Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE
Arbitrary integrated multimode interferometers for the elaboration of photonic qubits
Andrea Crespi, Roberta Ramponi, Daniel J. Brod, Ernesto F. Galvão, Nicolò Spagnolo, Chiara Vitelli, Linda Sansoni, Fabio Sciarrino, Paolo Mataloni, Roberto Osellame
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
Summary form only given. High-accuracy integrated photonic circuits are desired in many applications, ranging from telecommunications to sensing, especially where many optical modes or many wavelengths are involved. Particularly challenging are the requirements needed for quantum information applications [1], which have recently found in the integrated optics technology a quite unique and powerful platform [2]. In fact, quantum and classical interference effects are ubiquitously exploited in quantum photonic devices, thus requiring a tight fabrication control not only on the power splitting elements inside the circuit, but also on the phase induced by the various paths. Difficulties grow in case quantum simulation tasks [3] are addressed: the need to model other physical systems increases the circuit complexity and many elements need to be integrated without losing in precision.Femtosecond laser microfabrication has recently emerged as an ideal approach to fabricate integrated photonic circuits for quantum applications [4, 5]. *n the one hand it is appreciated for its low costs and fast-prototyping capabilities. *n the other hand, femtosecond laser written waveguides, due to their low birefringence, can support polarization-entangled two-photon states [5], which are useful to implement many quantum information protocols.In this work we demonstrate the capability of femtosecond laser writing technology to fabricate complex waveguide circuits, with tight phase control and polarization independent behaviour. Specifically, we manufacture optical circuits consisting of cascaded directional couplers, which implement discrete-time quantum walks of polarization entangled photon pairs. The scheme of a circuit realizing a four-steps quantum walk on an ordered one-dimensional lattice is shown in Fig. 1(a). To achieve a perfect polarization insensitive behaviour, directional couplers with an innovative three-dimensional geometry are employed (see the blow-up in Fig. 1(a)). In fact, waveguide birefringence causes a slight polarization dependence of the dimension and of the ellipticity of the guided mode, which may affect the coupling coefficients. We show that, by fabricating the two waveguides constituting the coupler on different planes, it is possible to find a condition in which the overlap integrals for differently polarized guided modes are equal, thus providing the desired polarization insensitivity in the coupling. In Fig. 1(b) the experimental two-photon correlations are reported, obtained by injecting polarization-entangled two-photon states with different symmetry, compared with the theoretical ones. This is equivalent to perform quantum walks of quantum particle pairs with bosonic or fermionic symmetry [6]. *ne can note the excellent agreement between the theory and the experiment, which testifies the accuracy of our fabrication process. We will also show how similar circuits, involving more optical modes and implementing arbitrary phase maps, enable to study quantum walks with disorder-induced effects and thus to observe phenomena such as Anderson localization.
Photonics is a powerful framework for testing in experiments quantum information ideas, which promise significant advantages in computation, cryptography, measurement and simulation tasks. Linear optics is in principle sufficient to achieve universal quantum computation, but stability requirements become severe when experiments have to be implemented with bulk components. Integrated photonic circuits, on the contrary, due to their compact monolithic structure, easily overcome stability and size limitations of bench-top setups. Anyway, for quantum information applications, they have been operated so far only with fixed polarization states of the photons. On the other hand, many important quantum information processes and sources of entangled photon states are based on the polarization degree of freedom. In our work we demonstrate femtosecond laser fabrication of novel integrated components which are able to support and manipulate polarization entangled photons. The low birefringence and the unique possibility of engineering three-dimensional circuit layouts, allow femtosecond laser written waveguides to be eminently suited for quantum optics applications. In fact, this technology enables to realize polarization insensitive circuits which have been employed for entangled Bell state filtration and implementation of discrete quantum walk of entangled photons. Polarization sensitive devices can also be fabricated, such as partially polarizing directional couplers, which have enabled on-chip integration of quantum logic gates reaching high fidelity operation.
