Quantum interference between transverse spatial waveguide modes

ARTICLE Received 24 Jun 2016 | Accepted 18 Nov 2016 | Published 20 Jan 2017 DOI: 10.1038/ncomms14010 OPEN Quantum interference between transverse spatial waveguide modes Aseema Mohanty1,2, Mian Zhang1,3, Avik Dutt1,2, Sven Ramelow4,5, Paulo Nussenzveig6 & Michal Lipson1,2,7 Integrated quantum optics has the potential to markedly reduce the footprint and resource requirements of quantum information processing systems, but its practical implementation demands broader utilization of the available degrees of freedom within the optical field. To date, integrated photonic quantum systems have primarily relied on path encoding. However, in the classical regime, the transverse spatial modes of a multi-mode waveguide have been easily manipulated using the waveguide geometry to densely encode information. Here, we demonstrate quantum interference between the transverse spatial modes within a single multi-mode waveguide using quantum circuit-building blocks. This work shows that spatial modes can be controlled to an unprecedented level and have the potential to enable practical and robust quantum information processing. 1 School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA. 2 Department of Electrical Engineering, Columbia University, New York, New York 10027, USA. 3 School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. 4 School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA. 5 Institute for Physics, Humboldt-University Berlin, 12489 Berlin, Germany. 6 Instituto de Fisica, Universidade de São Paulo, P.O. Box 66318, São Paulo 05315-970, Brazil. 7 Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA. Correspondence and requests for materials should be addressed to M.L. (email: ). NATURE COMMUNICATIONS | 8:14010 | DOI: 10.1038/ncomms14010 | www.nature.com/naturecommunications 1 ARTICLE I NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14010 ntegrated 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 simulation1–7. 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, but 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 frequency to encode more information per carrier will enable scalability by simplifying quantum computational architectures8, increasing security and noise tolerance in quantum communication channels9,10, and simulating richer quantum phenomena11. These degrees of freedom have previously been explored in free-space and fibre quantum systems to encode qudits and implement higher-dimensional entanglement12–16. Currently, integrated quantum photonic circuits are primarily limited to path-encoding information, but the use of a higher-dimensional Hilbert space within each path will increase the information capacity and security of quantum systems. Higher dimensionality allows one to encode more information per photon, relieving resource requirements on photon generation and detection9,10. Consequently, this leads to more efficient logic gates and noise-resilient communications, making quantum systems more scalable and practical8,17. In integrated schemes, a few demonstrations have been developed for polarization18 and time19. In free-space optics, orbital angular momentum and Hermite–Gaussian modes have both been used to encode information within a higher-dimensional space as qudits (d-level logic units)12–16. The higher-order waveguide modes in a multi-mode interferometer have been used to passively mix single-mode inputs for quantum interference, and transfer polarization and path-encoded states20,21. However, the spatial modes have never been controlled individually to encode quantum information to date22,23. The transverse spatial degree of freedom is an untapped resource that can be manipulated using simple photonic structures and does not require exotic material properties. In the classical regime, the orthogonal spatial modes of an integrated waveguide have been shown to markedly scale data transmission rates24–28. A waveguide can support many copropagating modes, which can be used as parallel channels within a single waveguide. Progress in the field has overcome the challenge of achieving controlled coupling while avoiding unwanted coupling between different modes, for example, in bends and tapers29,30. Mode conversion based on waveguide structuring has significant potential in the quantum regime31–33. Here, we demonstrate a scalable platform for photonic quantum information processing using waveguide quantum circuit-building blocks based on the transverse spatial mode degree of freedom: spatial mode multiplexers and spatial mode beamsplitters. A multi-mode waveguide is inherently a densely packed system of spatial and polarization modes that can be coupled by perturbations to the waveguide. We design a multi-mode waveguide consisting of three spatial modes (per polarization) and a nanoscale grating beamsplitter to show tunable quantum interference between pairs of photons in different transverse spatial modes. We also cascade these structures and demonstrate NOON state interferometry within a multi-mode waveguide. We show that interference between different transverse spatial waveguide modes and active tuning can be achieved with high visibility using this platform. These devices have potential to perform transformations on more modes and be integrated with existing architectures, providing a scalable path to higher-dimensional Hilbert spaces and entanglement. 2 Results Hong–Ou–Mandel interference using spatial waveguide modes. To show the potential utility of the integrated transverse spatial degree of freedom for scalable quantum information processing, we demonstrate Hong–Ou–Mandel (HOM) interference between two different quasi-transverse electric (TE) waveguide modes (TE0 and TE2). HOM interference is a useful proof of principle because it is the basis of many other quantum operations, such as higher-dimensional entanglement, teleportation, quantum logic gates and boson-sampling1–4,15,16,34. In the original HOM experiment, a path beamsplitter is used to combine two originally orthogonal paths of two single photons, making them indistinguishable. The probability amplitudes of the two cases that contribute to detection of the two photons in coincidence destructively interfere owing to the bosonic nature of photons, if the two paths are indistinguishable35. As an example, we consider a silicon nitride multi-mode waveguide with a sub-micron cross section containing six modes: three sp (...truncated)