Julio Gea-Banacloche

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level system coupled to a quantum harmonic oscillator. Such devices may allow the exploration of parameter regimes outside the near-resonance and weak-coupling assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating other theoretical approaches. One such approach is an adiabatic approximation in the limit that the oscillator frequency is much larger than the characteristic frequency of the two-level system. A derivation of the approximation is presented, together with a discussion of its applicability in a system consisting of a Cooper-pair box coupled to a nanomechanical resonator. Within this approximation the time evolution of the two-level-system occupation probability is calculated using both thermal- and coherent-state initial conditions for the oscillator, focusing particularly on collapse and revival phenomena. For thermal-state initial conditions parameter regimes are found in which collapse and revival regions may be clearly distinguished, unlike the erratic evolution of the thermal-state RWA model. Coherent-state initial conditions lead to complex behavior, which exhibits sensitive dependence on the coupling strength and the initial amplitude of the oscillator state. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the weak-coupling limit, which provides insight into the differences between the thermal- and coherent-state models. Finally, potential experimental observations in solid-state systems, particularly the Cooper-pair box—nanomechanical resonator system, are discussed and found to be promising.

Evanescent light-wave atom mirrors, resonators, waveguides, and traps

Publisher Summary This chapter presents an overview of atom mirrors, resonators, waveguides, and traps that operate for the most part on the evanescent light-wave mechanism for atom manipulation. For many years, it has been known that light can be used to trap and manipulate small dielectric particles and atoms. In particular, the intense coherent light of lasers has been used to cool neutral atoms down to the micro-Kelvin and now even the nano-Kelvin regimes. The chapter discusses several convex, evanescent light-wave traps or guides in which at least one field is red-detuned, and hence attractive but a centrifugal force or a blue-detuned field provides a repulsive counterforce to allow the atoms to remain confined in stable orbits around the convex, dielectric, and optical resonator. The chapter focuses on the use of the evanescent field for making atom mirrors, resonators, waveguides, and traps. One of the principal experimental drawbacks of the evanescent light-wave mirror is that it requires quite high laser power to produce a sufficiently large potential barrier to reflect atoms with any realistic component of velocity normal to the surface, while not introducing an unacceptable degree of spontaneous emission probability.

A quantum bouncing ball

The dynamics of a quantum wave packet bouncing on a hard surface under the influence of gravity are studied. This is a system that might be realized experimentally with cold atoms dropped onto an “atomic mirror.” The classical limit is discussed and interesting departures from classical behavior are pointed out and explained.

Hiding messages in quantum data

A method is proposed to hide messages in arbitrary quantum data files. The messages may act as “watermarks,” to secure the authenticity and/or integrity of the data. With the help of classical secret keys, they can be made unreadable by other parties and to reveal whether thay have been tampered with. The basic idea is to encode the data using a quantum error-correcting code and hide the message as (correctible) errors, deliberately inserted, which can be read out from the error syndrome. Also discussed briefly is a “reverse encoding,” which would involve putting the actual data in the error syndrome, and letting the encoded qubit itself carry the message.

Future Directions in Electronic Computing and Information Processing

We are facing a slowing down of the evolution of microprocessor performance. This is part of a more general slowing down which is indicated by, among others, the fact that IBM has recently given up its PC market. By applying the principles of physics, we discuss some characteristic features of the current situation and consider if some exotic new technologies such as nanoelectronics or quantum computing would be able to save us from this slowdown.

A new look at the Jaynes-Cummings model for large fields: Bloch sphere evolution and detuning effects

Abstract This paper elaborates on the recently discovered asymptotic solution for the Jaynes-Cummings model for large, coherent-like initial fields. The nature of the asymptotic solution and its physical meaning are explored. A connection to the prediction of the neoclassical theory is established. The various aspects of the atomic state evolution, including collapses and revivals, quasi-pure state evolution, and state preparation, are illustrated using the Bloch sphere. It is shown that the asymptotic solution provides qualitative insights even for rather low initial fields. The results are also extended to include the effects of detuning. Quasi-pure state evolution is still obtained when the initial state is one of the semiclassical stationary states, but for large detuning an atom prepared in an arbitrary initial state no longer evolves towards a unique pure state at half-revival time.

Entangled and Disentangled Evolution for a Single Atom in a Driven Cavity

For an atom in a driven cavity we find states that are highly entangled, and that spontaneous emission can transiently increase entanglement. We propose a correlation function measurement and discuss time evolution of entanglement.

Comparison of Energy Requirements for Classical and Quantum Information Processing

By considering the energy requirements of quantum and classical computers we propose a criterion to separate the classical from the quantum regime and show that the classical scaling laws are much more favorable for conventional, general purpose computation.

Steady State Entanglement in Cavity QED

We investigate steady state entanglement in an open quantum system, specifically a single atom in a driven optical cavity with cavity loss and spontaneous emission. The system reaches a steady pure state when driven very weakly. Under these conditions, there is an optimal value for atom-field coupling to maximize entanglement, as larger coupling favors a loss port due to the cavity enhanced spontaneous emission. We address ways to implement measurements of the entanglement and find that normalized cross-correlation functions are indicators of the entanglement in the system. The equal time intensity-field cross correlation between the transmitted field of the cavity and the fluorescence intensity is proportional to the entanglement of formation for weak driving fields.

Splitting the wave function of a particle in a box

This paper addresses the question of what happens to a particle in a box that is initially in the ground state, when the box is split into two slightly unequal halves. If the splitting is done sufficiently slowly, it is found that the particle always ends up in the bigger half of the box, regardless of how small the difference in sizes of the two halves may be. Approximate analytical expressions that describe the process are derived, and an optical analogy is presented.