneous four-wave mixing, where two photons from the pump are symmetrically up- and down-converted in the Fourier domain. This phenomenon can only be understood and analyzed from a fully quantum perspective as a consequence of the coupling between …
We experimentally demonstrate the conversion of a Gaussian beam to an approximate Bessel-Gauss mode by making use of a non-collinear four-wave mixing process in hot atomic vapor. The presence of a strong, spatially non-Gaussian pump both converts the probe beam into a non-Gaussian mode, and generates a conjugate beam that is in a similar non-Gaussian mode. The resulting probe and conjugate modes are compared to the output of a Gaussian beam incident on an annular aperture that is then spatially filtered according to the phase-matching conditions imposed by the four-wave mixing process. We find…
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.
We consider integrated photon pair sources based on spontaneous four-wave mixing and derive expressions for the pump powers at which various nonlinear processes become relevant for a variety of source materials and structures. These expressions serve as rules of thumb in identifying reasonable parameter regimes for the design of such sources. We demonstrate that if pump powers are kept low enough to suppress cross-phase modulation, multi-pair events as well as many other nonlinear effects are often also constrained to negligible levels.
Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. While the polarization degree of freedom of the photon is a common choice for many studies, it is restricted to only two orthogonal states, hence qubits for manipulation. In this paper, we theoretically model as well as experimentally verify a novel scheme of approximating photonic qutrits by modulating the pump beam in a spontaneous parametric down conversion process using a three-slit aperture. The emerging bi-photon fields behave like qutrits and are found to b…
Coherent, purely-dispersive three-wave mixing systems in optics and superconducting microwave circuits can be operated as parametric amplifiers, generating from a pump wave at one frequency amplified signal and idler waves at lower frequencies. Here we demonstrate the reciprocal process using a Josephson amplifier in which coherently imposed signal and idler beams up-convert to the pump frequency. For signal and idler beams strong enough to significantly deplete the pump, we show that this reciprocal process ("coherent cancellation") leads to large, phase-sensitive modulation and even enhancem…
We demonstrate an unseeded, multimode four-wave mixing process in hot $^{85}$Rb vapor, using two pump beams of the same frequency that cross at a small angle. This results in the simultaneous fulfillment of multiple phase-matching conditions that reinforce one another to produce four intensity-stabilized bright output modes at two different frequencies. Each generated photon is directly correlated to exactly two others, resulting in the preferred four-mode output, in contrast to other multimode four-wave mixing experiments. This provides significant insight into the optimal configuration of th…
Frequency mixing in ferrimagnetic resonators based on yttrium and calcium vanadium iron garnets (YIG and CVBIG) is employed for studying their nonlinear interactions. The ferrimagnetic Kittel mode is driven by applying a pump tone at a frequency close to resonance. We explore two nonlinear frequency mixing configurations. In the first one, mixing between a transverse pump tone and an added longitudinal weak signal is explored, and the experimental results are compared with the predictions of the Landau-Zener-Stuckelberg model. In the second one, intermodulation measurements are employed by mix…
Continuous-variable model for arbitrary image propagation via Dirac-comb expansion in Four-Wave Mixing
Universidad de Chile（智利大学）；Millennium Institute for Research in Optics - MIRO（光学研究千年研究所）；Universidade Federal do ABC–UFABC（圣安德烈联邦大学）；Universidad de Concepción（康塞普西翁大学）
We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm0.1)$ and $(-21.2\pm0.1)$ dB in the two outputs, with a corresponding transmission of 97 and 99 %. This technique avoids the need to use spatial separation of four-wave mixing modes and thus opens the…
We describe a method for non-degenerate four-wave mixing in a cold sample of 4-level atoms. An integral part of the four-wave mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase-matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur, rather the density modulation acts to "self phase-match" the fields durin…
We measure the time-energy correlation of broadband, spontaneously generated four wave mixing (FWM), and demonstrate novel time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband (>100nm), sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down conversion, its unique dependence on pump inte…
Possibilities of generation of lower order and higher order intermodal entanglement in 87Rb 5S-5P-5D hyperfine manifold are rigorously investigated using Sen-Mandal perturbative technique by showing the equivalence of the system with the four-wave mixing (FWM) process. The investigation has revealed that for a set of experimentally realizable/relevant parameters we can observe lower order and higher order intermodal entanglement between pump and signal modes, signal and idler modes, and idler and pump modes in a FWM process associated with the 87Rb 5S-5P-5D hyperfine manifold. In addition, tri…
Single photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at sub-watt pump powers. Using a quantum-mechanical Hamiltonian formalism, we present a detailed theoretical analysis of the conversion dynamics in these systems, and show that they are capable of converting single- and multi-photon quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability dens…
