We report experimental determination of the phase-matching function for type-II three-wave mixing in a periodically poled KTiOPO_4 waveguide in the 792-815 nm spectral region. The measurement was performed by sum-frequency generation of spectrally tuned fundamental components. Strong dependence of the observed signal on the excited spatial modes in the waveguide has been observed and fully interpreted. These results indicate a route to employ the waveguide for spontaneous parametric down-conversion producing photon pairs in well-defined spatial modes.
We generated -2.2 dB of broadband amplitude squeezing at 1064 nm in a periodically poled KTiOPO_4 (PPKTP) waveguide, by coupling of the fundamental and second harmonic continuous-wave fields. This is the largest amount of squeezing obtained to date in a KTP waveguide, limited by propagation losses. This result paves the way for further improvements by use of lower-loss buried ion-exchanged waveguides.
We demonstrate generation of high-purity photon pairs at 1560 nm in a single spatial mode from a periodically-poled KTiOPO_4 (PPKTP) waveguide. With nearly lossless spectral filtering, the PPKTP waveguide source shows approximately 80 % single-mode fiber coupling efficiency and is well suited for high-dimensional time-energy entanglement-based quantum key distribution. Using high-count-rate self-differencing InGaAs single-photon avalanche photodiodes configured with either square or sinusoidal gating, we achieve > 1 Mbit/s raw key generation with 3 bits-per-photon encoding, and, to the best of…
We report generation of near-infrared photon pairs in fundamental spatial modes via type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide supporting multiple transverse modes. This demonstrates experimentally a versatile scheme for controlling the spatial characteristics of the produced nonclassical light based on exploitation of intermodal dispersion. The down-converted photons are characterized by the measurement of the beam quality factors in the heralded regime.
We report the generation of a type-I multimode two-photon state on a rubidium D$_2$ line (780 nm) using periodically poled KTiOPO$_4$ crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function, the cross-correlation between two photons shows a cavity bandwidth of about 7.8 MHz. We also use a Fabry-P$\acute{\rm{e}}$rot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retr…
We present a scheme for generating and manipulating three-mode squeezed states with genuine tripartite entanglement by injecting single-mode squeezed light into an array of coupled optical waveguides. We explore the possibility to selectively generate single-mode squeezing or multimode squeezing at the output of an elliptical waveguides array, determined solely by the input light polarization. We study the effect of losses in the waveguides array and show that quantum correlations and squeezing are preserved for realistic parameters. Our results show that arrays of optical waveguides are suita…
We report the observation of correlated photon pairs generated by spontaneous parametric down-conversion in a quasi-phase matched KTiOPO4 nonlinear waveguide. The highest ratio of coincidence to single photon count rates observed in the 830 nm wavelength region exceeds 18%. This makes nonlinear waveguides a promising source of correlated photons for metrology and quantum information processing applications. We also discuss possibilities of controlling the spatial characteristics of the down-converted photons produced in multimode waveguide structures.
We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of $N$-partical quantum entangled states is generated by using $N$ independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve $\sqrt{N}$ enhancement over the precision of the measurement $N$ times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization…
We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.
We present a study of the propagation of higher-order spatial modes in a waveguided parametric down-conversion photon pair source. Observing the multimode photon pair spectrum from a periodically poled KTiOPO$_4$ waveguide allowed us to isolate individual spatial modes through their distinctive spectral properties. We have measured directly the spatial distribution of each mode of the photon pairs, confirming the findings of our waveguide model, and demonstrated by coincidence measurements that the total parity of the modes is conserved in the nonlinear interaction. Furthermore, we show that w…
We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine-tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to charact…
We present experimental realization of type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide. We demonstrate that by careful exploitation of intermodal dispersion in the waveguide it is feasible to produce photon pairs in well defined transverse modes without any additional spatial filtering at the output. Spatial characteristics is verified by measurements of the M2 beam quality factors. We also prepared a postselected polarization-entangled two-photon state shown to violate Bell's inequality. Similar techniques based …
We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\cal PT$ or $\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first tim…
Configurable and scalable continuous variable quantum networks for measurement-based quantum information protocols or multipartite quantum communication schemes can be obtained via parametric down conversion (PDC) in non-linear waveguides. In this work, we exploit symmetric group velocity matching (SGVM) to engineer the properties of the squeezed modes of the PDC. We identify type II PDC in a single waveguide as the best suited process, since multiple modes with non-negligible amount of squeezing can be obtained. We explore, for the first time, the waveguide dimensions, usually only set to ens…
We compare phase matching for four-wave mixing using one, two, three, and four waveguide modes. For the comparison, we use numerical optimizations and an estimate of the generated idler power. We present results for few-mode fibers and nano-rib waveguides and show that for both waveguide types, four-wave mixing bandwidths and idler powers are best for one- and two-mode operation and that four-mode four-wave mixing is not feasible at all. Some nano-rib waveguides support three-mode four-wave mixing, albeit with much reduced bandwidth and reduced idler power.
