Entanglement of atom-field states in the anti-Jaynes-Cummings interaction: rabi oscillations and quantum teleportation of entangled atomic qubits

Abstract

The quantum Rabi model (QRM), the simplest single-mode spin-boson model, was initially simplified using rotating wave approximation (RWA), yielding the Jaynes Cummings (JC) model in rotating frame (RF). The QRM was later symmetrised into its rotating JC and counter-rotating (CR) anti-Jaynes-Cummings (AJC) components, yielding an exactly solvable AJC model in the counter-rotating frame (CRF). This work presents the dynamics generated when a two-level atom (fermionic system) interacts with a quantised electromagnetic field mode (bosonic system) in the AJC model. The evolution of the atomic state during the AJC interaction with field mode initially and separately in three basic non-classical states of light is considered. In each respective atom-field interaction, we provided the corresponding extensively studied JC interaction as a com parison. We have shown that when the field mode is in an initial Fock state (idealised light), Rabi oscillations during the AJC interaction occur in the reverse sense relative to that during the JC interaction. In addition, quantum teleportation of a two-atom entan gled anti-symmetric state at unit fidelity indicates that maximally entangled atom-field states generated in the AJC interaction are effective quantum channels, and the observed long-lived entanglement during the AJC interaction specify that the atomic qubits ex hibit long coherence time vital for computational processes. What is more, two-qubit controlled-NOT (C-NOT) gate operation and single qubit Walsh-Hadamard gate oper ation is demonstrated each giving standard outcomes as expected. In the former, the target qubit is flipped when the control qubit is in an initial ground state |g⟩ and remain unchanged when the control qubit is in an initial excited state |e⟩ while in the latter the atomic basis states {|e⟩, |g⟩} were rotated into diagonal basis states {|+⟩, |−⟩}. When the field mode in an initial coherent state is considered during the AJC interaction, fully quantised atom-field interaction is realised since the field is dominantly sub-Poissonian. Finally, when an initial squeezed coherent state is considered during the AJC interaction, at all time intervals the atom-field quantum systems are entangled (mixed), i.e, at no point did the quantum systems evolve to pure state, the degree of mixedness increased with every increase in the squeeze parameter and ringing revivals at an expected col lapse phase are observed when higher values of squeeze parameter is applied. This thesis work presents the first ever demonstration of quantum Rabi oscillations, entanglement dynamics, successful quantum teleportation, photon statistics and effective quantum gate operations in an AJC interaction between a two-level atom and a quantised electromag netic field mode. In contrast to the standard JC interaction which has generally been iv used in quantum information theory (QIT) and quantum computation, the AJC inter action provides the advantage of starting with both an atom and field mode each in an initial ground state, i.e, an atom in spin-down state and field mode in vacuum state, a property which is essentially unachievable in the JC interaction when an initial Fock state is considered. We now recommend application of the AJC model in the emerging field of quantum technology, which has a potential to revolutionise a wide range of industries and applications, from finance and logistics to healthcare and energy. More specifically, the results of this work in its present form, will be of immense contribution to QIT and physical realisation of quantum computation