The localization of phonons in ion traps with controlled quantum disorder (original) (raw)

Local probe of single phonon dynamics in warm ion crystals

2017

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

Quantum phases of interacting phonons in ion traps

Physical Review A, 2008

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose-Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, like models with attractive or site-dependent phonon-phonon interactions.

Optical Signatures of Energy-Level Statistics in a Disordered Quantum System

Physical Review Letters, 2000

Time-resolved measurements of the resonant Rayleigh scattering from quantum well excitons are shown to provide information on the energy-level statistics of the localized exciton states. The signal transients are reproduced by a microscopic quantum model of the exciton two-dimensional motion in presence of spatially correlated disorder. This model allows quantitative determination of the average energy separation between the localized states. Here this quantity turns out to be only a few times smaller than the average disorder amplitude, proving that spatial correlation and quantum mechanics are equally important in the description of the exciton localization process. PACS numbers: 78.47. + p, The study of the fundamental properties of disordered systems mostly relies on transport measurements in metals . In these systems, however, the density of carriers is fixed and the physics is governed by the strong interplay between disorder and many-body Coulomb correlations . In addition, transport measurements probe the highest occupied energy levels, close to the Fermi energy, which are only weakly affected by the underlying disorder. On the theoretical side, a general understanding of many-body disordered systems is far from being achieved [2] (see, e.g., the recent debate on interaction-induced delocalization of electrons [3]). Besides, many aspects of single-particle disordered quantum systems, such as weak localization in two dimensions or the effects of spatial correlation, still leave open questions. For this reason, an experimental environment with noninteracting particles would be of great interest for the understanding of the basic aspects in the physics of disorder and localization. Excitons in semiconductor heterostructures could be eligible for such a role. Indeed, excitons are globally neutral and their mutual dipole-dipole interaction has thus a shorter range. Furthermore, excitons are produced by optical excitation and their density can be adjusted within a wide range. This allows one to minimize many-body effects and basically perform experiments in an ideal noninteracting regime. Finally, excitons are probed by means of optical spectroscopy. The selection rules for the optical transitions imply that only the lowest exciton levels-those mostly subject to localization-are probed.

Signatures of Anderson localization and delocalized random quantum states

Chemical Physics, 2018

We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest model of a 1D disordered chain and we analyse both the dynamics of an initially localized state and the dynamics of quantum states drawn at random from the ensemble corresponding to the minimum knowledge about the initial state. While in the former case the site distribution remains confined in a limited portion of the chain, the site distribution of random pure state fluctuates around an equilibrium average that is delocalized over the entire chain. A clear connection between the equilibration observed when the system is initialized in a fully localized state and the amplitude of dynamical fluctuations of a typical random pure state is established.

Three-dimensional localization of ultracold atoms in an optical disordered potential

In disordered media, quantum interference effects are expected to induce complete suppression of electron conduction. The phenomenon, known as Anderson localization, has a counterpart with classical waves that has been observed in acoustics, electromagnetism and optics, but a direct observation for particles remains elusive. Here, we report the observation of the three-dimensional localization of ultracold atoms in a disordered potential created by a speckle laser field. A phenomenological analysis of our data distinguishes a localized component of the resulting density profile from a diffusive component. The observed localization cannot be interpreted as the classical trapping of particles with energy below the classical percolation threshold in the disorder, nor can it be understood as quantum trapping in local potential minima. Instead, our data are compatible with the self-consistent theory of Anderson localization tailored to our system, involving a heuristic energy shift that offers scope for future interpretation.

Localization dynamics in weakly disordered systems

The time dependence of the localization of a quantum particle in a disordered system is considered. It is assumed that the particle is placed into the system at the initial instant, and the character of its transition to a stationary localized state is tracked. In the one-dimensional case this problem can be solved exactly in all of time, starting with the atomic scale. The final dependence is found to be quite simple and reflects some new features of one-dimensional localization. The ensuing physical properties of the observable quantities are indicated. In the case of systems of large dimensionality, the spreading is discussed within the framework of perturbation theory and of the Mott description of the resonance states.

Probing Anderson localization using the dynamics of a qubit

2017

Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a given energy or frequency. Here we show that this decay affects the dynamics of a qubit coupled to the disordered system and we express the relaxation rate of the qubit in terms of the localization properties. Conversely, adding static disorder to a channel coupled to a qubit will reduce the decoherence rate of the qubit. Hence, when designing electrodes that couple to qubits, it is possible to improve their performance by adding impurities to the channel.

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

Journal of Modern Optics, 2000

We investigate single ions of 40Ca+^{40}Ca^+40Ca+ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state ∣n=0>|n=0>∣n=0>, we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190 ms. We also report on ground state cooling of two ions.

Quantum theory of heating of a single trapped ion

The heating of trapped ions due to the interaction with a quantized environment is studied without performing the Born-Markov approximation. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method.