We consider a generalized Jaynes–Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition. The intermediate levels associated with the multiphoton process are adiabatically eliminated using the non-resonant conditions for these transitions. Under such general conditions, the infinite atom–multiphoton interaction is effectively mapped onto an equivalent reduced 2 × 2 bipartite qubit system that facilitates the study of the nonclassical features of the interaction using known information-theoretic measures. We observe that the bipartite pure system is highly entangled as quantified by its entanglement of formation. Furthermore, it is shown that the dynamics of the mapped system can be generated using optically truncated, quantum scissored states that reduce the infinite atom–multiphoton interaction to a finite 2 × k system, where k is a suitable truncation number. This allows us to introduce atomic dephasing and study the mixed state dynamics, characterized by the decay of quantum correlations such as quantum discord, which is observed to be more robust than entanglement. The quantum correlation dynamics of the dissipative system qualitatively complements the behaviour of collapse and revival of the Rabi oscillations in the system. The effective mapping of the composite system proves to be an efficient tool for measuring information-theoretic properties.
We consider a generalized Jaynes–Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition. The intermediate levels associated with the multiphoton process are adiabatically eliminated using the non-resonant conditions for these transitions. Under such general conditions, the infinite atom–multiphoton interaction is effectively mapped onto an equivalent reduced 2 × 2 bipartite qubit system that facilitates the study of the nonclassical features of the interaction using known information-theoretic measures. We observe that the bipartite pure system is highly entangled as quantified by its entanglement of formation. Furthermore, it is shown that the dynamics of the mapped system can be generated using optically truncated, quantum scissored states that reduce the infinite atom–multiphoton interaction to a finite 2 × k system, where k is a suitable truncation number. This allows us to introduce atomic dephasing and study the mixed state dynamics, characterized by the decay of quantum correlations such as quantum discord, which is observed to be more robust than entanglement. The quantum correlation dynamics of the dissipative system qualitatively complements the behaviour of collapse and revival of the Rabi oscillations in the system. The effective mapping of the composite system proves to be an efficient tool for measuring information-theoretic properties.
We consider a generalized Jaynes–Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition. The intermediate levels associated with the multiphoton process are adiabatically eliminated using the non-resonant conditions for these transitions. Under such general conditions, the infinite atom–multiphoton interaction is effectively mapped onto an equivalent reduced 2 ×2 bipartite qubit system that facilitates the study of the nonclassical features of the interaction using known information-theoretic measures. We observe that the bipartite pure system is highly entangled as quantified by its entanglement of formation. Furthermore, it is shown that the dynamics of the mapped system can be generated using optically truncated, quantum scissored states that reduce the infinite atom–multiphoton interaction to a finite 2 × k system, where k is a suitable truncation number. This allows us to introduce atomic dephasing and study the mixed state dynamics, characterized by the decay of quantum correlations such as quantum discord, which is observed to be more robust than entanglement. The quantum correlation dynamics of the dissipative system qualitatively complements the behaviour of collapse and revival of the Rabi oscillations in the system. The effective mapping of the composite system proves to be an efficient tool for measuring information-theoretic properties.
Summary form only given. We study the behavior of classical and quantum correlations between a two level atom and a quantised electromagnetic field mode in a thermal state interacting according to the Jaynes Cummings model (JCM). This model predicts collapses and revivals of Rabi oscillations which is also seen in experiments, providing direct evidence for the quantum mechanical nature of the electromagnetic field. It also has an analytical solution for arbitrary coupling constants and can easily be extended to include a variety of initial conditions,dissipation and damping, multiple atoms, multilevel atoms, multimode fields and more elaborated interactions such as multiphoton or intensity-dependent interaction.
Harnessing entanglement and quantum coherence plays a central role in advancing quantum technologies. In quantum optical light-atom platforms, these two fundamental resources are often associated with a Jaynes-Cummings model description describing the coherent exchange of a photon between an optical resonator mode and a two-level spin. In a generic nonlinear spin-boson system, more photons and more modes will take part in the interactions. Here we consider such a generalization: the two-mode multiphoton Jaynes-Cummings (MPJC) model. We demonstrate how entanglement and quantum coherence can be optimally generated and subsequently manipulated in experimentally accessible parameter regimes. A detailed comparative analysis of this model reveals that nonlinearities within the MPJC interactions produce genuinely non-Gaussian entanglement, devoid of Gaussian contributions, from noisy resources. More specifically, strong coherent sources may be replaced by weaker, incoherent ones, significantly reducing the resource overhead, though at the expense of reduced efficiency. At the same time, increasing the multiphoton order of the MPJC interactions expedites the entanglement generation process, thus rendering the whole generation scheme again more efficient and robust. We further explore the use of additional dispersive spin-boson interactions and Kerr nonlinearities in order to create spin coherence solely from incoherent sources and to enhance the quantum correlations, respectively. As for the latter, somewhat unexpectedly, there is not necessarily an increase in quantum correlations due to the augmented nonlinearity. Towards possible applications of the MPJC model, we show how, with appropriately chosen experimental parameters, we can engineer arbitrary NOON states as well as the tripartite W state. Published by the American Physical Society 2024
The Jaynes-Cummings model of optical resonance describes the simplest fully quantized interaction between two quantum systems of different nature: a two-level atom (fermionic system) and a quantized field mode (bosonic system). This interaction leads to extreme quantum entanglement of the atom and field. However, the model also predicts that, at precisely half of the revival time, the atom and field become asymptotically disentangled. This disentanglement becomes more exact as the coherent-state amplitude increases. In this paper we investigate the nature of the pure-field-state superposition generated at such times. We show that this superposition is of distinguishable states of the field with the same amplitude but opposite phase. Interference between these components leads to nonclassical oscillations in photon-number distributions and squeezing in quadratures of the field. The Schr\"odinger-cat states of the field are highly transient, and depend very sensitively on the interaction time, the initial intensity of the field, and the atom-field detuning.
In this paper, we propose a model to describe the geometry of quantum correlations and entanglement through their distinct physical significance in quantum information processing and modern communications. However, geometric discord, using trace, Hilbert–Schmidt distances, and entanglement of formation, is engineered to be a well-defined non-classical correlation measure of an atomic field system. It consists of employing Jaynes–Cummings model to study the interaction between an excited atom at two levels and a single electromagnetic field mode inside an electrodynamic cavity in two cases, namely resonance and non-resonance. In fact, the dynamics of these measures depends decisively on the atom-field initial parameters where, importantly, the field parameters can be specified as control settings to implement an optimal teleportation protocol. The obtained results reveal that the behaviors of teleported geometric quantum discord and entanglement are similar to those displayed for maximum fidelity in terms of fully entanglement fraction. Therefore, since fidelity always exceeds the classical limit, one can design a quantum teleportation scheme with robust fidelity superior to any conventional communication protocol.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.