Quantum memory is a fundamental building block for large-scale quantum networks. On-demand optical storage with a large bandwidth, a high multimode capacity and an integrated structure simultaneously is crucial for practical application. However, this has not been demonstrated yet. Here, we fabricate an on-chip waveguide in a $\mathrm {^{151}Eu^{3+}:Y_2SiO_5}$ crystal with insertion losses of 0.2 dB, and propose a novel pumping scheme to enable spin-wave atomic frequency comb (AFC) storage with a bandwidth of 11 MHz inside the waveguide. Based on this, we demonstrate the storage of 200 tempora…
Multimode-cavity picture of non-Markovian waveguide QED
Universität Ulm（乌尔姆大学）；NEST, Istituto Nanoscienze-CNR（意大利国家纳米科学技术研究所（NEST））；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole-dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited…
Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study has focused on atomic or atomic-like local quantum systems due to their strong light-matter interaction useful for quantum applications. Here, we study few-photon transport via a waveguide-coupled multimode optical cavity with second-order bulk nonlinearity. We develop a Feynman diagram approach and compute the scattering matrix of the one- and two-photon transport. Based on the calculated scattering matrix, we show highly nonclassical photonic effect…
We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.
We report the realization of a bright ultrafast two-mode squeezer based on type II parametric downconversion (PDC) in periodically poled $\mathrm{KTiOPO_4}$ (PP-KTP) waveguides. It produces a pulsed two-mode squeezed vacuum state: a photon-number entangled pair of truly single-mode pulses or, in terms of continuous variables quantum optics, a pulsed, single mode Einstein-Podolsky-Rosen (EPR) state in the telecom regime. We prove the single mode character of our source by measuring its $g^{(2)}$ correlation function and demonstrate a mean photon number of up to 2.5 per pulse, equivalent to 11dB…
Wavevector quasi-phase matching was devised in the 1960s as a way to boost nonlinear interactions with efficient quantum noise squeezing as one outstanding outcome. In the era of quantum technologies, we propose a new coupling quasi-phase matching for efficient generation of multimode downconverted quantum light in nonlinear waveguide arrays. We highlight this technique achieving multimode quantum entanglement and Einstein-Podolsky-Rosen steering buildup. We discuss the feasibility of this method with current technology and demonstrate its competitiveness as a resource for continuous variables…
Integrated quantum optics has drastically reduced the size of table-top optical experiments to the chip-scale, allowing for demonstrations of large-scale quantum information processing and quantum simulation. However, despite these advances, practical implementations of quantum photonic circuits remain limited because they consist of large networks of waveguide interferometers that path encode information which do not easily scale. Increasing the dimensionality of current quantum systems using higher degrees of freedom such as transverse spatial field distribution, polarization, time, and freq…
We study light scattering off a two-dimensional (2D) array of atoms driven to Rydberg levels. We show that the problem can be mapped to a generalized model of waveguide QED, consisting of multiple 1D photonic channels (transverse modes), each of which directionally coupled to a corresponding Rydberg surface mode of the array. In the Rydberg blockade regime, collective excitations of different surface modes block each other, leading to multi-channel correlated photonic states. Using an analytical approach, we characterize inter-channel quantum correlations, and elucidate the role of collective …
Based on the interaction between different spatial modes, semiconductor Bragg-reflection waveguides provide a highly functional platform for non-linear optics. Therefore, the control and engineering of the properties of each spatial mode is essential. Despite the multimodeness of our waveguide, the well-established Fabry-Perot technique for recording fringes in the optical transmission spectrum can successfully be employed for a detailed linear optical characterization when combined with Fourier analysis. A prerequisite for the modal sensitivity is a finely resolved transmission spectrum that …
Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic and scalable way to generate these states consists of fully exciting $N$ quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted $N$-photon state turns out to be a highly entangled multimode state, and to characterise its metrological properties in this work we: (i) develop theoretical tools to compute the Quantum Fisher I…
