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Physical Review A

Quantum origin of dephasing and revivals in the coherent-state Jaynes-Cummings model

P. L. Knight, PAUL M. RADMORE

Published Jul 1, 1982• 137 citations
Publisher

Abstract

The Jaynes-Cummings model of a two-level system interacting with a single-mode coherent-state field is investigated in a transformed representation emphasizing quantum corrections to the semiclassical Rabi problem. We find an intuitive explanation of the collapse and revivals of oscillations in the population inversion.
DOI
10.1103/physreva.26.676

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Collapse and revivals in the Jaynes-Cummings model are studied within the context of the Mollow transformation for a single-mode coherent-state cavity field. The Mollow-transformed Jaynes-Cummings Hamiltonian has two atom-field terms, one corresponding to a classical field and the other to a quantized field driving the atomic transition. As such it maps onto the complementary problem of an atom in an optical cavity, whose field is initially in the vacuum state, driven by an external classical field. Both problems have the same atomic-state dynamics. It is shown that the revivals can be associated with two distinct properties of the quantized field of the transformed Hamiltonian. Revivals occurring at even (odd) multiples of the revival time are correlated with field states that are close to the initial field state and for which the average energy in the field is a minimum (maximum). Using semiclassical dressed states, we are able to map the problem for the field states onto one involving two uncoupled oscillators driven by off-resonant fields, provided effects related to dispersion are neglected. Analytic expressions for the photon number distribution of the transformed cavity field, including dispersion, are obtained for the even revival times.
The evolution of the atomic state in the resonant Jaynes-Cummings model (a two-level atom interacting with a single mode of the quantized radiation field) with the field initially in a coherent state is considered. It is shown that the atom is to a good approximation in a pure state in the middle of what has been traditionally called the ``collapse region.'' This pure state exhibits no Rabi oscillations and is reached independently of the initial state of the atom. For most initial states a total or partial ``collapse of the wave function'' takes place early during the interaction, at the conventional collapse time, following which the state vector is recreated, over a longer time scale.
Abstract In the photon-atom interaction, one of the most interesting phenomena can be collapse-revival effect in population inversion of atomic levels. Since a single-photon-transition Jaynes–Cummings model can be generalized to a multiphoton-transition Jaynes–Cummings model, of which the Hamiltonian can exhibit a supersymmetric Lie algebra structure, in this paper, quantum collapse and revival in atomic population inversion, which is a collaborative effect of a variety of quantum Rabi oscillations with various quantum Rabi frequencies, is studied for the supersymmetric multiphoton-transition Jaynes–Cummings model. In the literature, it has been pointed out that quantum collapse and revival might find an application in qubit design. We expect that a supersymmetric two-level system might serve as such a kind of qubits. Compared with ordinary two-level qubits, more information could be stored in the basis vectors of supersymmetric qubits, and this could increase the degrees of freedom of tensor product (multi-component extension) of basis vectors of this multiphoton-atom interacting system. For this reason, some characteristics of the collapse-revival effect driven by ordinary coherent states and Yurke–Stoler coherent states will be addressed in this paper. The influence of various characteristic parameters of this supersymmetric Jaynes–Cummings model and the quantized optical fields on the quantum collapse and revival in the population inversion will be indicated in some numerical illustrative examples.
We study the dynamics of the Jaynes-Cummings Model for an array of NqN_qNq​ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state ∣α>| \alpha >∣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 `Schr\odinger Cat' state.
A two-level atom interacting with a cavity field initialized in a coherent state exhibits the collapse and revival features in its population inversion dynamics under the Jaynes–Cummings interaction. When the cavity field is prepared in a number-state filtered coherent state, obtained by filtering the number state | m 〉 from a coherent state | α 〉 , we observe micro-Rabi oscillations in the collapse region instead of a perfect collapse. We find that the Rabi frequency of these micro oscillations depends only on the filtered photo-number m, whereas the amplitude depends on both m and α . This dependence enables one to infer the filtered number state from the coherent-state distribution by analyzing the time evolution of the atomic population inversion. Conversely, the amplitude and frequency of the micro-Rabi oscillations can be tuned by filtering an appropriate number state. Furthermore, we investigate the effect of filtering multiple number states from a coherent state on the atomic population inversion dynamics.
We study the dynamics of the Jaynes-Cummings Model for an array of NqN_qNq​ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state ∣α>| α>∣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.