Entropy Dynamics of Phonon Quantum States Generated by Optical Excitation of a Two-Level System

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.

Thermodynamics of an Empty Box

“…This kind of relation has already been exploited in a preliminary fashion to derive the Boltzmann distribution in a previous work by one of the authors [59]. Moreover, it is also made plausible by the applications of entropy to entanglement [58], which is also a correlation. All in all, the fraction of the boundary volume Φ B has been identified as a further DoF and the extended internal energy now reads…”

“…This "entanglement entropy" vanishes for a pure state. Since this entropy is, in general, difficult to calculate, one can instead use the linear entropy S l = Tr(ρ) − Tr(ρ 2 ) [58]. (The difference, of course, is that here, one would consider the linear entropy to be the approximate one.…”

Remote Phonon Control of Quantum Dots and Other Artificial Atoms

“…Single pulses with a fine-tuned duration and pulse area lead to such superpositions shown in Figure 10b (right). [200] Double pulse sequences can be used to create cat states, [201][202][203] similar to those realized with superconducting artificial atoms coupled to mechanical resonators. [189] However, the difference between semiconductor QDs and superconducting qubits is not only the coupling mechanism to the phonons but also an enormous size discrepancy.…”

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

“…1d is given by ⟨e kin ⟩ y = 1 L ∫ dy nd e kin (⃗ r nd ) . For the figures, the local kinetic energy density was calculated via a mass redistribution technique 16 .…”

“…Wigner functions provide a description of quantum systems in phase space. Since their initial development [1], they have found a significant number of applications [2][3][4][5] in fields such as atomic physics [6], quantum optics [7][8][9], visualization of quantum effects [10,11], computational electronics [12][13][14], and solid-state theory [15][16][17][18][19]. Besides these practical aspects, they are also of interest for fundamental questions in quantum mechanics such as the theory of quantum chaos [20].…”