Entanglement and boundary critical phenomena

We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S-alpha, which includes the von Neumann entropy (alpha -> 1) and the single-copy entanglement (alpha ->infinity) as special cases. We identify the contribution of the boundaries to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g theorem, is a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.

Coexistence of spin polarization and pairing correlations in metallic grains

We investigate the competition between magnetic depairing interactions, due to spin-exchange mechanism and∕or to spin-dependent asymmetric bandwidths, and pairing coupling in metallic grains. We present a detailed analysis of the quantum ground state in different regimes arising from the interplay between ferromagnetic and pairing correlations for different fillings. We find out that the occurrence of a ground state with coexisting spin-polarization and pairing correlations is enhanced when the asymmetric spin-dependent distribution of the single-particle energies is considered. The mechanisms leading to such a stable quantum state are finally clarified.

Utilização de pulsos de radiofrequência fortemente modulados no processamento de informação quântica via ressonância magnética nuclear

Nesta dissertação apresentamos um trabalho de desenvolvimento e utilização de pulsos de radiofreqüência modulados simultaneamente em freqüência, amplitude e fase (pulsos fortemente modulados, SMP, do inglês Strongly Modulated Pulses) para criar estados iniciais e executar operações unitárias que servem como blocos básicos para processamento da informação quântica utilizando Ressonância Magnética Nuclear (RMN). As implementações experimentais foram realizas em um sistema de 3 q-bits constituído por spins nucleares de Césio 133 (spin nuclear 7/2) em uma amostra de cristal líquido em fase nemática. Os pulsos SMP´s foram construídos teoricamente utilizando um programa especialmente desenvolvido para esse fim, sendo o mesmo baseado no processo de otimização numérica Simplex Nelder-Mead. Através deste programa, os pulsos SMP foram otimizados de modo a executarem as operações lógicas desejadas com durações consideravelmente menores que aquelas realizadas usando o procedimento usual de RMN, ou seja, seqüências de pulsos e evoluções livres. Isso tem a vantagem de reduzir os efeitos de descoerência decorrentes da relaxação do sistema. Os conceitos teóricos envolvidos na criação dos SMPs são apresentados e as principais dificuldades (experimentais e teóricas) que podem surgir devido ao uso desses procedimentos são discutidas. Como exemplos de aplicação, foram produzidos os estados pseudo-puros usados como estados iniciais de operações lógicas em RMN, bem como operações lógicas que foram posteriormente aplicadas aos mesmos. Utilizando os SMP\'s também foi possível realizar experimentalmente os algoritmos quânticos de Grover e Deutsch-Jozsa para 3 q-bits. A fidelidade das implementações experimentais foi determinadas utilizando as matrizes densidade experimentais obtidas utilizando um método de tomografia da matriz densidade previamente desenvolvido.

DEVELOPMENT OF A CONDENSED PHASE VELOCITY MAP IMAGING APPARATUS: DISSOCIATION PHOTODYNAMICS OF NITROGEN DIOXIDE AT 355 NM

The photochemistry of the polar regions of Earth, as well as the interstellar medium, is driven by the effect of ultraviolet radiation on ice surfaces and on the materials trapped within them. While the area of ice photochemistry is vast and much research has been completed, it has only recently been possible to study the dynamics of these processes on a microscopic level. One of the leading techniques for studying photoreaction dynamics is Velocity Map Imaging (VMI). This technique has been used extensively to study several types of reaction dynamics processes. Although the majority of these studies have utilized molecular beams as the main medium for reactants, new studies showed the versatility of the technique when applied to molecular dynamics of molecules adsorbed on metal surfaces. Herein the development of a velocity map imaging apparatus capable of studying the photochemistry of condensed phase materials is described. The apparatus is used to study of the photo-reactivity of NO2 condensed within argon matrices to illustrate its capabilities. A doped ice surface is formed by condensing Ar and NO2 gas onto a sapphire rod which is cooled using a helium compressor to 20 K. The matrix is irradiated using an Nd:YAG laser at 355 nm, and the resulting NO fragment is state-selectively ionized using an excimer-pumped dye laser. In all, we are able to detect transient photochemically generated species and can collect information on their quantum state and kinetic energy distribution. It is found that the REMPI spectra changes as different sections of the dissociating cloud are probed. The rotational and translational energy populations are found to be bimodal with a low temperature component roughly at the temperature of the matrix, and a second component with much higher temperature, the rotational temperature showing a possible population inversion, and the translational temperature of 100-200 K. The low temperature translational component is found to dominate at long delay times between dissociation and ionization, while at short time delays the high temperature component plays a larger role. The velocity map imaging technique allows for the detection of both the axial and radial components of the translational energy. The distribution of excess energy over the rotational, electronic and translational states of the NO photofragments provides evidence for collisional quenching of the fragments in the Ar-matrix prior to their desorption.

