Box 1: Physics of photon–photon interactions.
The interaction between an atom and a photon, confined to a beam of diameter d, can be understood from simple geometrical considerations (a). At resonance, the atom has a maximal scattering cross-section that is proportional to the square of the optical wavelength, σ ≈ λ2. The probability that a single photon in the beam interacts with the atom is therefore p ≈ λ2/d2, which is typically much smaller than unity. This can be enhanced by using an optical cavity to make a photon interact with an atom multiple times, or by confining light to subwavelength dimensions. The excitation spectrum of a single atom is extremely nonlinear, as the absorption of a single photon saturates the atomic response. This results in strong photon–photon interactions when the atom–photon interaction probability p approaches unity.
The different regimes of nonlinear optical phenomena can be characterized by the interaction strength per photon and the number of photons involved (b). In conventional optical media, the interaction strength per photon is weak, which corresponds to linear optics at a low photon number (light grey box). At a higher photon number, we enter the regime of classical nonlinear optics (dark grey box). Quantum nonlinear optical phenomena occur when the interaction strength per photon becomes large. For a small photon number, strong interactions can be used to achieve quantum control of light fields photon-by-photon (blue box), and to implement photonic quantum gates. A novel regime occurs when many photons interact simultaneously to produce strongly correlated many-body behaviour (yellow box).
Institut de Ciències Fotòniques (ICFO), Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
- Darrick E. Chang
Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Vladan Vuletić
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Mikhail D. Lukin
The authors contributed equally to this work.
Competing financial interests
The authors declare no competing financial interests.
Darrick E. Chang
Mikhail D. Lukin