# Quantum Photonic Simulation of Spin-Magnetic Field Coupling and Atom-Optical Field Interaction
###### Abstract  
In this work, we present the physical simulation of the dynamical and topological properties of atom-field quantum interacting systems by means of integrated quantum photonic devices. In particular, we simulate mechanical systems used, for example, for quantum processing and requiring a very complex technology such as a spin-\(1/2\) particle interacting with an external classical time-dependent magnetic field and a two-level atom under the action of an external classical time-dependent electric (optical) field (light-matter interaction). The photonic device consists of integrated optical waveguides supporting two collinear or codirectional modes, which are coupled by integrated optical gratings. We show that the single-photon quantum description of the dynamics of this photonic device is a quantum physical simulation of both aforementioned interacting systems. The two-mode photonic device with a single-photon quantum state represents the quantum system, and the optical grating corresponds to an external field. Likewise, we also present the generation of Aharonov-Anandan geometric phases within this photonic device, which also appear in the simulated systems. On the other hand, this photonic simulator can be regarded as a basic brick for constructing more complex photonic simulators. We present a few examples where optical gratings interacting with several collinear and/or codirectional modes are used in order to illustrate the new possibilities for quantum simulation. integrated photonics; quantum optics; quantum simulation Article Quantum Photonic Simulation of Spin-Magnetic Field Coupling and Atom-Optical Field Interaction  
10 8850 2020 10 8850 202  
to mimic its behavior (evolution) by means of other very different system. This last system, which is required to be fully controllable by the experimenter, constitutes a quantum simulator [3,4] of the system of interest. On the other hand, the importance of making quantum simulations obeys various reasons. First of all, whether classical or quantum, simulation is often an indispensable tool in science. Physical systems can be very complicated to study. If we find a way to mimic their behavior in a manageable way, their dynamics can be analyzed with much less difficulty, much less expensively, and much faster [3]. For instance, we can imagine that the system of interest is one whose working conditions are fragile and very sensitive to small perturbations. It could also be that those conditions are very specific and/or hard (even impossible) to achieve in the laboratory. Simulating these complicated systems will, in principle, improve our knowledge about them with much ease. Secondly, quantum simulation offers a crucial advantage over classical simulation. Quantum systems have a greater information storing capacity than classical systems; thus, a quantum simulator, which is a quantum system itself, will require much fewer physical resources than a classical simulator to store the same amount of information. Furthermore, classical simulations find difficulties simulating quantum systems when strong entanglement is present [3]. Finally, it is possible that the potential applications of a quantum system may be better implemented using a quantum simulation [5], if it happens that the quantum simulation parameters are easier to handle, compared to those of the quantum system of interest, in the sense of greater tunability [4]. All of this strongly suggests the need for quantum simulations. Formally, one has a quantum device, called the quantum simulator, which reproduces the evolution of the system of interest, the quantum system. Following [4], let us call the initial input state of the quantum system \(|\phi(0)\rangle\), which evolves to \(|\phi(\zeta)\rangle\), where \(\zeta\) stands either for time or some spatial coordinate, under the evolution operator \(\hat{U}=\exp\left(i\hat{O}\zeta/\hbar\right)\). Here, \(\hat{O}\) can be a Hamiltonian (\(-\hat{H}\)) or a momentum operator (\(\hat{M}\)).