Giant Kerr nonlinearity induced by interacting dark resonances

A scheme for giant enhancement of the Kerr nonlinearity in a four-level system with double dark resonances is proposed. Compared with that generated in a single-dark-resonance system, the Kerr nonlinearity can be enhanced by several orders of magnitude with vanishing linear absorption. We attribute this dramatic enhancement to the interaction of dark resonances. (c) 2005 Optical Society of America.

High efficiency four-wave mixing induced by double-dark resonances in a five-level tripod system

A five-level tripod scheme is proposed for obtaining a high efficiency four-wave-mixing (FWM) process. The existence of double-dark resonances leads to a strong modification of the absorption and dispersion properties against a pump wave at two transparency windows. We show that both of them can be used to open the four-wave mixing channel and produce efficient mixing waves. In particular, higher FWM efficiency is always produced at the transparent window corresponding to the relatively weak-coupling field. By manipulating the intensity of the two coupling fields, the conversion efficiency of FWM can be controlled.

Wetlands and coastal water quality: Should wetland size matter?

Generally, wetlands are thought to perform water purification functions, removing contaminants as water flows through sediment and vegetation. This paradigm was challenged when Grant et al. (2001) reported that Talbert Salt Marsh (Figure 1.) increased fecal indicator bacteria (FIB) output to coastal waters, contributing to poor coastal water quality. Like most southern California wetlands, Talbert Salt Marsh has been severely degraded. It is a small (10 ha), restored wetland, only 1/100th its original size, and located at the base of a highly urbanized watershed. Is it reasonable to expect that this or any severely altered wetland will perform the same water purification benefits as a natural wetland? To determine how a more pristine southern California coastal wetland attenuated bacterial contaminants, we investigated FIB concentrations entering and exiting Carpinteria Salt Marsh (Figure 2.), a 93 ha, moderate-sized, relatively natural wetland.(PDF contains 4 pages)

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Controllable atom localization via double-dark resonances in a tripod system

We propose an atom localization scheme for a tripod-type atom making use of the sharp absorption peak resulting from interacting double-dark resonances. It is demonstrated that the probability of finding the atom at a particular position, as well as the localization precision, can be dramatically enhanced. The probability can be doubled by adjusting the Rabi frequency of the control field to the maximum Rabi frequency of the standing-wave field. Moreover, much better spatial resolution can be achieved for smaller detunings of the control and the standing-wave fields. (c) 2006 Optical Society of America.

Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice

In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Atom localization via interference of dark resonances

A scheme of atom localization based on the interference of resonance of double-dark states is proposed, in which the atom interacts with a classical standing-wave field. It is found that the localization property is significantly improved due to the interaction of double-dark resonances. It is realized that the atom is localized just at the nodes of the standing-wave field with higher precision. Moreover, an improvement by a factor of 2 in the detecting probability of a single atom within the subwavelength domain can be achieved by adjusting the probe-field detuning. This scheme shows more advantages than other schemes of atom localization.

The search for gravitational waves from the coalescence of black hole binary systems in data from the LIGO and Virgo detectors. Or: A dark walk through a random forest

The LIGO and Virgo gravitational-wave observatories are complex and extremely sensitive strain detectors that can be used to search for a wide variety of gravitational waves from astrophysical and cosmological sources. In this thesis, I motivate the search for the gravitational wave signals from coalescing black hole binary systems with total mass between 25 and 100 solar masses. The mechanisms for formation of such systems are not well-understood, and we do not have many observational constraints on the parameters that guide the formation scenarios. Detection of gravitational waves from such systems — or, in the absence of detection, the tightening of upper limits on the rate of such coalescences — will provide valuable information that can inform the astrophysics of the formation of these systems. I review the search for these systems and place upper limits on the rate of black hole binary coalescences with total mass between 25 and 100 solar masses. I then show how the sensitivity of this search can be improved by up to 40% by the the application of the multivariate statistical classifier known as a random forest of bagged decision trees to more effectively discriminate between signal and non-Gaussian instrumental noise. I also discuss the use of this classifier in the search for the ringdown signal from the merger of two black holes with total mass between 50 and 450 solar masses and present upper limits. I also apply multivariate statistical classifiers to the problem of quantifying the non-Gaussianity of LIGO data. Despite these improvements, no gravitational-wave signals have been detected in LIGO data so far. However, the use of multivariate statistical classification can significantly improve the sensitivity of the Advanced LIGO detectors to such signals.