We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that the distribution function of the transmitted pulse can be negative for the nonclassical input (i.e., single-photon Fock state). This reveals the quasiprobability nature of photon distribution. Analytical expressions for photon densities in the momentum space as well as in the coordinate space are obtained for the mentioned single-photon Gaussian input. We als…
In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., Phys. Rev. Appl. $\bf{14}$, 044025 (2020). We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solut…
Compared to traditional nonlinear optical crystals, like BaB$_2$O$_4$, KTiOPO$_4$ or LiNbO$_3$, semiconductor integrated sources of photon pairs may operate at pump wavelengths much closer to the bandgap of the materials. This is also the case for Bragg-reflection waveguides (BRW) targeting parametric down-conversion (PDC) to the telecom C-band. The large nonlinear coefficient of the AlGaAs alloy and the strong confinement of the light enable extremely bright integrated photon pair sources. However, under certain circumstances, a significant amount of detrimental broadband photoluminescence ha…
We study the process of multimode Spontaneous Parametric Down--Conversion (SPDC) in the lossy, one dimensional waveguide. We propose a description using first order Correlation Functions (CF) in the fluorescence fields, as a very fruitful and easy approach providing us with a complete information about the final multimode state. We formulate the equation of the evolution of the multimode CF along the crystal using four characteristic length scales. We solve it analytically in the one mode case and numerically in the multimode case. We capture simultaneous effects of three wave mixing with ultr…
Harnessing multimode waves allows high information capacity through modal expansions. Although passive multimode devices including waveguides, couplers, and multiplexers have been demonstrated for broadband responses in momentum or frequency domains, collective switching of multimodes remains a challenge, due to the difficulty in imposing consistent dynamics on all eigenmodes. Here we overcome this limitation by realizing digital switching of spatially random waves, based on supersymmetric pairs of multimode potentials. We reveal that supersymmetric transformations of any parity-symmetric pote…
The addition of nonlinearity to an harmonic resonator provides a route to complex dynamical behaviour of resonant modes, including coupling between them. We present a superconducting device that makes use of the nonlinearity of Josephson junctions to introduce a controlled, tunable, nonlinear inductance to a thin film coplanar waveguide resonator. Considering the device as a potential quantum optical component in the microwave regime, we create a sensitive bifurcation amplifier and then demonstrate spectroscopy of other resonant modes via the intermode coupling. We find that the sensitivity of…
Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter single- and two-photon components of an input pulse into orthogonal temporal modes with a fidelity $\gtrsim 0.9997$. We develop a general theory to characterize and optimize this process and observe an interesting dynamics in the two-photon scattering regime: while the first emitter gives rise to a complex multimode field, the second emitter recombines the field …
Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk optics-like proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently-available integrated device without bulk-optics analog: the array of nonli…
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）
We study experimentally the free-space electro-magnetic field emitted from a multimode rectangular waveguide equipped with a diagonal-horn antenna. Using the frequency range of 215-580 GHz, a photo-mixer is used to launch a free-space circularly-polarized electro-magnetic field, exciting multiple modes at the input of the rectangular waveguide via an input diagonal-horn antenna. A second photo-mixer is used, together with a silicon mirror Fresnel scatterer, to act as a polarization-sensitive coherent detector to characterize the emitted field. We find that the radiated field, excited by the fu…
Optical fibers confine and guide light almost unattenuated and thus convey light forces to polarizable nano-particles over very long distances. Radiation pressure forces arise from scattering of guided photons into free space while gradient forces are based on coherent scattering between different fiber modes or propagation directions. Interestingly, even scattering between co-propagating modes induces longitudinal forces as the transverse confinement of the light modes creates mode dependent longitudinal wave-vectors and photon momenta. We generalize a proven scattering matrix based approach …
