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New Journal of Physics

Coherence and catalysis in the Jaynes–Cummings model

Anette Messinger, Atirach Ritboon, Frances Crimin, Sarah Croke, Stephen Mark Barnett

Published Feb 13, 2020• 15 citations
Publisher

Abstract

Abstract There has been substantial interest of late on the issue of coherence as a resource in quantum thermodynamics. To date, however, analyses have focused on somewhat artificial theoretical models. We seek to bring these ideas closer to experimental investigation by examining the ‘catalytic’ nature of quantum optical coherence. Here the interaction of a coherent state cavity field with a sequence of two-level atoms is considered, a state ubiquitous in quantum optics as a model of a stable, classical source of light. The Jaynes–Cummings interaction Hamiltonian is used, so that an exact solution for the dynamics can be formed, and the evolution of the atomic and cavity states with each atom-field interaction analysed. In this way, the degradation of the coherent state is examined as coherence is transferred to the sequence of atoms. The associated degradation of the coherence in the cavity mode is significant in the context of the use of coherence as a thermodynamic resource.

DOI
10.1088/1367-2630/ab7607

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Abstract There has been substantial interest of late on the issue of coherence as a resource in quantum thermodynamics. To date, however, analyses have focused on somewhat artificial theoretical models. We seek to bring these ideas closer to experimental investigation by examining the ‘catalytic’ nature of quantum optical coherence. Here the interaction of a coherent state cavity field with a sequence of two-level atoms is considered, a state ubiquitous in quantum optics as a model of a stable, classical source of light. The Jaynes–Cummings interaction Hamiltonian is used, so that an exact solution for the dynamics can be formed, and the evolution of the atomic and cavity states with each atom-field interaction analysed. In this way, the degradation of the coherent state is examined as coherence is transferred to the sequence of atoms. The associated degradation of the coherence in the cavity mode is significant in the context of the use of coherence as a thermodynamic resource.
Catalysis plays a key role in many scientific areas, most notably in chemistry and biology. Here we present a catalytic process in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst, and it allows for the deterministic generation of nonclassical light in the cavity. Considering a cavity prepared in a “classical” coherent state, and choosing appropriately the atomic state and the interaction time, we obtain an evolution with the following properties. First, the state of the cavity has been modified, and it now features nonclassicality, as witnessed by sub-Poissonian statistics or Wigner negativity. Second, the process is catalytic in the sense that the atom is deterministically returned to its initial state exactly, and it can be reused multiple times. What is more, we also show that our findings are robust under dissipation and can be applied to scenarios featuring cavity loss and atomic decay. Finally, we investigate the mechanism of this catalytic process, in particular highlighting the key role of correlations and quantum coherence. Published by the American Physical Society 2024
We uncover new features on the study of a two-level atom interacting with one of two cavities in a coherent superposition. The James-Cummings model is used to describe the atom-field interaction and to study the effects of quantum indefiniteness on such an interaction. We show that coherent control of the two cavities in an undefined manner allows novel possibilities to manipulate the atomic dynamics on demand which are not achievable in the conventional way. In addition, it is shown that the coherent control of the atom creates highly entangled states of the cavity fields taking a Bell-like or Schrödinger-cat-like state form. Our results are a step forward to understand and harness quantum systems in a coherent control, and open a new research avenue in the study of atom-field interaction exploiting quantum indefiniteness.
The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results are then used to analyse the general time evolution of a bipartite atom-field system and its properties, such as entanglement. We extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio, Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that interact with an atom. Our scheme allows to produce states that are arbitrarily close to a Bell state with a success probability greater than 0.75, whereas the success rate of the original method tends to 0 for perfect fidelity. Further, we extend both schemes by allowing the atom or the cavity to be in a thermal state and find that the fidelity of the produced states is reduced with increasing temperature. Finally, we apply our scheme to quantum teleportation, where we find that the fidelity of the teleported state compared to the original state also decreases as the temperature is increased.
In this paper, we explore the optical tomography and quantum coherence dynamics for a coherent cavity field interacting with a two-level atom via intensity dependent coupling. We derive a specific solution to the master equation for the Jaynes–Cummings model, considering cavity damping. This solution reveals how the atom coherent-cavity interactions can produce new coherent states when the initial dissipative cavity-field state is coherent state or even coherent state. The effects of the atom-coherent-cavity interactions and the cavity damping, on the dynamics of the initial coherent state optical tomography and coherence is examined. In addition to the nonclassical properties, the atom–cavity interactions have a remarkable capacity to form distinct cavity field states linked to certain optical tomography distributions. Additionally, we investigate the maximal optical tomography dynamics for coherent state and even coherent state considering a range of cavity damping and detuning values.
In this work, we uncover new features on the study of a two-level atom interacting with one of two cavities in a coherent superposition. The James-Cummings model is used to describe the atom-field interaction and to study the effects of quantum indefiniteness on such an interaction. We show that coherent control of the two cavities in an undefined manner allows novel possibilities to manipulate the atomic dynamics on demand which are not achievable in the conventional way. In addition, it is shown that the coherent control of the atom creates highly entangled states of the cavity fields taking a Bell-like or Schrödinger-cat-like state form. Our results are a step forward to understand and harness quantum systems in a coherent control, and open a new research avenue in the study of atom-field interaction exploiting quantum indefiniteness.
In this thesis, I investigate various aspects of one of the most fundamental questions in thermodynamics: what state transformations can quantum systems undergo while interacting with a thermal bath under specific constraints? These constraints may involve total energy conservation, memory effects, or finite-size considerations. Addressing this question leads to (i) a characterisation of the structure of the thermodynamic arrow of time, (ii) a framework bridging the gap between memoryless and arbitrarily non-Markovian thermodynamic processes, and (iii) a derivation of the famous fluctuation-dissipation relation within a quantum information framework. Finally, the last part of this thesis focuses on studying a ubiquitous phenomenon in science, so-called catalysis. It involves using an auxiliary system (a catalyst) to enable processes that would otherwise be impossible. Over the last two decades, this notion has spread to the field of quantum physics. However, this effect is typically described within a highly abstract framework. Despite its successes, this approach struggles to fully capture the behaviour of physically realisable systems, thereby limiting the applicability of quantum catalysis in practical scenarios. Strikingly, I will demonstrate this effect in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst and allows for the deterministic generation of non-classical light in the cavity, as evidenced by sub-Poissonian statistics or Wigner negativity.