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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Experimental Multiphase Estimation in an Integrated Reconfigurable Multi-Arm Interferometer

Emanuele Polino, Martina Riva, Mauro Valeri, Raffaele Silvestri, Giacomo Corrielli, Andrea Crespi, Nicolò Spagnolo, Roberto Osellame, Fabio Sciarrino

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Summary form only given. Phase estimation represents one of the most notable examples in the context of the quantum metrology. The aim is to improve the capabilities to measure an unknown phase shift between the arms of an interferometer with respect to classical strategies by adopting quantum resources. Applications of the phase estimation task can be found in different contexts, such as imaging, measurements on biological systems, or gravitational wave detection [1]. While the theoretical and experimental frameworks for the single parameter case are well established, several open questions arise when extending the scenario to multiparameter estimation. Indeed, when the number of parameters to be estimated is larger than one, it is not trivial to saturate the ultimate bounds for all parameters simultaneously [2]. Hence, it becomes crucial to identify and implement experimentally a suitable platform to develop appropriate protocols for efficient multiphase estimation protocols. Here, we report [3] the experimental implementation of an interferometric platform to investigate experimentally multiphase estimation protocols. Such platform, shown in Fig. 1, is implemented by adopting the femtosecond laser micromachining technology, that allows to realize integrated photonic circuits including several optical elements. The implemented interferometer (Fig. 1) is composed of a first unitary transformation for state preparation, namely a balanced tritter [4,5], a second stage for internal phases, and a second unitary transformation for measurement of the output state. Reconfigurability in the device is inserted by means of thermo-optic phase shifters, that allow to tune the optical phases by applying a voltage on gold-plated resistors placed on top of the waveguides [6]. Resistors pattern on the device has been realized by using the same laser writing technology employed to implement the interferometric structure. We have then performed a multiphase estimation experiment by injecting two-photon input states within the interferometer for simultaneous measurement of two phases.

DOI
10.1109/cleoe-eqec.2019.8873184

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Summary form only given. Phase estimation represents one of the most notable examples in the context of the quantum metrology. The aim is to improve the capabilities to measure an unknown phase shift between the arms of an interferometer with respect to classical strategies by adopting quantum resources. Applications of the phase estimation task can be found in different contexts, such as imaging, measurements on biological systems, or gravitational wave detection [1]. While the theoretical and experimental frameworks for the single parameter case are well established, several open questions arise when extending the scenario to multiparameter estimation. Indeed, when the number of parameters to be estimated is larger than one, it is not trivial to saturate the ultimate bounds for all parameters simultaneously [2]. Hence, it becomes crucial to identify and implement experimentally a suitable platform to develop appropriate protocols for efficient multiphase estimation protocols. Here, we report [3] the experimental implementation of an interferometric platform to investigate experimentally multiphase estimation protocols. Such platform, shown in Fig. 1, is implemented by adopting the femtosecond laser micromachining technology, that allows to realize integrated photonic circuits including several optical elements. The implemented interferometer (Fig. 1) is composed of a first unitary transformation for state preparation, namely a balanced tritter [4,5], a second stage for internal phases, and a second unitary transformation for measurement of the output state. Reconfigurability in the device is inserted by means of thermo-optic phase shifters, that allow to tune the optical phases by applying a voltage on gold-plated resistors placed on top of the waveguides [6]. Resistors pattern on the device has been realized by using the same laser writing technology employed to implement the interferometric structure. We have then performed a multiphase estimation experiment by injecting two-photon input states within the interferometer for simultaneous measurement of two phases.
Multiparameter estimation is a general problem that aims at measuring unknown physical quantities, obtaining high precision in the process. In this context, the adoption of quantum resources promises a substantial boost in the achievable performances with respect to the classical case. However, several open problems remain to be addressed in the multiparameter scenario. A crucial requirement is the identification of suitable platforms to develop and experimentally test novel efficient methodologies that can be employed in this general framework. We report the experimental implementation of a reconfigurable integrated multimode interferometer designed for the simultaneous estimation of two optical phases. We verify the high-fidelity operation of the implemented device, and demonstrate quantum-enhanced performances in two-phase estimation with respect to the best classical case, post-selected to the number of detected coincidences. This device can be employed to test general adaptive multiphase protocols due to its high reconfigurability level, and represents a powerful platform to investigate the multiparameter estimation scenario.
Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.
Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices. These can be implemented by femtosecond laser waveguide writing, recently adopted for quantum applications. In particular, multiarm interferometers include "tritter" and "quarter" as basic elements, corresponding to the generalization of a beam splitter to a 3- and 4-port splitter, respectively. By injecting Fock states in the input ports of such interferometers, fringe patterns characterized by nonclassical visibilities are expected. This enables outperforming the quantum Fisher information obtained with classical fields in phase estimation. We also discuss the possibility of achieving the simultaneous estimation of more than one optical phase. This approach is expected to open new perspectives to quantum enhanced sensing and metrology performed in integrated photonics.
Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation beyond what reachable within classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful entanglement (among multimode particles, qudits) for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.
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.
Traditional quantum metrology assesses precision using the figures of merit of continuous-valued parameter estimation. Recently, quantum digital estimation was introduced: it evaluates the performance information-theoretically by quantifying the number of significant bits of the parameter, redefining key benchmarks like the Heisenberg bound. Here, we report the first experimental realization of a Quantum Analog-to-Digital Converter for quantum metrology, that takes an input continuous parameter and outputs a bit string, using an advanced photonic platform, comprising a fully reconfigurable integrated circuit and a quantum dot source of highly indistinguishable photons. We implement a protocol for digital phase estimation that is capable of surpassing the standard quantum limit, through the simultaneous use of different entangled state resources. We tackle experimental imperfections by employing machine learning techniques for noise deconvolution and estimation process refinement. Our protocol is experimentally benchmarked against classical strategies via the number of recoverable bits of the unknown parameter. Our results open new perspectives for future implementation of quantum digital estimation strategies.