The coherent interaction between matter and radiation - A tutorial on the Jaynes-Cummings model

The Jaynes-Cummings (JC) model is a milestone in the theory of coherent interaction between a two-level system and a single bosonic field mode. This tutorial aims to give a complete description of the model, analyzing the Hamiltonian of the system, its eigenvalues and eigestates, in order to characterize the dynamics of system and subsystems. The Rabi oscillations, together with the collapse and revival effects, are distinguishing features of the JC model and are important for applications in Quantum Information theory. The framework of cavity quantum electrodynamics (cQED) is chosen and two fundamental experiments on the coherent interaction between Rydberg atoms and a single cavity field mode are described.Comment: 22 pages, 7 figures. Tutorial. Submitted to a special issue of EPJ - ST devoted to the memory of Federico Casagrand

Solvable model of dissipative dynamics in the deep strong coupling regime

We describe the dynamics of a qubit interacting with a bosonic mode coupled to a zero-temperature bath in the deep strong coupling (DSC) regime. We provide an analytical solution for this open system dynamics in the off-resonance case of the qubit-mode interaction. Collapses and revivals of parity chain populations and the oscillatory behavior of the mean photon number are predicted. At the same time, photon number wave packets, propagating back and forth along parity chains, become incoherently mixed. Finally, we investigate numerically the effect of detuning on the validity of the analytical solution.Comment: 6 pages, 8 figure

Numerical analysis of the radio-frequency single-electron transistor operation

We have analyzed numerically the response and noise-limited charge sensitivity of a radio-frequency single-electron transistor (RF-SET) in a non-superconducting state using the orthodox theory. In particular, we have studied the performance dependence on the quality factor Q of the tank circuit for Q both below and above the value corresponding to the impedance matching between the coaxial cable and SET.Comment: 14 page

Quantum nanomechanics: A new perspective on the quantum harmonic oscillator

The standard mathematical formalism of cavity QED leads us to consider photons as excitations of a quantum harmonic oscillator. Although it is one of the most familiar problems of quantum mechanics, some aspects of the quantum harmonic oscillator remain difficult to visualize, particularly in the rather abstract context of an electromagnetic field. Recently, modern microfabrication and refrigeration techniques have begun to allow the creation of nanoscale mechanical oscillators which can be cooled close to the quantum regime. Despite the extreme physical differences between an electromagnetic cavity and a nanomechanical resonator, both systems may be approximated by the same quantum harmonic oscillator model. However, the conceptual consequences of quantum behavior, and the challenges to physical intuition, are quite different in the two cases. Taking a mechanical point of view therefore allows fresh insight into the quantum harmonic oscillator problem. To illustrate the connection and how it may aid our understanding of light, the mathematical parallelism between an electromagnetic cavity and a mechanical resonator is demonstrated. Current nanomechanics experiments are discussed, and some possible quantum measurements are introduced. Finally, the discrepancies between the predictions of quantum mechanics and our experience of classical vibrating beams are considered, with an emphasis on how nanomechanics may be able to offer a new perspective on the nature of photons

Defining the semiclassical limit of the quantum Rabi Hamiltonian

The crossover from quantum to semiclassical behavior in the seminal Rabi model of light-matter interaction still, surprisingly, lacks a complete and rigorous understanding. A formalism for deriving the semiclassical model directly from the quantum Hamiltonian is developed here. Working in a displaced Fock-state basis |?, n?, the semiclassical limit is obtained by taking |?| ? ? and the coupling to zero. This resolves the discrepancy between coherent-state dynamics and semiclassical Rabi oscillations in both standard and ultrastrong coupling/driving regimes. Furthermore, it provides a framework for studying the quantum-to-semiclassical transition, with potential applications in quantum technologies

Vibration-assisted resonance in photosynthetic excitation-energy transfer

Understanding how the effectiveness of natural photosynthetic energy-harvesting systems arises from the interplay between quantum coherence and environmental noise represents a significant challenge for quantum theory. Recently it has begun to be appreciated that discrete molecular vibrational modes may play an important role in the dynamics of such systems. Here we present a microscopic mechanism by which intramolecular vibrations may be able to contribute to the efficiency and directionality of energy transfer. Excited vibrational states create resonant pathways through the system, supporting fast and efficient energy transport. Vibrational damping together with the natural downhill arrangement of molecular energy levels gives intrinsic directionality to the energy flow. Analytical and numerical results demonstrate a significant enhancement of the efficiency and directionality of energy transport that can be directly related to the existence of resonances between vibrational and excitonic levels

Energy measurements and preparation of canonical phase states of a nano-mechanical resonator

We show that a continuous quantum non-demolition measurement of the energy of a nanomechanical resonator can be achieved by monitoring the resonator with a single-electron transistor, or a quantum point contact, via a Cooper-pair box. This technique can further be used to prepare highly entangled states of two resonators, such as canonical phase reference states, and so-called noon states

Quantum phase transition of polaritonic excitations in a multi-excitation coupled array

We analyze the quantum phase transition-like behavior in the lowest energy state of a two-site coupled atom-cavity system, where each cavity contains one atom but the total excitation number is not limited to two. Under the large-detuning condition, we identify an interesting coexisting phase involving characteristics of both photonic superfluid and atomic insulator, which has not been previously revealed. For small hopping, we find that the signature of the photonic superfluid state becomes more pronounced with the increase in total excitation number, and that the boundaries of the various phases shift with respect to the case of two excitations. In the limit of small atom-field interaction, the polaritonic superfluid region becomes broader as the total excitation number increases. We use alternative order parameters to characterize the nonclassical property in the lowest-energy state, and find that the entanglement of photons in the photonic superfluid state has an approximately quadratic-like dependence on the total excitation number within the large-detuning limits. The second-order cross-correlation function is demonstrated to become inversely proportional to the total excitation number in the large detuning limits