Nowadays, single photons have been known as the ideal quantum information carriers due to their high propagation speed and the weak interaction with the environment. To control the single photon propagation in photon circuits, we need quantum beam splitters that redirect the propagating single photons and send to different channels. The quantum beam splitter plays an important role in the quantum information processing as the key element to control the quantum signals. For this purpose, the quantum dots are often coupled to the waveguides. We proposed a theoretical model that can work for a symmetric/asymmetric single photon beamsplitter. Based on the real space method, we investigated the beam splitting properties of the system, especially the control of the symmetry of the routing spectra.
As you can see in Figure, the proposed system includes two plasmonic waveguides and they are configurated as T-shape. We call the horizontal one "waveguide a" and the vertical one "waveguide b". And the system has 3 quantum dots (QD-1, QD-2, QD-3) that are coupled to the waveguide a. Well, the QD-2 is coupled to the both waveguides at the junction of them. The quantum dots are two-level systems that have ground state |g>j and excited state |e>j. Here we consider the dipole-dipole interaction between the adjacent quantum dots, i.e. QD-1 and QD-2, QD-2 and QD-3, assuming that the distances between them are comparable to the wavelength of the photon. In this system, the single photon that enters from the waveguide b interacts with the quantum dots and is split stochastically to the right or left of waveguide a.
The Hamiltonian of the system is given by H=HF+HI+HD. The first part describes the Hamiltonian of the two quantum dots and the free-propagating photon in two waveguides. And the second part is the Hamiltonian of the interaction between the QDs and the propagating photon. Finally, the third part describes the DDI between the quantum dots.
In this system, we can adjust the reflectance and transfer rates of the single photon by controlling parameters such as the detuning, QD-waveguide coupling strength and the DDI strength between the quantum dots. Especially, we can realize the symmetric or asymmetric beam splitting to the left and right outputs of the system by changing the symmetry of DDI or the QD-waveguide coupling. This result gives us intuitive the possibility to control the quantum beam splitting and to use it in quantum information processing such as quantum switches, quantum logic gates, and quantum routers. In particular, the proposed system can be used as a multi-channel single photon quantum router in the quantum networking with multiple users.
Above result has been published in the "Indian Journal of Physics" under the title of "The Control of the Symmetry of Quantum Beam Splitting in the Hybrid Nanosystem" (https://doi.org/10.1007/s12648-024-03319-9).
