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Journal of the Korean Physical Society

Photon absorption and emission statistics of a two-level atom in a cavity

Chang J. Lee

Published Mar 1, 2012• 0 citations
Publisher

Abstract

The absorption and the emission of photons by an atom involves quantum jumps between states. We investigate the quantum jump statistics for the system of a two-level atom and a single-mode cavity field. We use the Jaynes-Cummings model for this problem, perform Monte Carlo numerical simulations, and give a detailed exact analysis on these simulations. These studies reveal that the waiting-time distribution (WTD) for photon absorptions (emissions) has a unique novel statistic, and that the photon absorption (emission) rate is not uniform, but counter-intuitively depends on the position in the Rabi cycle. The effects of the nonclassical nature of the field on the WTD is discussed.

DOI
10.3938/jkps.60.766

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The absorption and the emission of photons by an atom involves quantum jumps between states. We investigate the quantum jump statistics for the system of a two-level atom and a single-mode cavity field. We use the Jaynes-Cummings model for this problem, perform Monte Carlo numerical simulations, and give a detailed exact analysis on these simulations. These studies reveal that the waiting-time distribution (WTD) for photon absorptions (emissions) has a unique novel statistic, and that the photon absorption (emission) rate is not uniform, but counter-intuitively depends on the position in the Rabi cycle. The effects of the nonclassical nature of the field on the WTD is discussed.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
Two-photon states are essential for fundamental applications in quantum information. One of the primary methods of two-photon generation is based on parametric down-conversion, but this suffers from low efficiency and a large footprint. This work presents a detailed theoretical investigation of an alternative approach: two-photon generation from an emitter in a doubly resonant cavity. The system is modelled by the Lindblad master Equation, and an approximate analytical solution is derived to determine the experimentally achievable limits on efficiency and brightness. Additionally, the optimal cavity parameters for achieving these limits are also identified. For experimentally feasible parameters, the maximum efficiency is approximately 35%, which is significantly higher than that of parametric down-conversion-based methods. The optimal rate and efficiency for two-photon generation are achieved when the outcoupling rate of the cavity mode at the two-photon emission frequency matches the single-photon atom-field coupling strength. Moreover, the outcoupling rate of the cavity mode at the one-photon emission frequency for single photons should be minimized. The cavity field properties are also examined by studying the second-order correlation function at zero time delay and the Mandel Q parameter, revealing highly bunched two-photon emission and super-Poissonian statistics. The quantum-jump framework, combined with Monte Carlo simulations, is used to characterize the mechanism of two-photon emission and the emission spectra of the cavity. Two-photon emission is demonstrated to be a rapid cascade process of quantum jumps, and its spectrum consists of three prominent peaks corresponding to transitions between the dressed states of the system.
We study the dynamics of a system composed of two coupled cavities, each interacting with a single Rydberg atom. The interplay between Rydberg-Rydberg interaction and photon hopping enables the transition of the atoms from the collective ground state to the double Rydberg excitation state by individually interacting with the optical normal modes and suppressing the upconversion process between them. The atomic transition is accompanied by the two-photon absorption and emission of the normal modes. Since the energy level structure of the atom-cavity system is photon number dependent there is only a pair of states being in the two-photon resonance. Therefore, the system can act as a quantum nonlinear absorption filter through the nonclassical quantum process, converting coherent light field into a nonclassical state. Meanwhile, the vacuum field in the cavity inspires the Rydberg atoms to simultaneously emit two photons into the normal mode, resulting in obvious emission enhancement of the mode.
We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The atoms interact with the cavity field via an intensity-dependent, non-degenerate two-photon transition. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the two-mode cavity photon field result in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle, gt, is calculated for the two-mode Fock state field, coherent field, and thermal field, respectively, inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number in two modes has been studied.
The interaction between the pair of cold two-level atoms and the single-mode cavity field is investigated. The two-level atoms in the pair are supposed to be indistinguishable. This problem generalizes the two-photon Jaynes-Cummings model of a single two-level atom interacting with the squeezed vacuum. The model of the pair of indistinguishable two-level atoms is equivalent to the problem of the equidistant three-level radiator with equal dipole moment matrix transition elements between the adjacent energy levels. Supposing that at the initial moment the field is in the squeezed vacuum state we obtain the exact analytical solution for the atom-field state-vector. By using this solution the quantum-statistical and squeezing properties of the radiation field are investigated. The obtained results are compared with those for the single two-level atom system. We observe that in the model of the pair of cold two-level atoms the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one.
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a setup, where a voltage-biased Josephson junction is connected in series with a microwave cavity. We focus here on the emission processes of photons and analyze the underlying time-dependent statistics using the second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ and the waiting-time distribution $w(\ensuremath{\tau})$. Both observables highlight the crossover from a coherent light source to a single-photon source. Due to the nonlinearity of the Josephson junction, tunneling Cooper pairs can create a great variety of nonclassical states of light even at weak driving. Analytical results for the weak driving as well as the classical regime are complemented by a numerical treatment for the full nonlinear case. We also address the question of possible relations between ${g}^{(2)}(\ensuremath{\tau})$ and $w(\ensuremath{\tau})$ as well as the specific information which is provided by each of them.