In this work, we theoretically analyze the behavior of a Bose-Einstein condensate when it is submitted to oscillatory interactions. For that, a homogeneous magnetic field is applied, tuned near a Feshbach resonance, and then it is set to oscillate in time. This variation of the magnetic field causes a scattering length oscillation, which oscillates to interatomic interaction. Thus, we study collective and topological excitations due this oscillation in the interaction. In addition, we have seen a coupling between collective modes as well a dynamical phase transition associated to topological excitation / Neste trabalho, analisamos teoricamente o comportamento de um condensado de Bose-Einstein quando submetido a interações oscilatórias. Para tal, é aplicado um campo magnético homogêneo, sintonizado próximo a uma ressonância de Feshbach e então colocado a oscilar no tempo. Esta variação do campo magnético faz com que o comprimento de espalhamento oscile, oscilando portanto a interação entre os átomos. Com isso, estudamos as excitações coletivas e topológicas provocadas devido a oscilação da interação. Além disso, vimos o acoplamento entre modos coletivos e uma transição de fase dinâmica associada a excitação topológica

The two-particle correlation function is measured for neutral current DIS events with 5 < Q2 < 100 GeV2 with data taken by the H1 detector at HERA with -vFs = 300 GeV during the 1994 run period corresponding to an integrated luminosity of 1.3 pb-1. The diffractive and non-diffractive selections of the data are analysed separately, and both exhibit an enhanced correlation for small 4-momentum difference for like-sign pairs as expected from Bose-Einstein interference in the production amplitudes for identical boson pairs. Fits using a Gaussian parametrisation of the enhancement yield no statistically significant difference between the diffractive and non-diffractive samples. The non-diffractive data sample is further separately analysed in three bins of each of the kinematic variables x, Q2, and W as well as mean particle density, (dn/dry*), in the hadronic centre of mass frame. Of these a strong evolution of the Gaussian fit parameters is observed with increasing particle density only. The non-diffractive data are also compared to three fit parameterisations: Gaussian, exponential, and power-law. The most favourable X2 is obtained for the exponential fit, though the power-law attains a similarly successful description of the data in the region of low 4-momentum difference.

Ma, Kwok Wai = 相互作用的超冷原子於一維系統之有關課題 / 馬國威. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 69-74). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Ma, Kwok Wai = Xiang hu zuo yong de chao leng yuan zi yu yi wei xi tong zhi you guan ke ti / Ma Guowei.

An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.

