Thesis (M. S.)--Physics, Georgia Institute of Technology, 2010. / Committee Chair: Kennedy, Brian; Committee Member: Chapman, Michael; Committee Member: Zangwill, Andrew. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Among the many examples of Bose condensation considered in physics, electron-hole-pair (exciton) condensation has maintained special interest because it has been difficult to realize experimentally, and because of controversy about condensate properties. In this thesis, we studied the various aspects of spontaneous symmetry broken state of exciton in bilayer using mean field theory. We calculated the photoluminescence of excitonic condensation created by laser. We developed a one-dimensional toy model of excitonic supercurrent using mean field theory plus non-equilibrium Green’s function (NEGF) which give qualitatively consistent results with experiments. We proposed graphene bilayer as a novel system for excitonic condensation to occur and estimate it to exist even at temperature as high as room temperature. / text

In this dissertation, the applications of many-body physics in neutral bosons and electronic systems in transition metal oxides are discussed. In the first part of the thesis, I will introduce the concepts of Bose condensation, emphasize the significance of the order parameter in superfluids (macroscopic wave function), and its consequence such as the emergence of exotic vortex states under rotation. Dated back to the importance of the vortex dynamics in the properties of high T[subscript c] superconductors, people have introduced a dual vortex description to describe the dynamics of charged bosons in a magnetic field. Similarly, the dual description is adapted to the problems of neutral bosons under rotation. Based on that picture, vortices behave like charges in an effective magnetic field which has been known to demonstrate different quantum phases such as Wigner crystal phase, and fractional quantum Hall liquid phases depending on the relative fraction of the number of bosons and vortices. In this work, we would like to address the validity of the picture by low energy effective theory. We can identify the origin of the vortex masse and the parameter regimes in which the vortex dual description is appropriate. In the second part of the dissertation, density functional theory is used to describe the strongly correlated matters with local density approximation and local Hubbard U interaction(LDA+U). We are particularly interested in the interface states in the heterojunction systems of two different perovskite oxides. What we found is that the interface states can be engineered to appear in certain transitional metal oxide layers by controlling the number of positive and negative charged layers, leading to the formation of quantum wells in two dimension. This type of systems ignite the hope to search for broken symmetry states in the interface which can be tunable with chemical doping or electric field doping. Even room temperature superconducting state may or may not exist in the interface is still an intriguing issue. / text

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

An apparatus for producing atomic-gas Bose-Einstein condensates (BECs) of 87-Rb atoms is described. The apparatus produces 87-Rb BECs in a dual-chamber vacuumsystem that incorporates magnetic transport of trapped atoms from the magneto-optical trapping cell to the BEC production cell via the operation of a series of overlapping magnet coils. The design, construction, and operation of the apparatus are described in detail.The apparatus is used to study the creation of quantized vortices in BECs by the merging and interference of multiple trapped condensates. In this experiment, a single harmonic potential well is partitioned into three sections by an optical barrier,enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either merge together during their growth, or, for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.

Cooperative effects in many-particle systems can be exploited to achieve measurement outcomes not possible with independent probe particles. We explore two measurement applications based on the cooperative phenomenon of superradiance or on correlated quantum states closely related to superradiance. In the first application we study the off-resonant superradiant Raman scattering of light from an ultracold Bose atomic vapor. We investigate the temperature dependence of superradiance for a trapped vapor and show that in the regime where superradiance occurs on a timescale comparable to a trap frequency, scattering takes place preferentially from atoms in the lowest trap levels due to Doppler dephasing. As a consequence, below the critical temperature for Bose condensation, absorption images of transmitted light serve as a direct probe of the condensed state. Subsequently, we consider a pure condensate and study the time-dependent spatial features of transmitted light, obtaining good qualitative agreement with recent imaging experiments. Inclusion of quantum fluctuations in the initial stages of the superradiant emission accounts well for shot-to-shot fluctuations. Secondly, we have used simulated annealing, a global optimization strategy, to systematically search for correlated quantum interferometer input states that approach the Heisenberg limited uncertainty in estimates of the interferometer phase shift. That limit improves over the standard quantum limit to the phase sensitivity of interferometric measurements by a factor of 1√N, where N is the number of interfering particles. We compare the performance of these states to that of other non-classical states already known to yield Heisenberg limited uncertainty.

Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.

