Photons, the particles of light, do not contain any charge and hence typically do not interact with each other. In fact, they are so aloof that when you shine a beam of light from a torch onto one from another, they cross each other’s path and move on as if the other beam does not exist.
While this property makes them excellent candidates for long distance communication, it also serves as a hindrance for applications in optical information processing and realization of all-optical circuits, where photon-photon interaction at the level of individual photons (for example, controlling the motion of a single photon with another photon) is highly desired. The question now is this: How do we achieve photon-photon interactions at the level of individual photons?
One way would be to tap into what is known as nonlinear optical behavior, which is exhibited by certain materials that change their refractive index as a function of the intensity of incident light. As a consequence, the propagation of light in the interior of such materials can be controlled by another beam. This gives rise to effective interaction between otherwise noninteracting light beams. Intensity-dependent refractive index is routinely employed in many nonlinear optical devices in laboratory optics and in technology. Could this feature of nonlinear optics be used to make individual or at most a few photons interact?
Unfortunately, the electric fields (and hence the intensity) associated with individual photons is tiny; therefore a vast number of photons are required to realize optical nonlinearity in the interior of any known nonlinear optical material. Let us take a minute here to ponder this question: why do we need a large number of photons to generate nonlinear behavior in a material? Answering this question could point one in the right direction towards achieving nonlinearity with a few photons. Let us consider a cylindrical light beam of diameter ‘d’ incident upon a material made up of atoms. The chance that one photon will “see” one atom in the material is given by the ratio of the effective size of the atom as seen by a photon and the transverse area of the beam. The word, “see” is in inverted quotes because of the following: how well a photon sees an atom is dependent on how well the energy of the photon matches the energy levels of the atom; the closer they are more the chance of interaction. When the energy of the photons matches the energy levels of the atom, the effective size of the atom is approximately the square of the wavelength of the incident photon. The beam diameter is usually much greater than the photon wavelength, and hence the chance of one photon interacting with an atom in bulk materials is very very small. Right away, we see that to improve the chances of interaction and hence nonlinearity we need a lot of photons (which we do not want, since we are aiming for nonlinearity with a few photons) or—here is our aha moment—reduce the diameter of the light beam ‘d’ to such a small value, in fact far below the wavelength of photons, and couple it to an artificial atom whose effective size is far greater than any existing real atom.
Enhanced atom-photon coupling with just a few photons, leading to strong optical nonlinearity, is achieved by confining the photons into tiny spaces with dimensions much smaller than the wavelength of the photons. This has been experimentally realized by squeezing the photons along with individual atoms in confined geometries such as waveguides. One-dimensional waveguides such as superconducting transmission lines can confine microwave photons to deeply sub-wavelength sizes in their transverse dimensions. When we couple an atom (a superconducting qubit here) with a large transition dipole (equivalent to a large effective size) to such confined photons, strong optical nonlinearity may be manifested with a just few photons. In such a case, photons are transversely focused to an area comparable with the scattering cross-section of the atom, and their electric field at the atom becomes large enough to excite the atom (which means that atom absorbs energy from the incident photon and goes to a higher energy state) with very high probability.
In a recent colloquium, Dr. Dibyendu Roy from the Raman Research Institute along with international collaborators has discussed the topic of photons interacting strongly when confined to a one-dimensional geometry from experimental and theoretical perspectives.
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Figure caption: A superconducting qubit (indicated in orange) embedded in a one dimensional transmission line waveguide. The waveguide confines light to deeply sub-wavelength dimensions in the transverse direction.