Non-reciprocal phase shift induced by an effective magnetic flux for light

Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work1,2 has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer3–7. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials. The interaction of light and a magnetic field would enable new physical phenomena for photons, such as bending the direction of light and one-way edge modes1,2. Because photons are neutral particles, their interaction with a magnetic field relies on using magneto-optical materials. Recently, there have been demonstrations of on-chip isolators8–10 and topologically protected edge modes11–15 based on magneto-optical materials. However, magneto-optical materials are difficult to integrate on-chip and the magneto-optic effect is weak in the near-infrared and visible domains. Isolator schemes using dynamic modulation instead of magneto-optical materials have been demonstrated in optical fibres16 and more recently in on-chip silicon and InP waveguides17–19. However, these works do not demonstrate an effective magnetic field. This leads to the fundamental question of whether one can generate an effective magnetic field directly coupled with photons in the optical domain while not being limited to the use of magneto-optical materials. As shown by Fang et al.1,2, an effective magnetic field for photons could be created if one could break the reciprocity of light such that its phase depends on its propagation direction. The link between the magnetic field B (and its associated gauge potential, A) and the direction-dependent phase is equivalent to the Aharonov–Bohm effect20 for electrons, where the electrons acquire a direction-dependent phase (f = (e/h) ∫r r A · dr̂, where B = ∇ × A, e is the unit charge and h is Planck’s constant) in the presence of a magnetic field. Recently, the effective magnetic field for radiofrequency photons was observed using a photonic Aharonov–Bohm interferometer21. The demonstration of such an effect in the on-chip optical domain provides a new functionality for on-chip light manipulation. Here, we probe the phase of light using a Ramsey-type interferometer3–7. The basic form of a Ramsey-type interferometer is shown in Fig. 1a. In an atomic Ramsey interferometer, as an atom in the ground state enters the interferometer, the first laser (left) interacts with it, and the atomic state is rendered in a linear superposition of the ground and excited state. These two states have different propagation phases (Δφa, due to rotation and gravitation, for example). A second laser excitation, in phase with the first, again transforms the atomic ground and excited states into linear superpositions. Thus, the probability of finding an atom exiting the interferometer in the ground state exhibits an interference profile depending on cos(Δφa). In a photonic Ramsey interferometer (Fig. 1b), we replace the two atomic states and laser excitations with two photonic states (in our case even and odd modes in a waveguide; see later) and modulators, respectively. As light in the even mode (ground state) enters the interferometer, the first modulator (left) induces a refractive index perturbation and couples a portion of light in the even mode to the odd mode (excited state). Note that this transition is classical, in contrast to the atomic Ramsey interferometer. Following excitation (that is, coupling), similar to the atomic case, the propagating light is in a superposition of the even and odd modes. The two modes experience different phases