We extend study of the Jaynes-Cummings model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantised field. We investigate the effects of replacing the radiation field mode with a ‘big spin’, comprising a collection of N qubits, or spin-1/2 particles. We demonstrate the similarities of this set-up to the qubits-field model in terms of the qubits state probability, occurrence of attractor states, generation of Schr¨odinger cat state, and in particular the collapse and revival of the entanglement between the two qubits in the qubit subsystem. We extend our analysis by taking into account a decoherence effect due to qubit imperfections. We study two cases of ‘error’ in the system for both the field mode and ‘big spin’ cases. In the first part, we consider the case of systems with non-resonance frequencies, and secondly we let the systems evolve with a difference in the dipole interaction strengths of the two qubits. We average over the errors in both of these parameters with distributions of varying width. We demonstrate the effects of such error modeling in both the field mode and the ‘big spin’ scenarios. We discover that increasing the width \nof the ‘error’ distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits. We also find out that the decoherence effects are more significant in the system with difference in the coupling strength as opposed to the nonresonance case that has higher robustness against errors. At the end of the study, we investigate the qubit-big spin system with a modest value of N to identify the smallest size of the big spin that exhibits the important events in such interacting \nmodel.
We extend study of the Jaynes-Cummings model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantised field. We investigate the effects of replacing the radiation field mode with a ‘big spin’, comprising a collection of N qubits, or spin-1/2 particles. We demonstrate the similarities of this set-up to the qubits-field model in terms of the qubits state probability, occurrence of attractor states, generation of Schr¨odinger cat state, and in particular the collapse and revival of the entanglement between the two qubits in the qubit subsystem. We extend our analysis by taking into account a decoherence effect due to qubit imperfections. We study two cases of ‘error’ in the system for both the field mode and ‘big spin’ cases. In the first part, we consider the case of systems with non-resonance frequencies, and secondly we let the systems evolve with a difference in the dipole interaction strengths of the two qubits. We average over the errors in both of these parameters with distributions of varying width. We demonstrate the effects of such error modeling in both the field mode and the ‘big spin’ scenarios. We discover that increasing the width \nof the ‘error’ distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits. We also find out that the decoherence effects are more significant in the system with difference in the coupling strength as opposed to the nonresonance case that has higher robustness against errors. At the end of the study, we investigate the qubit-big spin system with a modest value of N to identify the smallest size of the big spin that exhibits the important events in such interacting \nmodel.
We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.
Recalling that counter rotating terms (CRTs) in atom–field interaction are not always ignorable, particularly in the strong coupling regimes of atom–field systems, in this paper we are going to study the interaction between two qubits (two-level atoms) with a two-mode field in a high quality cavity by considering CRTs while the dipole–dipole (D–D) interaction is also taken into account. Indeed, by performing an appropriate dynamical Hamiltonian associated with the Jaynes–Cummings and anti-Jaynes–Cummings terms, as well as the D–D interaction for the system, we solve the corresponding time-dependent Schrödinger equation with specific initial conditions for atoms and field. In the continuation, concurrence, as an appropriate measure of the degree of entanglement of the two qubits, and atomic population inversion of the qubits, as the rate of energy exchange between atoms and field, are evaluated. Meanwhile, we investigate the influence of CRTs and D–D interaction (as well as other involved parameters in the model interaction) on the mentioned quantities. Our numerical results indicate that collapse-revival phenomenon can be observed in the absence of D–D interaction with or without rotating wave approximation, however, CRTs cause an increase or decrease in the number of collapse-revivals in a finite interval of time, depending on the chosen parameters. In fact, by entering the D–D interaction term, this phenomenon is destroyed and the time behaviour of the quantities experiences irregular oscillations. Noticing that the initial field is considered in the vacuum state, the occurrence of collapse-revival in the population inversion of the two qubits is an interesting feature of this work. As is shown, the degree of entanglement and atomic population inversion of the qubits can generally be tuned, and the death of entanglement can be prevented, both by adjusting the evolved parameters in the model.
We study the dynamics of the Jaynes–Cummings model for two two-level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus), extending this to the macroscopic case of an array of Nq qubits. For an initial cavity coherent state |α⟩ and the qubit system in a specified “basin of attraction” in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a “Schrödinger cat” state.
We study the dynamics of the Jaynes-Cummings Model for two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or `quantum bus'). We show that there is a time in between the collapse and revival of Rabi oscillations when the state of the qubit sub-system, $| ψ\_{attractor} $, is largely independent of its initial state. This generalizes to many qubits the discovery by Gea-Banacloche for the one qubit case. The qubits in such `attractor' states are not entangled either with the field or among themselves, even if they were in the initial state. Subsequently the entanglement between the qubits revives. Finally, it is argued that the collapse and revival of entanglement and the persistence of `non-classicality' is a generic feature of multiple qubits interacting via a `quantum bus'.
Background. The study of entangled states in Jaynes–Cummings models and its multiqubit generalizations and extensions remains an important and relevant topic in modern quantum optics, quantum information science and solid state physics. This is due to the fact that such models naturally describe the dynamics of interaction of logical elements of quantum devices, such as quantum computers or quantum networks (qubits) with microwave fields of resonators used to control the states of qubits. In this regard, it is very important to search for the most efficient schemes of generation, control and monitoring of entangled qubit states within the framework of Jaynes–Cummings type models. Aim. To investigate the entanglement dynamics of a pair of qubits, each of which is locked in a single-mode resonator and interacts non-resonantly with the vacuum field mode, in the presence of detuning between frequencies of transitions in the qubits and frequencies of resonator modes and dipole-dipole interaction of the qubits. Methods. To analyze the dynamics of the considered system, the solution of the time-dependent quantum Schrödinger equation is investigated. The exact solution of the above equation in the case of entangled Bell-type initial qubits states is found. This is used to calculate the criterion of entanglement of a pair of qubits – negativity. Numerical modeling of the time dependence of negativity for different values of the parameters of the considered model has been carried out. Results. It is shown that the presence of detuning, the difference in the qubit-photon couplings and the intensity of the dipole-dipole interaction significantly affect the maximum degree of entanglement of the qubit subsystem during its evolution. It is found that for certain parameters of the model under consideration, the initial Bell entangled states of qubits can be considered as long-lived stable states. Conclusion. The possibility of realization of long-lived and robust two-qubit entangled states in the system under consideration has been established. The obtained results can be used for effective control and manipulation of the degree of entanglement of qubits interacting with microwave fields of resonators.
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.