Polarisation-resolved identification of spontaneous four-wave mixing processes in a multimode fused tapered fibre coupler
University of Ottawa（渥太华大学）；National Research Council of Canada（加拿大国家研究委员会）；Nexus for Quantum Technologies, Department of Physics, University of Ottawa（渥太华大学物理系量子技术联盟）；Département de physique et astronomie, Université de Moncton（蒙克顿大学物理与天文学系）；Quantinuum；Corning Incorporated（康宁公司）
The characterisation of loss in optical waveguides is essential in understanding the performance of these devices and their limitations. Whilst interferometric-based methods generally provide the best results for low-loss waveguides, they are almost exclusively used to provide characterization in cases where the waveguide is spatially single-mode. Here, we introduce a Fabry-Pérot-based scheme to estimate the losses of a nonlinear (birefringent or quasi-phase matched) waveguide at a wavelength where it is multi-mode. The method involves measuring the generated second harmonic power as the pump …
We suggest a novel optical parametric generator (OPG) in which one of the down-converted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump rather than being degraded by it. As a result the generated beams, signal and idler, are bright, due to a high conversion efficiency, spatially nearly single-mode, due to the preferred direction of the Poynting vector, tuneable over a wide range of wavelengths, and broadband. The two beams are also correlated in frequency and in the pho…
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 exp…
We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-de…
Temporal coherence of individual signal or idler beam, determined by the spectral correlation property of photon pairs, is important for realizing quantum interference among independent sources. To understand the effect of chirp on the temporal coherence property, two series of experiments are investigated by introducing different amount of chirp into either the pulsed pump or individual signal (idler) beam. In the first one, based on spontaneous four wave mixing in a piece of optical fiber, the intensity correlation function of the filtered individual signal beam, which characterizes the degr…
The development of a quantum network relies on the advances of hybrid systems which includes ground to ground communication. However, the atmospheric turbulence of the environment poses a severe challenge to the optical quantum link. In this paper, we outline a theoretical and experimental investigation of the influence of atmospheric turbulence on the coincidence detection of the entangled photon pairs using a fully and partially spatially coherent pump beam. A spatial light modulator is encoded with Kolmogorov model to mimic the atmospheric turbulence strength. The results show that the phot…
We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering co…
We present the optimal design for an on-chip single-photon source based on spontaneous four-wave mixing in a system of coupled ring microresonators, which provides frequency uncorrelated joint spectral amplitude of the biphoton field and thereby generation of pure single-photon heralded states. A simple method is proposed for suppressing negative dispersion effects by optimizing the controlled spectroscopic parameters of the system. It shown that the optimal coupling parameters, in combination with the optimal spectral width of the pump pulse, give rise to the highest purity of the heralded ph…
We performed an experiment to observe the storages of an input probe field and an idler field generated through an off-axis four-wave mixing (FWM) process via a double-lambda configuration in a cold atomic ensemble. We analyzed the underlying physics in detail and found that the retrieved idler field came from two parts if there was no single-photon detuning for pump pulse: part 1 was from the collective atomic spin (the input probe field, the coupling field and the pump field combined to generate the idle field through FWM, then the idler was stored through electromagnetically induced transpa…
We develop a theoretical analysis of four-wave mixing used to generate photon pairs useful for quantum information processing. The analysis applies to a single mode microstructured fibre pumped by an ultra-short coherent pulse in the normal dispersion region. Given the values of the optical propagation constant inside the fibre, we can estimate the created number of photon pairs per pulse, their central wavelength and their respective bandwidth. We use the experimental results from a picosecond source of correlated photon pairs using a micro-structured fibre to validate the model. The fibre is…
Four-wave mixing (4WM) is a known source of intense non-classical twin beams. It can be generated when an intense laser beam (the pump) and a weak laser beam (the seed) overlap in a $χ^{(3)}$ medium (here cesium vapor), with frequencies close to resonance with atomic transitions. The twin beams generated by 4WM have frequencies naturally close to atomic transitions, and can be intense (gain $\gg 1$) even in the CW pump regime, which is not the case for PDC $χ^{(2)}$ phenomenon in non-linear crystals. So, 4WM is well suited for atom-light interaction and atom-based quantum protocols. Here we pr…
We study photon pair generation through scalar spontaneous four-wave mixing in single-mode fibre and for frequency-degenerate pumps; we concentrate on source geometries which fulfil full group velocity matching (GVM), i.e. where the pump, signal and idler propagate at identical group velocities. We discuss two experimental techniques which permit the attainment of full GVM, and discuss the resulting two-photon state properties. In particular, we show that full GVM can lead to sources which approach phasematching unconstrained by dispersion and therefore with a remarkably large bandwidth. We al…
