Phase Coherence Properties Research Articles

Quantum degeneracy and Bose–Einstein condensation in low-dimensional trapped gases

At present, there are significant efforts to create 2D or 1D trapped gases by (tightly) confining the particle motion to zero point oscillations in one or two directions. The goal of this article is to show that the reduction of the spatial dimensionality in trapped Bose gases drastically changes the nature of the Bose-condensed state. In 2D and 1D gases, one can get a peculiar Bose-condensed state (quasicondensate) where the density fluctuations are suppressed, but the phase still fluctuates. The quasicondensate has the same density profile and local correlation properties as true condensates. However, it is very different with regard to phase coherence properties. We discuss how the phase coherence can be studied in experiments with 2D and 1D trapped gases.

Josephson plasma resonance in Bi 2Sr 2CaCu 2O 8+ y crystals with macroscopic inhomogeneities

The Josephson plasma resonance (JPR) is studied in Bi 2Sr 2CaCu 2O 8+ y (BSCCO) crystals with macroscopic inhomogeneities, which are introduced by two methods; fabricating the crystal in the form having arrays of mesa structures (20×20 μm 2 ∼ 100×100 μm 2) or bu irradiating heavy-ions in half of the crystal. The JPR in BSCCO with mesa array shows an additional resonance peak indicating that the length scale where phase coherence is averaged is smaller than the size of the mesas. On the other hand, the resonance fields in the half-irradiated BSCCO and those after cutting the crystal into two are different, suggesting the presence of some kind of interference between regions which have different macroscopically averaged phase coherence properties.

Binary mixtures of Bose-Einstein condensates: Phase dynamics and spatial dynamics

We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles. Analytical results are presented for the breathe-together solution, an extension of previously known scaling solution to the case of a binary mixture of condensates. When the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other, a dramatic increase of the phase coherence time is predicted. Numerical results are presented for the parameters of the recent JILA experiments.

Measurement of the spatial coherence of a trapped Bose gas at the phase transition

The experimental realization of Bose-Einstein condensates of dilute gases has allowed investigations of fundamental concepts in quantum mechanics at ultra-low temperatures, such as wave-like behaviour and interference phenomena. The formation of an interference pattern depends fundamentally on the phase coherence of a system; the latter may be quantified by the spatial correlation function. Phase coherence over a long range is the essential factor underlying Bose-Einstein condensation and related macroscopic quantum phenomena, such as superconductivity and superfluidity. Here we report a direct measurement of the phase coherence properties of a weakly interacting Bose gas of rubidium atoms. Effectively, we create a double slit for magnetically trapped atoms using a radio wave field with two frequency components. The correlation function of the system is determined by evaluating the interference pattern of two matter waves originating from the spatially separated 'slit' regions of the trapped gas. Above the critical temperature for Bose-Einstein condensation, the correlation function shows a rapid gaussian decay, as expected for a thermal gas. Below the critical temperature, the correlation function has a different shape: a slow decay towards a plateau is observed, indicating the long-range phase coherence of the condensate fraction.

Phase synchronization of chaotic oscillators by external driving

We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed. and the phase dynamics of a single self-sustanined chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external force. This effect is demonstrated for periodic and noisy driving. This phase synchronization is characterized via direct calculation of the phase, as well as by implicit indications, such as the resonant growth of the discrete component in the power spectrum and the appearance of a macroscopic average field in an ensemble of driven oscillators. The Rössler and the Lorenz systems are shown to provide examples of different phase coherence properties, with different response to the external force. A relation between the phase synchronization and the properties of the Lyapunov spectrum is discussed.

Quantum phase diagrams in periodic and glassy arrays of ultra-small Josephson junctions

Recent advances in submicrometer technology have made it possible to fabricate relatively large arrays of ultra-small Josephson junctions. The areas of these junctions can vary from a few microns to submicron sizes. Under these circumstances the long-range phase coherent properties of the Josephson junction arrays crucially depend on the interplay between the Josephson and charging energies. In this paper we will present a brief review of some of our recent results on the relevance of ultra-small capacitances in periodic and disordered arrays as well as the evidence for or against a low-temperature quantum0fluctuation-induced phase transition (QUIT), both for zero and full frustration. We also discuss results from a study of a quantum superconducting glass model, obtained from using different approximate analytic techniques. We mention a direct comparison between our results and those obtained in periodic arrays.

One-flipped-spin sector of the Hubbard model: A search for non-Fermi-liquid behavior.

One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in $^{3}\mathrm{He}$ is pointed out.