We have obtained spectra of 10 vibrational bands of the Cs₂ (2)³∏_u ← ϰ³∑⁺₉ system. The molecules were formed in a supersonic free jet expansion, and were excited by light from a single mode CW dye laser. The total laser induced fluorescence was measured at 90° to the incident light and molecular beam, using a photomultiplier. Using a slit system to image a selected part of the interaction region, we have reduced the Doppler width to about 350MHz. We have been able to resolve the discrepancy between the different vibrational band positions given in two previous papers. Our vibrational bands show broad rotational contours, but we have not been able to resolve individual rotational lines. We have also obtained rotationally resolved spectra of the bandhead region of 22 vibrational bands of the Β¹∏₉ ← X¹∑⁺_u system. We found that the frequencies of the bandheads agreed with the bandhead positions deduced from the Dunham coefficients of a previous work. We have developed a theoretical model of the rotational structure and intensity distribution, taking into account optical pumping and the small solid angle subtended by the detector. By fitting this model to the experimental spectrum of the v' = 3,u∿ = 0 band using least squares optimization, we were able to extract rotational constants and line positions. We found that these line positions were in good agreement with those from the previous work. We have discussed how such spectroscopic data may be used in a determination of the s-wave scattering length of caesium, and we have reviewed the validity of the scattering length and other pararneterisations of low energy Cs-Cs interactions.

The Double-TOP trap is a new type of magnetic trap for neutral atoms, and is suitable for Bose-Einstein condensates (BECs) and evaporatively cooled atoms. It combines features from two other magnetic traps, the Time-averaged Orbiting Potential (TOP) and Ioffe-Pritchard traps, so that a potential barrier can be raised in an otherwise parabolic potential. The cigar-like cloud of atoms (in the single-well configuration) is divided halfway along its length when the barrier is lifted. A theoretical model of the trap is presented. The double-well is characterised by the barrier height and well separation, which are weakly coupled. The accessible parameter space is found by considering experimental limits such as noise, yielding well separations from 230 [mu]m up to several millimetres, and barrier heights from 65 pK to 28 [mu]K (where the energies are scaled by Boltzmann�s constant). Potential experiments for Bose-Einstein condensates in this trap are considered. A Double-TOP trap has been constructed using the 3-coil style of Ioffe-Pritchard trap. Details of the design, construction and current control for these coils are given. Experiments on splitting thermal clouds were carried out, which revealed a tilt in the potential. Two independent BECs were simultaneously created by applying evaporative cooling to a divided thermal cloud. The Double-TOP trap is used to form a linear collider, allowing direct imaging of the interference between the s and d partial waves. By jumping from a double to single-well trap configuration, two ultra-cold clouds are launched towards a collision at the trap bottom. The available collision energies are centred on a d-wave shape resonance so that interference between the s and d partial waves is pronounced. Absorption imaging allows complete scattering information to be collected, and the images show a striking change in the angular distribution of atoms post-collision. The results are compared to a theoretical model, verifying that the technique is a useful new way to study cold collisions.

Grand-canonical inverse-temperature calculations of a single mode Bose-Hubbard model are presented, using the Gaussian phase space representation. Simulation of 100 particles is achieved in the ground state, having started with a low-particle-number thermal state. A preliminary foray into a three-mode lattice is made, but the sampling error appears to be too large for the simple approach taken here to be successful in larger systems. The quantum (real-time) dynamics of a one-dimensional Bose gas with two-particle losses are investigated. The Positive-P equations for this system are unstable, and this causes Positive-P simulations to `die' after a certain amount of time. Gauges are used to (sometimes partially) stabilise the equations. The effects on simulation times of various gauges, branching methods, and non-square diffusion matrix factorisations on simulation times are investigated. Despite the absence of repulsive inter-particle interactions, it is observed that $g^{(2)}$ rises above 1 at a finite particle separation. A phase space method for spin systems is introduced, based on SU(2) coherent states. This is essentially a spin analogue of the Positive-P method. The system of stochastic differential equations arising out of this method require weighted averages to be taken, and the weights can vary exponentially, leading to inefficient sampling. For the case of the Ising model, a transform is made to a set of equations which relaxes (in a dummy time variable) to the partition function at a given temperature, and allows unweighted ensemble averages to be taken. This allows accurate simulations to be achieved at a range of temperatures, with nearest-neighbour correlation functions agreeing with theory. This represents a proof of principle for the use of stochastic phase space methods in spin systems, and furthermore the method should be suited to open spin systems, at least for a small number of qubits.