Pathways for the uptake of dissolved organic matter (DOM) by aquatic animals

In this article, pathways from freshwater and marine environments are described. DOM is defined operationally as all the organic compounds which pass through a filter of pore size 0.45 microm., those retained on the surface of the filter being particulate organic matter (POM). DOM can be taken up directly by animals by transfer across the body wall, but more commonly DOM is obtained from ingested food. Once ingested POM from food particles are broken down in the gut, small molecules of DOM are released for transfer across the gut wall. Some ingested particles are attacked by micro-organisms living in the gut, thereby making the DOM available to the host animal. The importance of the microbial loop is discussed, as well as aggregation processes between the fractions of DOM which are more obviously particulate in nature. (DBO)

Temperature, organic matter and the sustainability of aquatic systems

Changes in sustainability of aquatic ecosystems are likely to be brought about by the global warming that has been widely predicted. In this article, the effects of water temperature on water-bodies (lakes, oceans and rivers) are reviewed followed by the effects of temperature on aquatic organisms. Almost all aquatic organisms require exogenous heat before they can metabolise efficiently. An organism that is adapted to warm temperatures will have a higher rate of metabolism of food organisms and this increases feeding rate. In addition, an increase in temperature raises the metabolism of food organisms, so food quality can be altered. Where populations have a different tolerance to temperature the result is habitat partitioning. One effect of prolonged high temperature is that it causes water to evaporate readily. In the marine littoral this is not an important problem as tides will replenish water in pools. Small rain pools are found in many tropical countries during the rainy season and these become incompletely dried at intervals. The biota of such pools must have resistant stages within the life cycle that enable them to cope with periods of drying. The most important potential effects of global warming include (i) the alteration of existing coastlines, (ii) the development of more deserts on some land masses, (iii) higher productivity producing higher crop production but a greater threat of algal blooms and (iv) the processing of organic matter at surface microlayers.

Quantum superchemistry in an output coupler of coherent matter waves

We investigate the quantum superchemistry or Bose-enhanced atom-molecule conversions in a coherent output coupler of matter waves, as a simple generalization of the two-color photoassociation. The stimulated effects of molecular output step and atomic revivals are exhibited by steering the rf output couplings. The quantum noise-induced molecular damping occurs near a total conversion in a levitation trap. This suggests a feasible two-trap scheme to make a stable coherent molecular beam.

Temperature dependence of dark lines in coherent population trapping

We measure the signal amplitude and linewidth of a dark line in coherent population trapping in the Rb vapour cell filled with mixed buffer gas N-2 and Ar as a function of cell temperature. We find that the dark line signal amplitude increases with temperature up to a maximum at 49 degrees C and then drops at higher temperatures due to quenching effects of N-2. The linewidth of the dark line remains basically constant, at 1080 Hz. We also measure the linewidth of the dark line as a function of laser intensity. The linewidth increases linearly with laser intensity. An intrinsic linewidth (FWHM=896 Hz at 3.4 GHz) of the Rb cell is obtained.

A movable-cavity cold atom space clock

We present an experimental scheme of a cold atom space clock with a movable cavity. By using a single microwave cavity, we find that the clock has a significant advantage, i.e. the longitudinal cavity phase shift is eliminated. A theoretical analysis has been carried out in terms of the relation between the atomic transition probability and the velocity of the moving cavity by taking into account the velocity distribution of cold atoms. The requirements for the microwave power and its stability for atomic pi/2 excitation at different moving velocities of the cavity lead to the determination of the proper working parameters of the rubidium clock in frequency accuracy 10(-17). Finally, the mechanical stability for the scheme is analysed and the ways of solving the possible mechanical instability of the device are proposed.