Turbulence is a young field of research which is characterized by chaotic spinning flow regimes which appears in many important processes in nature. Vorticity, in superfluid systems, may present the simplest form of turbulence, and be a gateway to the study of this phenomenon in quantum gases. A 87Rb Bose condensate was used to observe and investigate the emergence of quantum turbulence, a few years back in our group. The vortices are created on the condensed-thermal interface and propagate across the cloud, setting up the experimental conditions favorable to the emergence of turbulence. Once the turbulent regime is set, the condensate is released and expands under free fall. Then, the atomic density profile is acquired, after some time-of-flight, and used to determine the in situ momentum distribution of the BEC. In this work, we have observed that, the perturbed density profiles are characteristic and different from the standard, non-perturbed ones. We have seen evidences of power law in the studied momentum and energy distributions and also coupling of quadrupolar mode to the momentum distribution of the excited condensate which is the main part of our findings. Additional features of the system, such as the condensates excited collective modes which plays a very important role on the roadmap to the turbulence regime, are discussed. We are currently setting up an experiment to be able to further investigate such features, and also to unfold the effects of interactions on the energy and momentum spectra associated to the density profiles. In doing so, we will further develop the tools and techniques needed to acquire more accurate and reliable results. / Um dos tópicos recentes das pesquisas em superfluidos atômicos é o estudo da turbulência quântica. Em fluídos, a turbulência é caracterizada pelo regime caótico no escoamento dos fluidos e aparece em muitos importantes processos na natureza. Em sistemas superfluidos, a forma mais simples da turbulência é apresentada pelo enovelamento de vórtices. Assim, o estudo de vórtices nesses sistemas torna-se um ponto de partida para estudar o fenômeno da turbulência em gases quânticos. Há alguns anos atrás, em nosso grupo de pesquisa, um condensado de Bose-Einstein de 87Rb foi usado para observar e investigar a emergência de turbulência quântica. Em continuidade a esses estudos, aplicamos uma excitação oscilatória na nuvem atômica aprisionada e os vórtices são criados na interface entre o condensado e a nuvem térmica, que se propagam para o interior da nuvem, atingindo as condições ideais para o aparecimento de um regime turbulento. Uma vez que esse regime é atingido, o condensado é diagnosticado através de uma imagem de absorção obtida após a sua expansão balística em tempo de voo. O perfil de densidade obtido é usado para determinar a distribuição de momento do condensado aprisionado. Neste trabalho, observamos que os perfis de densidade dos condensados excitados possuem uma forma característica e diferente dos condensados não-excitados. Nos estudos da distribuição de momento e energia dessas nuvens excitadas, vimos uma evidência de uma lei de potência (parecida com a lei de Kolmogorov para turbulência) e, além disso, um acoplamento entre o modo quadrupolar de oscilação da nuvem e a distribuição de momentos dessa nuvem. Também discutimos algumas propriedades adicionais do sistema, por exemplo, os modos coletivos de excitação do condensado, o que tem um papel muito importante na rota para o regime de turbulência quântica. Para continuarmos com os estudos neste tópico de pesquisa, estamos melhorando nosso sistema experimental a fim de investigarmos melhor estas propriedades dinâmicas do superfluido, através dos efeitos dos modos coletivos no espectro de momentos da nuvem atômica. Para isso, pretendemos desenvolver novas técnicas e ferramentas necessárias para realizar medidas mais precisas e reprodutivas.

Orientador: Antonio José Accioly / Mestre

In this work, we theoretically analyze the behavior of a Bose-Einstein condensate when it is submitted to oscillatory interactions. For that, a homogeneous magnetic field is applied, tuned near a Feshbach resonance, and then it is set to oscillate in time. This variation of the magnetic field causes a scattering length oscillation, which oscillates to interatomic interaction. Thus, we study collective and topological excitations due this oscillation in the interaction. In addition, we have seen a coupling between collective modes as well a dynamical phase transition associated to topological excitation / Neste trabalho, analisamos teoricamente o comportamento de um condensado de Bose-Einstein quando submetido a interações oscilatórias. Para tal, é aplicado um campo magnético homogêneo, sintonizado próximo a uma ressonância de Feshbach e então colocado a oscilar no tempo. Esta variação do campo magnético faz com que o comprimento de espalhamento oscile, oscilando portanto a interação entre os átomos. Com isso, estudamos as excitações coletivas e topológicas provocadas devido a oscilação da interação. Além disso, vimos o acoplamento entre modos coletivos e uma transição de fase dinâmica associada a excitação topológica

Liu, Xiaopi = 光格子势中玻色爱因斯坦凝聚体的压缩,纠缠与激发谱 / 刘小披. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 97-100). / Abstracts in English and Chinese. / Liu, Xiaopi = Guang ge zi shi zhong bo se ai yin si tan ning ju ti de ya suo, jiu chan yu ji fa pu / Liu Xiaopi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Review of Superfluidity and B.E. Condensation --- p.1 / Chapter 1.2 --- Our Understanding of superfluidity --- p.4 / Chapter 1.3 --- Non-classicality in Quantum Mechanics --- p.8 / Chapter 2 --- One-Component BECs in optical lattices --- p.16 / Chapter 2.1 --- Introduction: The Hamiltonian --- p.16 / Chapter 2.2 --- The Hamiltonian in Quasi-momentum space --- p.19 / Chapter 2.3 --- Bogoliubov Method and Equation of Motion --- p.21 / Chapter 2.3.1 --- Squeezing and Condensation --- p.27 / Chapter 2.3.2 --- Two-mode Entanglement and Squeezing --- p.31 / Chapter 3 --- Matrix method approach to ground state BECs --- p.39 / Chapter 3.1 --- Matrix method --- p.39 / Chapter 3.2 --- Ground state and Particle Distribution --- p.42 / Chapter 3.3 --- Correlation in Pair Ground State --- p.46 / Chapter 4 --- Attractive BECs in optical lattices --- p.50 / Chapter 5 --- 2-component BECs in optical lattice --- p.56 / Chapter 5.1 --- Model Hamiltonian --- p.56 / Chapter 5.2 --- Excitation Spectrum and Critical super-fluid velocity --- p.59 / Chapter 5.3 --- Excitation spectrum and Phase Separation Dynamics --- p.63 / Chapter 5.4 --- Excitation Spectrum for Asymmetric 2-component BECs --- p.67 / Chapter 6 --- Multi-Mode Squeezing of 2-component BECs in optical lattices --- p.69 / Chapter 6.1 --- Simultaneous Diagonalization --- p.69 / Chapter 6.2 --- Equation of Motion and Variance Matrix --- p.70 / Chapter 6.3 --- U(n) Squeezing of Variance Matrix --- p.75 / Chapter 6.4 --- Squeezing in the case qA≠ qB and nA≠ nB --- p.82 / Chapter 7 --- Entanglement between 2-component BECs in optical lattices --- p.83 / Chapter 7.1 --- Variance matrix in block diagonal --- p.83 / Chapter 7.2 --- 2-component entangled variance matrix --- p.86 / Chapter 7.3 --- Logarithmic negativity --- p.89 / Chapter 7.4 --- Beat oscillation mode of logarithmic negativity --- p.91 / Chapter 8 --- Conclusion and Outlook --- p.95 / Bibliography --- p.97

The experimental realisation of Bose-Einstein condensation in 1995 opened up a wealth of opportunities for probing quantum states of matter. The development of many tools used to manipulate such ultracold samples and the rapid progress on understanding these systems will ultimately lead to great technological advances. The work described in this thesis contributes to this worldwide effort and here we present experiments which investigate the properties and behaviour of ultracold atoms. In the first experiments presented here, we have studied features of Bose-Einstein condensates loaded into an optical lattice formed by the interference of two laser beams. By altering the phase of the lattice at the Bragg condition, we investigate the effect of the phase shift on the dressed-atom states. We find that by applying a +(-)[pi]/2 phase shift after a [pi]/2 (3[pi]/2) lattice pulse, we are able to quickly and precisely load the ground and first excited eigenstates of the lattice. In another experiment, we use a periodically pulsed stationary optical lattice and a tightly-confined Bose-Einstein condensate to investigate the nonlinear kicked harmonic oscillator at quantum anti-resonance. We observe periodic behaviour in the energy of the condensate, however we show that the nonlinearity is not strong enough to enter the predicted chaotic regime. In addition, the amplitude of the energy oscillations damps to an average value and we relate this to dephasing of the coupling across the finite momentum width of the condensate. In the second series of experiments, we use a double-well magnetic collider to investigate cold collisions between ultracold atoms. By creating two ultracold clouds in a double-well magnetic trap and then transforming the trap to a single well, we accelerate the clouds together to initiate a collision between them. We describe in detail the analysis method that we use to extract the partial-wave phase shifts from the matter-wave interference patterns associated with the scattered atoms. We then implement a two-photon pulse, which is applied prior to the collision to convert one of the clouds to a different spin state. This enables the study of scattering between distinguishable states which exhibited anti-symmetric p-wave scattering via the interference with the s- and d-waves previously observed for indistinguishable states. We find the position of the d-wave shape resonance and compare our data to a coupled-channels model.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.