I. Lizuain

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 ω (g/ω≳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 wave packets 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.

Shortcut to Adiabatic Passage in Two- and Three-Level Atoms

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

Transitionless quantum drivings for the harmonic oscillator

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

Zeno physics in ultrastrong-coupling circuit QED

We study the Zeno and anti-Zeno effects in a superconducting qubit interacting strongly and ultrastrongly with a microwave resonator. Using a model of a frequently measured two-level system interacting with a quantized mode, we show different behaviors and total control of the Zeno times depending on whether the rotating-wave approximation can be applied in the Jaynes-Cummings model, or not. We exemplify showing the strong dependence of our results with the properties of the initial field states and suggest applications for quantum tomography.

Generalized relation between pulsed and continuous measurements in the quantum Zeno effect

A relation is found between pulsed measurements of the excited-state probability of a two-level atom illuminated by a driving laser and a continuous measurement by a second laser coupling the excited state to a third state which decays rapidly and irreversibly. We find the time between pulses to achieve the same average detection time as a given continuous measurement in strong, weak or intermediate coupling regimes, generalizing the results of Schulman (1998 Phys. Rev. A 57 1509).

Vibronic Rabi resonances in harmonic and hard-wall ion traps for arbitrary laser intensity and detuning

We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.

Ramsey interferometry with a two-level Tonks-Girardeau gas

We propose a solvable generalization of the Tonks-Girardeau model that describes a coherent one-dimensional (1D) gas of cold two-level bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by idealized, infinitely strong contact potentials, with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal bosons. The dual system of this gas, an ideal gas of two-level fermions coupled by the interaction with the separated fields, produces the same fringes and noise fluctuations. The cases of time-separated and spatially separated fields are studied. For spatially separated fields the fringes may be broadened slightly by increasing the number of particles, but only for large particle numbers far from present experiments with Tonks-Girardeau gases. The uncertainty in the determination of the atomic transition frequency diminishes, essentially with the inverse root of the particle number. The difficulties to implement the model experimentally and possible shortcomings of strongly interacting 1D gases for frequency standards and atomic clocks are discussed.

Short-time-interaction quantum measurement through an incoherent mediator

We propose a method of indirect measurements where a probe is able to read, in short interaction times, the quantum state of a remote system through an incoherent third party, hereafter called a mediator. The probe and system can interact briefly with the mediator in an incoherent state but not directly among themselves and, nevertheless, the transfer of quantum information can be achieved with robustness. We exemplify our measurement scheme with a paradigmatic example of this tripartite problem---a qubit-oscillator-qubit setup---and discuss different physical scenarios, pointing out the associated advantages and limitations.

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 extreme values. Thus the concept of avoided crossing resonance can be defined in different ways, which do not coincide in the general case. These definitions are applied to optimize the fidelity and speed of trapped-ion quantum gates.

Atom laser dynamics in a tight waveguide

We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. The time dependent density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir.