We investigate the phase-space representation of quantum mechanics as a platform to perform Monte Carlo simulation of the non-interacting Jaynes-Cummings-Rabi (JCR) model involving a two-level hydrogen atom as a qubit and a quantum har-monic oscillator as a photonic cavity. Our algorithm starts by defining a trial wave function for solving the JCR model and then implement it on the “epistemically-restricted” phase-space representation, known as Budiyono-Rochrlich theory, with a Monte-Carlo sampling for the phase-space distribution, which is useful to obtain the average energy of our JCR model. We find that the numerical results are close to the analytical ones for every separate system in the JCR model, i.e., the hydrogen and the oscillator, calculated independently. Combining the two components in the non-interacting JCR model, the calculated energy values for the ground and the first excited states are then found to be —0.91 a.u. and 0.41 a.u. with corresponding standard errors of 9.12×10−8 a.u. and 1.95×10−8 a.u., respectively. We expect that the method presented in this paper can be an alternative approach to solving various qubit-photon systems.
A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum technologies. One of the most fundamental interaction models in quantum optics is the so-called Jaynes-Cummings model (JCM), which has been massively studied theoretically and experimentally. However, the expected essential dynamics of the field states under the resonant JCM has not been observed experimentally due to the lack of a proper reconstruction scheme. In this paper, we further develop a highly efficient vacuum measurement scheme and study the JCM dynamics in a trapped ion system with the capability of the vacuum measurement to reconstruct its quasiprobability
Q function, which is a preferred choice to study the core of the dynamics of a quantum state in phase space. During the JCM dynamics, the Gaussian peak of the initial coherent state bifurcates and rotates around the origin of phase space. They merge at the so-called revival time at the other side of phase space. The measured
Q function agrees with the theoretical prediction. Moreover, we reconstruct the Wigner function by deconvoluting the
Q function and observe the quantum interference in the Wigner function at half of the revival time, where the vibrational state becomes nearly disentangled from the internal energy states and forms a superposition of two composite states. The scheme can be applied to other physical setups including cavity or circuit-QED and optomechanical systems.