# Photon Enhanced Interaction and Entanglement in Semiconductor Position-Based Qubits
## 2 Statement of the Problem  
The quantum structure under study is realized in a CMOS fully depleted silicon-on-insulator (FDSOI) technology. A transistor-like CMOS device is depicted in Figure 1a. When operating at cryogenic temperatures, such devices can be seen as artificial atoms, giving rise to a double-quantum-dot (DQD). DQDs can be arranged in series forming a quantum register of an arbitrary number of qubits. The quantum transport can be achieved electrostatically by manipulating the electrical potential, i.e., by applying appropriate DC and pulsed voltages at the gates. For a more detailed description of this system, an interested reader can refer to [26]. In Figure 1b, the concept of coupling two qubits over longer distances, in the case electrostatic (Coulomb) interaction is negligible, is demonstrated. The coupling is expected to be achieved through a waveguide by means of a high-\(\epsilon\) material layer. Figure 1c visualizes a top-view layout of two coupled DQDs with a waveguide. Each DQD realizes a qubit. In this work, we will focus on the modelling of a qubit coupled into a cavity and two coupled qubits coupled via a waveguide. As visualized in Figure 1d, each qubit has two states, denoted as \(|0\rangle\) and \(|1\rangle\). These are localized states which correspond to the presence of a particle in a given well of an electrostatically shaped potential energy profile. In other words, the quantum logic in such a system is based on the position of the particle in a given quantum register. By manipulating the potential energy of a particle one can achieve photon emission and absorption. An example of the potential energy on the surface of silicon channel of a quantum register, as obtained from electrostatic finite-element-method (COMSOL) simulations, is shown in Figure 2a. At the beginning (and also at the end) of the chain, the first (and the last) device serves as a reconfigurable injector/detector. The injector, in this context, is typically a single-electron device responsible for injecting individual electrons into the quantum register. The detector is an analog circuit which can detect (by a weak or strong measurement, depending on a particular configuration) a presence of a single electron. In the schematic, \"S\" and \"D\" denote Source and Drain regions (i.e., highly doped silicon), while \"\(I_{1}\)-\(I_{7}\)\" denote imposers (gates). One can apply precisely controlled DC voltages and pulses to the source/drain and the imposers to achieve desired modes of operation. Figure 1: (**a**) Cross-section of an FDSOI transistor-like ‘quantum’ device, without the source/drain diffused regions. Details of the specific technology are omitted. As the device dimensions decrease, one can achieve quantum operation at cryogenic temperatures. Various layers of the device facilitate different properties which are essential to the resulting potential energy profile. (**b**) Each device can facilitate a double-quantum-dot (DQD). When interconnected via a waveguide, it can couple the entangled qubits. This can be achieved with the use of high-\(\epsilon\) materials and proper isolation of the quantum core from the rest of the surrounding circuitry of a chip. (**c**) Top-view of a layout structure of two coupled DQDs interconnected via a waveguide. (**d**) 1D representation of two coupled (DQDs). Each DQD can facilitate a qubit. In the schematic, the two states of each qubit are denoted, as \(|0\rangle_{A,B}\), corresponding to a particle in the left QD of system-A or system-B (of the corresponding potential energy profile of a device), and as \(|1\rangle_{A,B}\), corresponding to a particle in the right QD. (**e**) 1D schematic representation of a potential energy profile formed by a chain of devices forming a series of QDs. The absorption of a photon can cause a transition to a higher energy level. Similarly, the emission of a photon can occur when a particle transitions from a higher energy level to a lower energy level.