Quantum information science has shown that harnessing quantum mechanical effects can dramatically improve performance for certain tasks in communication, computation and measurement. Already a number of photonic quantum circuits have been realized for quantum metrology, lithography and quantum logic gates. However, these demonstrations have relied on large-scale (bulk) optical elements bolted to large optical tables, thereby making them inherently unscalable and confining them to the research laboratory. This paper reports on the implementation of quantum optic integrated circuits, which not only dramatically reduces the footprint of quantum circuits, but allows unprecedented stability and control of the optical path length; this reveals the possibility for realizing previously unfeasible large scale quantum circuits. Results from femtosecond laser directly-written quantum circuits are also discussed. A large range of chip-scale "photonic building blocks" have been realized using this so-called direct-write technique and they include multimode optical interconnects, directional couplers and interferometers. The directly written quantum circuits exhibited high 2 and 3-photon Hong-Ou-Mandel (HOM) interference visibilities of 95.8% plusmn 0.5 and 84% plusmn 3% respectively.
Summary form only given. The main features of quantum mechanics reside into interference deriving from the superposition of different quantum objects. The Hong-Ou-Mandel effect is a purely quantum phenomenon deriving from the interference of two photons. It is a consequence of the bosonic nature of light and can be observed when two identical photons impinge simultaneously on a two-port balanced beam splitter and, as a result, both are forced to exit from the same port. While current quantum optical technology enables two-photon interference both in bulk and integrated systems, simultaneous interference of more than two particles, leading to richer quantum phenomena, is still a challenging task.The emergence of integrated quantum photonics have opened exciting perspectives for the realization of scalable, miniaturized and intrinsically stable optical setups. In particular, the ultrafast laser-writing technique has proved to be a powerful tool for demonstrating new quantum integrated-optics devices, able to perform quantum logic operations as well as two-photon quantum walks. Here we report the experimental observation of threephoton interference in an integrated three-port directional coupler realized by ultrafast laser-writing. By exploiting the capability of this technique to produce three-dimensional structures, we realized and tested in the quantum regime a three-photon beam splitter, namely a tritter, which allowed us to observe bosonic coalescence of three photons [1]. Such a system can be exploited as a building block to implement a generalized class of multi-arm interferometers. We introduce the concept of 3D multi-photon interferometry [2], and we discuss their application in the context of quantum interferometry and quantum phase estimation. We propose novel geometries for integrated multi-arm interferometers based on three-port (tritter) and four-port (quarter) devices, and we discuss possible measurement protocols, based on the injection of multi-photon Fock states in this kind of multi-port devices, demonstrating relevant metrological advantages in phase-estimation tasks. Furthermore, we provide a first insight on the application of this technology in the still unexplored field of multiparameter estimation.Several other contexts may benefit from the adoption of 3-dimensional integrated interferometers realized by femtosecond laser-writing. For instance, they can be adopted for the realization of “proof-of-principle” quantum simulators [3], and, combined in a modular structure, they can be used to realize full-scale quantum simulators for large size quantum systems. The adoption of multiphoton-multimode platforms may indeed disclose the “hardto-simulate” scenario by adopting linear optics to implement a computational power beyond the one of a classical computer.
Boson sampling is a leading platform for exploring many-body quantum interference in linear optical systems. However, identifying circuit-level operating regimes where quantum signatures remain robust under realistic conditions remains challenging. In this work, multimode photonic boson sampling is investigated using a programmable six mode integrated photonic circuit composed of cascaded beam splitters and tunable phase shifters. Each beam splitter is realized through directional couplers combined with local phase control, enabling arbitrary unitary transformations within the linear optical circuit. The circuit is modeled using a tight-binding Hamiltonian allowing controlled manipulation of optical phases and inter-mode coupling that directly governs multiphoton interference pathways. This set up is utilised to do the analysis of Heavy Output Generation (HOG), Total Variation Distance (TVD) and Linear Cross-Entropy Benchmarking (XEB), together with configuration-resolved probability differences, for up to five photons. Distinct dynamic regimes associated with coherent evolution, optimal interference and phase dispersion induced mixing is identified. The results further reveal a photon number dependent complexity–fragility trade-off and demonstrate the robustness of TVD to symmetric photon loss under post-selection. Overall, this work establishes a circuit-relevant validation framework linking programmable interferometer parameters, phase control and quantum interference metrics, providing guidance for scalable photonic boson-sampling implementations in the NISQ regime.