Abstract
In quantum physics, two prototypical model systems stand out due to their wide range of applications. These are the two-level system (TLS) and the harmonic oscillator. The former is often an ideal model for confined charge or spin systems and the latter for lattice vibrations, i.e., phonons. Here, we couple these two systems, which leads to numerous fascinating physical phenomena. Practically, we consider different optical excitations and decay scenarios of a TLS, focusing on the generated dynamics of a single phonon mode that couples to the TLS. Special emphasis is placed on the entropy of the different parts of the system, predominantly the phonons. While, without any decay, the entire system is always in a pure state, resulting in a vanishing entropy, the complex interplay between the single parts results in non-vanishing respective entanglement entropies and non-trivial dynamics of them. Taking a decay of the TLS into account leads to a non-vanishing entropy of the full system and additional aspects in its dynamics. We demonstrate that all aspects of the entropy’s behavior can be traced back to the purity of the states and are illustrated by phonon Wigner functions in phase space.
Highlights
Entropy is one of the most fundamental concepts in physics
The second law of thermodynamics prohibits the decrease of the entropy of a closed system; this does not hold for the entropy of a subsystem which is interacting with other subsystems or with its surroundings [5,6]
In the following, we fix this value to γ = 2 in order to separate the different parts of the Wigner function in phase space, as will be seen later
Summary
Entropy is one of the most fundamental concepts in physics. According to the second law of thermodynamics, in a closed system, it never decreases, which has far reaching consequences, from the limited efficiency of thermodynamic machines [1] to cosmological implications [2,3]. The second law of thermodynamics prohibits the decrease of the entropy of a closed system; this does not hold for the entropy of a subsystem which is interacting with other subsystems or with its surroundings [5,6]. In this case, the study of the dynamics of the entropy of these subsystems provides valuable information on the evolution of the nature of the system’s state [7]. We will show that the analysis of the time-dependent entropy provides interesting insight into the nature of the quantum state of the two subsystems
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