Techniques for engineering quantum states

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.

Inline holographic coherent anti-Stokes Raman microscopy.

We demonstrate a simple approach for inline holographic coherent anti-Stokes Raman scattering (CARS) microscopy, in which a layer of uniform nonlinear medium is placed in front of a specimen to be imaged. The reference wave created by four-wave mixing in the nonlinear medium can interfere with the CARS signal generated in the specimen to result in an inline hologram. We experimentally and theoretically investigate the inline CARS holography and show that it has chemical selectivity and can allow for three-dimensional imaging.

Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system

Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light. © 2010 The American Physical Society.

Genuine multipartite nonlocality of entangled thermal states

We assess quantum nonlocality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger, W, and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditions. This opens up the possibility for coherent exploitation of multipartite quantum channels made out of entangled thermal states. Our study is accompanied by a detailed description of possible generation schemes for the states analyzed.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Coherent and stochastic contributions of compound resonances in atomic processes: Electron recombination, photoionization, and scattering

In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering, and recombination are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination or photon Raman scattering) are dominated by the stochastic contributions. Thus, the optical theorem provides a link between the stochastic and coherent contributions of the compound resonances. Similar conclusions are valid for reactions via compound states in molecules and nuclei.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

The Taylor rule under inquiry: Hidden states

This work empirically evaluates the Taylor rule for the US and Brazil using Markov-Switching Regimes. I find that the inflation parameter of the US Taylor rule is less than one in many periods, contrasting heavily with Clarida, Gal´ı and Gertler (2000), and the same happens with Brazilian data. When the inflation parameter is greater than one, it encompasses periods that these authors considered they should be less than one. Brazil is used for comparative purposes because it experienced a high level inflation until 1994 and then a major stabilization plan reduced the growth in prices to civilized levels. Thus, it is a natural laboratory to test theories designed to work in any environment. The findings point to a theoretical gap that deserves further investigation and show that monetary policy in Brazil has been ineffective, which is coherent with the general attitude of population in relation to this measure.

Leadership of portuguese community schools in the East Coast of the United States and the public policies of education: a multiple case studies

The Portuguese community schools of the United States located in the areas of larger Portuguese population concentration are social organizations that come materializing throughout decades the designs of the educative policies of the Portuguese government in relation to the expansion and preservation of the language, the culture and the history of Portugal. These designs of the educative policies are enrolled in the Constitution of the Republic (1976), in the Basic Law of Educative System (1986) and, over all, in the successive legislative norms (Decree-laws and ordinances) of the successive governments. Portuguese community schools in the United States are structuralized in analogous way to schools of the Portuguese geographic space. For this qualitative study (multiple case), four directors of Portuguese schools of the East Coast of the United States were interviewed; two schools are in the state of Rhode Island and the other two are in the state of Massachusetts. Also, it was administered the questionnaire on practices of leadership “Leadership Practices Inventory” (LPI) of Kouzes and Posner (2002) to collect additional data about practices of leadership on the directors of the schools. The LPI evaluates practices of leadership classifying them in five domains: (a) Model the way; (b) Inspire a shared vision; (c) Challenge the process; (d) Enable others to act; and, (e) Encourage the heart. Results of this qualitative research indicate that the Portuguese Government has not had an educative policy stimulant, coherent and consistent of support, incentive, maintenance and diffusion of the Portuguese language and culture and the directors of the studied schools they have a proactive and serving leadership style in conducting the management of Portuguese community schools. The five practices of leadership are highly practiced by the directors of the studied schools above all the practices “Enable others to act” and “Encourage the heart”.

Towards coherent optical control of a single hole spin: Rabi rotation of a trion conditional on the spin state of the hole

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Coherent properties and Rabi oscillations in two-level donor systems

Coherent properties and Rabi oscillations in two-level donor systems, under terahertz excitation, are theoretically investigated. Here we are concerned with donor states in bulk GaAs and GaAs-(Ga,Al)As quantum dots. We study confinement effects, in the presence of an applied magnetic field, on the electronic and on-center donor states in GaAs- (Ga,Al)As dots, as compared to the situation in bulk GaAs, and estimate some of the associated decay rate parameters. Using the optical Bloch equations with damping, we study the time evolution of the Is and 2p(+) states in the presence of an applied magnetic field and of a terahertz laser. We also discuss the role played by the distinct dephasing rates on the photocurrent and calculate the electric dipole transition moment. Results indicate that the Rabi oscillations are more robust as the total dephasing rate diminishes, corresponding to a favorable coherence time.