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 non-degenerate. Based on this analysis, we derive conditions on the pump frequencies and on the fiber dispersion parameters which guarantee the generation of ultra-broadband 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.…
We introduce a new kind of spontaneous four wave mixing process for the generation of photon pairs, in which the four waves involved counter-propagate in a guided-wave χ^{(3)} medium; we refer to this process as counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for the simplest CP-SFWM source, in which all waves propagate in the same polarization and transverse mode and in which self- and cross-phase modulation effects are negligible, phasematching is attained automatically regardless of dispersion in the fiber or waveguide. Furthermore, we show that in two distinct vers…
We propose an approach to generate strong quantum entanglement by the controllable four wave mixing mechanism in a single cavity, weak coupling optomechanical system. The optomechanical system is driven by a strong two tone pump field and a weak signal field, simultaneously. The two tone pump field consists of a lower and an upper sideband, which couple with the optical cavity and mechanical resonator, and generate the beam splitter and two mode squeezing interactions under the rotating wave approximation. This interaction mechanism modifies the effective susceptibility of the optomechanical c…
We propose to control spin-mixing dynamics in a gas of spinor atoms, via the combination of two off-resonant Raman transition pathways, enabled by a common cavity mode and a bichromatic pump laser. The mixing rate, which is proportional to the synthesized spin-exchange interaction strength, and the effective atomic quadratic Zeeman shift (QZS), can both be tuned by changing the pump laser parameters. Quench and driving dynamics of the atomic collective spin are shown to be controllable on a faster time scale than in existing experiments based on inherent spin-exchange collision interactions. T…
Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped non-seeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing.
An asymmetric double quantum wells (QWs) structure with resonant tunneling is suggested to achieve high efficient four wave mixing (FWM). We analytically demonstrate that the resonant tunneling can induce high efficient mixing wave in such a semiconductor structure with a low light pump wave. In particular, the FWM conversion efficiency can be enhanced dramatically in the vicinity of the center frequency. This interesting scheme may be used to generate coherent long-wavelength radiation in solid-state system.
Correlated photon pairs produced by a spontaneous parametric down conversion (SPDC) process can be used for secure quantum communication over long distances including free space transmission over a link through turbulent atmosphere. We experimentally investigate the possibility to utilize the intrinsic strong correlation between the pump and output photon spatial modes to mitigate the negative targeting effects of atmospheric beam wander. Our approach is based on a demonstration observing the deflection of the beam on a spatially resolved array of single photon avalanche diodes (SPAD-array).
We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber desig…
We present a general model, based on a Hamiltonian approach, for the joint quantum state of photon pairs generated through pulsed spontaneous four-wave mixing, including nonlinear phase-modulation and a finite material response time. For the case of a silica fiber, it is found that the pair-production rate depends weakly on the waveguide temperature, due to higher-order Raman scattering events, and more strongly on pump-pair frequency detuning. From the analytical model, a numerical scheme is derived, based on the well-known split-step method. This scheme allows computation of joint states whe…
Quantum-limited Josephson parametric amplifiers are crucial components in circuit QED readout chains. The dynamic range of state-of-the-art parametric amplifiers is limited by signal-induced Stark shifts that detune the amplifier from its operating point. Using a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) as an active component, we show the ability to in situ tune the device flux and pump to a dressed Kerr-free operating point, which provides a 10-fold increase in the number of photons that can be processed by our amplifier, compared to the nominal working point. Our propos…
We have fabricated a wide-bandwidth, high dynamic range, low-noise cryogenic amplifier based on a superconducting kinetic inductance traveling-wave device. The device was made from NbTiN and consisted of a long, coplanar waveguide on a silicon chip. By adding a DC current and an RF pump tone we are able to generate parametric amplification using three-wave mixing. The devices exhibit gain of more than 15 dB across an instantaneous bandwidth from 4 to 8 GHz. The total usable gain bandwidth, including both sides of the signal-idler gain region, is more than 6 GHz. The noise referred to the input…
We develop a concept of the traveling-wave Josephson parametric amplifier exploiting quadratic nonlinearity of a serial array of one-junction SQUIDs embedded in a superconducting transmission line. The external magnetic flux applied to the SQUIDs makes it possible to efficiently control the shape of their current-phase relation and, hence, the balance between quadratic and cubic (Kerr-like) nonlinearities. This property allows us to operate in the favorable three-wave-mixing mode with minimal phase mismatch, an exponential dependence of the power gain on number of sections $N$, a large bandwid…