Non-equilibrium properties of trapped ions under sudden application of a laser

Coherent quantum-state manipulation of trapped ions using classical laser fields is a trademark of modern quantum technologies. In this work, we study aspects of work statistics and irreversibility in a single trapped ion due to sudden interaction with the impinging laser. This is clearly an out-of-equilibrium process where work is performed through illumination of an ion by the laser. Starting with the explicit evaluation of the first moments of the work distribution, we proceed to a careful analysis of irreversibility as quantified by the nonequilibrium lag. The treatment employed here is not restricted to the Lamb-Dicke limit, what allows us to investigate the interplay between nonlinearities and irreversibility. We show, for instance, that in the resolved carrier and sideband regimes, variation of the Lamb-Dicke parameter may cause a non-monotonic behavior of the irreversibility indicator. Counterintuitively, we find a working point where nonlinearity helps reversibility, making the sudden quench of the Hamiltonian closer to what would have been obtained quasistatically and isothermally.

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. Full information of the state of light can only be gathered by a tomographic measurement. Here we demonstrate a tomographic interferometer readout by measuring arbitrary quadratures of the light field exiting a Michelson-Sagnac interferometer that contains a thermally excited high-quality silicon nitride membrane. A readout noise of 1.9 x 10(-16) mHz(-1/2) around the membrane's fundamental oscillation mode at 133 kHz has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

The accuracy in determining the quantum state of a system depends on the type of measurement performed. Homodyne and heterodyne detection are the two main schemes in continuous-variable quantum information. The former leads to a direct reconstruction of the Wigner function of the state, whereas the latter samples its Husimi Q function. We experimentally demonstrate that heterodyne detection outperforms homodyne detection for almost all Gaussian states, the details of which depend on the squeezing strength and thermal noise.

Resistively detected NMR of the nu=1 quantum Hall state: A tilted magnetic field study

Previous resistively detected NMR (RDNMR) studies on the nu approximate to 1 quantum Hall state have reported a ""dispersionlike"" line shape and extremely short nuclear-spin-lattice relaxation times, observations which have been attributed to the formation of a skyrme lattice. Here we examine the evolution of the RDNMR line shape and nuclear-spin relaxation for Zeeman: Coulomb energy ratios ranging from 0.012 to 0.036. According to theory, suppression of the skyrme crystal, along with the associated Goldstone mode nuclear-spin-relaxation mechanism, is expected at the upper end of this range. However, we find that the anomalous line shape persists at high Zeeman energy, and only a modest decrease in the RDNMR-detected nuclear-spin-relaxation rate is observed.

Ground-state functional for quantum spin chains with bond defects

We have developed a nonlocal functional of the exchange interaction for the ground-state energy of quantum spin chains described by the Heisenberg Hamiltonian. An alternating chain is used to obtain the correlation energy and a local unit-cell approximation is defined in the context of the density-functional theory. The agreement with our exact numerical data, for small chains, is significantly better than a previous formulation, even for chains with several ferromagnetic or antiferromagnetic bond defects. The results can be particularly relevant in the study of finite spin-1/2 Heisenberg chains, with exchange couplings changing, magnitude, or even sign, from bond-to-bond.

Measurement and state preparation via ion trap quantum computing

We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'HELON and G. J. MILBURN, Phys Rev. A 54, 5141 (1996)]. The performance of a measurement shows some interesting patterns which are closely related to searching.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Ground-state self-consistent calculation of quantum dots under magnetic fields: Addition spectrum

A density-functional self-consistent calculation of the ground-state electronic density of quantum dots under an arbitrary magnetic field is performed. We consider a parabolic lateral confining potential. The addition energy, E(N+1)-E(N), where N is the number of electrons, is compared with experimental data and the different contributions to the energy are analyzed. The Hamiltonian is modeled by a density functional, which includes the exchange and correlation interactions and the local formation of Landau levels for different equilibrium spin populations. We obtain an analytical expression for the critical density under which spontaneous polarization, induced by the exchange interaction, takes place.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.