Spin coherence generation in negatively charged self-assembled (In,Ga)As quantum dots by pumping excited trion states

Spin coherence generation in an ensemble of negatively charged (In,Ga)As/GaAs quantum dots was investigated by picosecond time-resolved pump-probe spectroscopy measuring ellipticity. Robust coherence of the ground-state electron spins is generated by pumping excited charged exciton (trion) states. The phase of the coherent state, as evidenced by the spin ensemble precession about an external magnetic field, varies relative to spin coherence generation resonant with the ground state. The phase variation depends on the pump photon energy. It is determined by (a) pumping dominantly either singlet or triplet excited states, leading to a phase inversion, and (b) the subsequent carrier relaxation into the ground states. From the dependence of the precession phase and the measured g factors, information about the quantum dot shell splitting and the exchange energy splitting between triplet and singlet states can be extracted in the ensemble.

Magneto-optical probe of quantum Hall states in a wide parabolic well modulated by random potential

Polarized photoluminescence from weakly coupled random multiple well quasi-three-dimensional electron system is studied in the regime of the integer quantum Hall effect. Two quantum Hall ferromagnetic ground states assigned to the uncorrelated miniband quantum Hall state and to the spontaneous interwell phase coherent dimer quantum Hall state are observed. Photoluminescence associated with these states exhibits features caused by finite-size skyrmions: dramatic reduction of the electron spin polarization when the magnetic field is increased past the filling factor nu = 1. The effective skyrmion size is larger than in two-dimensional electron systems.

Constructing correlated spin states with neutral atoms in optical lattices

This thesis reports on the experimental investigation of controlled spin dependent interactions in a sample of ultracold Rubidium atoms trapped in a periodic optical potential. In such a situation, the most basic interaction between only two atoms at one common potential well, forming a micro laboratory for this atom pair, can be investigated. Spin dependent interactions between the atoms can lead to an intriguing time evolution of the system. In this work, we present two examples of such spin interaction induced dynamics. First, we have been able to observe and control a coherent spin changing interaction. Second, we have achieved to examine and manipulate an interaction induced time evolution of the relative phase of a spin 1/2-system, both in the case of particle pairs and in the more general case of N interacting particles. The first part of this thesis elucidates the spin-changing interaction mechanism underlying many fascinating effects resulting from interacting spins at ultracold temperatures. This process changes the spin states of two colliding particles, while preserving total magnetization. If initial and final states have almost equal energy, this process is resonant and leads to large amplitude oscillations between different spin states. The measured coupling parameters of such a process allow to precisely infer atomic scattering length differences, that e.g. determine the nature of the magnetic ground state of the hyperfine states in Rubidium. Moreover, a method to tune the spin oscillations at will based on the AC-Zeeman effect has been implemented. This allowed us to use resonant spin changing collisions as a quantitative and non-destructive particle pair probe in the optical lattice. This led to a series of experiments shedding light on the Bosonic superfluid to Mott insulator transition. In a second series of experiments we have been able to coherently manipulate the interaction induced time evolution of the relative phase in an ensemble of spin 1/2-systems. For two particles, interactions can lead to an entanglement oscillation of the particle pair. For the general case of N interacting particles, the ideal time evolution leads to the creation of spin squeezed states and even Schrödinger cat states. In the experiment we have been able to control the underlying interactions by a Feshbach resonance. For particle pairs we could directly observe the entanglement oscillations. For the many particle case we have been able to observe and reverse the interaction induced dispersion of the relative phase. The presented results demonstrate how correlated spin states can be engineered through control of atomic interactions. Moreover, the results point towards the possibility to simulate quantum magnetism phenomena with ultracold atoms in optical traps, and to realize and analyze many novel quantum spin states which have not been experimentally realized so far.