European physicists have studied in detail the interaction of single photons in a photonic crystal waveguide containing a quantum dot. They showed that by varying the duration of the pulses and their delay, it is possible to achieve varying degrees of nonlinearity, as well as control the degree of correlation of light quanta. The study was published in Nature Physics.
In ordinary life, we practically never encounter a situation in which intersecting rays of light influence each other. This is because the equations that describe the propagation of light, for example, in air, glass or water, are linear, which means they can be solved independently for each beam of light. Nevertheless, there is still some approximation in this, since all media, even vacuum, exhibit nonlinearity to one degree or another.
From a quantum point of view, nonlinearity is a photon-photon interaction. Despite the fact that nonlinear optics has been around for almost a century, physicists have not been able to make the force of this interaction strong enough to force photons to form matter (and, for example, make a lightsaber), although there have been some advances in this direction.
Much more down-to-earth has become the use of optical nonlinearity to create all-photonic circuits for working with classical or quantum information. So, to make an optical transistor, it is necessary that the passage of one photon through it depends on the presence or absence of another photon. If one of the photons is in a state of quantum superposition with respect to this process, it will lead to entanglement of the photons. The efficiency of all-optical circuits depends directly on the strength of the photon-photon interaction, so physicists are trying different physics platforms to make it as intense and fast as possible.
Hanna Le Jeannic from the University of Copenhagen and colleagues from Germany, Denmark and Spain used a quantum dot placed in a waveguide for this purpose. This configuration allowed them to achieve strong coupling between the propagating mode and the emitter, which enabled nonlinearity at the single-photon level. They demonstrated on this platform how one photon controls the propagation of another, and also how two photons can become entangled as they scatter on a quantum dot.
The emitter in the physicists’ experiment was a neutral exciton excited in an InGaAs quantum dot. They placed the particle inside a waveguide formed inside a GaAs-based photonic crystal. The sample temperature was four kelvins throughout the entire experiment. This made it possible to reduce the influence of phonons on coherent processes, as well as to narrow the transition width to 755 megahertz with a lifetime of the excited state of the quantum dot equal to 229 picoseconds.
The interaction between photons in such a scheme was due to the fact that one of the light quanta, detuned from the resonance in the quantum dot, shifted its levels due to the dynamic Stark shift. Physicists were convinced of this by carrying out measurements in the pump-probe mode, where, by changing the properties of the pump laser (detuning, luminous flux), they monitored whether the probing photon was transmitted or reflected.
At the second stage of the experiment, the authors studied how the properties of a pulse containing two photons changed. They could change the duration of the pulses and the interval between them, which, together with the exciton lifetime, created several time scales. Their combination made it possible to switch the degree of linearity of propagation and the degree of correlation of a passing photon pair.
Thus, if both photons were separated by a time greater than the lifetime of the excited state, there was no interaction between them. Moreover, when the duration of the pulses was on the order of this time, the probabilities of photons passing through the quantum dot began to be affected by the effects of quantum interference.
A different situation occurred when the delay between pulses was minimal. In this case, the second-order correlation function measured by the authors with time resolution had a complex shape, which indicated a nonlinear interaction. As the pulse duration increased, the function degenerated into a straight line, signaling a strong correlation between photons. Smoothly controlling all timing parameters and studying correlations between transmitted and reflected photons allowed the scientists to see how the excitation mode of a quantum dot alternates between saturation and stimulated emission, as well as spontaneous emission, and how these modes differ at large and small intervals between photons.
Placing multiple quantum dots next to each other could complicate the correlations for larger numbers of photons, which could be used to generate entangled multiqubit states of light. Previously, we described how such states are proposed to be obtained using single atoms in a resonator and metasurfaces.