Avoided crossing resonances: structural and dynamical aspects

We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a two-level system coupled to a harmonic oscillator, of the type commonly found in quantum optics. Finally the results obtained are exemplified and applied to optimize the fidelity and speed of quantum gates in trapped ions.Comment: 4 pages, 1 figur

Deep Strong Coupling Regime of the Jaynes-Cummings model

We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency w (g/w > 1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wavepackets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.Comment: Published version, note change of title: DSC regime of the JC mode

Motional frequency shifts of trapped ions in the Lamb-Dicke regime

First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behaviour of their effect with respect to the Lamb-Dicke parameter. In particular, we give analytical expressions for the frequency shift, ``pulling'' or ``pushing'', produced in the carrier absorption band by the vibronic transitions both for Rabi and Ramsey schemes. This shift is shown to be independent of the initial vibrational state.Comment: 9 pages, 6 figure

Structural and dynamical aspects of avoided-crossing resonances in a 33-level Λ\Lambda system

In a recent publication [Phys. Rev. A 79, 065602 (2009)] it was shown that an avoided-crossing resonance can be defined in different ways, according to level-structural or dynamical aspects, which do not coincide in general. Here a simple $3$-level system in a $\Lambda$ configuration is discussed, where the difference between both definitions of the resonance may be observed. We also discuss the details of a proposed experiment to observe this difference, using microwave fields coupling hyperfine magnetic sublevels in alkali atoms.Comment: 7 pages, 5 figure

Circuit Quantum Electrodynamics with a Superconducting Quantum Point Contact

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.Comment: 5 pages, 4 figures. Updated version, accepted for publication as a Rapid Communication in Physical Review