Quantum technologies aim to harness superposition and entanglement to enhance communication security

1, provide exponential computational advantage for particular tasks

2,

3, including factoring

4, database search

5 and simulation of important quantum systems

6, and reach the ultimate limits of precision in measurement

7. Photons are an appealing information carrier for their inherently low-noise, high-speed transmission, and the fact that entangling interactions between photons can be achieved using only linear optical circuits

1,

8,

9,

10 or mediated by atom-like systems

12,

13. A photonics approach to these technologies requires complex, multiport quantum circuits—essentially multipath, multiphoton interferometers—that exhibit high fidelity quantum interference. Circuits fabricated from 2×2 directional couplers have demonstrated high performance

13,

14,

15,

16,

17; however, construction of more sophisticated multiport circuits would require their decomposition into a very large number of 2×2 directional couplers. For example, an arbitrary

*N*×

*N* mode unitary

18 would require a sequence of

*O*(

*n*^{2}) individual 2×2 directional couplers.

Multimode interference (MMI) devices are based on the self-imaging principle, by which an input field profile is reproduced in single or multiple images at periodic intervals along the propagation direction of a multimode waveguide

19,

20. The effect is based on the propagation properties of a guide with a large number of lateral modes that see different effective refractive indices. Each mode propagates at a specific velocity accumulating different phases that results in constructive and destructive interference along the multimode region. At the position in which all the modes re-phase the total electromagnetic field is the same as the input, resulting in a self-imaged condition. MMI devices allow the design of

*N*×

*M* splitters with superior performances, excellent tolerance to polarization and wavelength variations, and relaxed fabrication requirements compared with the other main beam-splitting technology, the directional couplers. Consequently, MMI couplers have found applications in a broad range of photonic systems

21, including phase diversity networks, light switching and modulators, in laser architectures and for optical-sensing applications. In the context of photonic quantum circuits, they promise to dramatically reduce the complexity of such circuits, including for example those required to generate maximally entangled path or 'NOON' states

22, W states

23 and the implementation of N×N unitaries

18.

In contrast to directional couplers, the self-imaging effect in MMIs allows the flexibility to directly realize symmetric N×N multiport devices with several input and output ports. Multiport circuits are particularly promising for quantum optics and information purposes, and fundamental experiments have been conducted to study the behaviour of non-classical interference of single photons in bulk optics

24 and fibre

25 circuits. However, their performance is limited by stability and control of the splitting ratios. The implementation of multiport splitters in MMI devices should allow higher performances because of the monolithic and scalable architecture. However, it is not clear that the multimode nature of MMI devices will allow quantum operations, in particular quantum interference.

Quantum interference with two photons is a defining distinction between classical and quantum states of light and is the key phenomenon that drives photonic quantum technologies. Quantum interference occurs when different quantum mechanical outcomes are indistinguishable. In the case of two photons entering the two input ports of a symmetric 2×2 unitary beamsplitter (one photon per input port), the outcomes of 'both photons reflected' and 'both photons transmitted' are indistinguishable. In this case, the interference is destructive so that the photons never leave in the two separate outputs, but a superposition of two photons in each output. This behaviour is in stark contrast to the case of two classical particles that would have a probability of 1/2 to leave in separate outputs. When the relative arrival time of the two photons is scanned, a characteristic Hong Ou Mandel (HOM) dip is observed

26, because the classical probability of 1/2 holds for finite delay and the quantum probability of zero holds for zero delay. The width of this HOM dip is given by the coherence time of the photons. The visibility

*V*[0, 1] of the dip (how close it gets to zero) is a measure of the degree of quantum interference. Any information that distinguishes the two probability amplitudes—for example, the photons have different polarizations, frequency, bandwidth and so on—reduces

*V*<1.

In this paper, after a description of the devices fabrication and the experimental setup, we report our results on a 2×2 MMI. Then we show operation of a 4×4 MMI with single photon pairs injected in all possible pairs of input ports. Finally, we describe and apply a technique to characterize the 4×4 device based on the measured HOM dip visibilities.