Dephasing of Bose-Einstein condensates

Abstract

We discuss some recent work on the dephasing of Bose-Einstein condensates of interacting atoms due to fluctuations in the chemical potential μ. At vanishing temperature such fluctuations are due to the uncertainty of the number of particles in the condensate caused by the depletion effect. The dephasing is in this case a non-diffusive (and in principle reversible) effect called ‘collapse’ (and ‘revival’). Above a certain cross-over temperature the dephasing proceeds mainly via a diffusive process which follows in time a short and ineffective phase collapse. The phase-diffusion constant is dominated by the temperature dependent condensate-number fluctuations caused by the scattering of low-energy excitations off the condensate. We also discuss the (in general subdominant) contribution of the occupation-number fluctuations in quasi-particle states in the thermal cloud. For simplicity we discuss here results for a box-like trapping potential.     

Dynamics of correlations in atomic Bose-Einstein condensates

Abstract

The Gross-Pitaevskii equation has been extremely successful in the theory of weakly interacting Bose-Einstein condensates. However, present-day experiments reach beyond the regime of its validity due to the significant role of correlations. We review a method for tackling the dynamics of correlations in Bose condensed gases, in terms of non-commutative cumulants. This new approach has a wide applicability in the areas of current interest, e.g. the production of molecules and the manipulation of interactions in condensates. It also offers an interesting perspective on the classical-field methods for partly condensed Bose gases.     

(Quantum) chaos in Bose-Einstein condensates

I discuss chaos in classical and quantum (wave) dynamics, extending this to considering chaotic dynamics in nonlinear wave equations, in particular how chaotic dynamics in the Gross-Pitaevskii equation relate to particle depletion from an initial Bose-Einstein condensate.     

Maximal length of trapped one-dimensional Bose-Einstein condensates

No Heading I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.     

Bose-Einstein condensates in 'giant' toroidal magnetic traps

The experimental realization of gaseous Bose—Einstein condensation (BEC) in 1995 sparked considerable interest in this intriguing quantum fluid. Here, progress towards the development of an ⁸⁷Rb BEC experiment in a large (≈ 10cm diameter) toroidal storage ring is reported. A BEC will be formed at a localized region within the toroidal magnetic trap, from whence it can be launched around the torus. The benefits of the system are manifold, as it should readily enable detailed investigations of persistent currents, Josephson effects, phase fluctuations and high-precision Sagnac or gravitational interferometry.     

Manipulation of Bose-Einstein condensates by dipole potentials

Abstract

The coherent manipulation of Bose-Einstein condensates by far blue detuned dipole potentials is discussed. ‘Classical’ atom optical elements, such as mirrors and waveguides, are realized and the dynamics of coherent matter waves interacting with these elements is investigated. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose-Einstein condensates and study their dynamics.     

Toroidal solitons in magnetic oxides,Bose-Einstein condensates,and other media

We consider toroidal soliton solutions in a number of nonlinear models of field theory (Skyrme, Faddeev, and Higgs models). Such models are used in various areas of solid-state chemistry and physics, chemical physics, astrophysics, and plasma chemistry and physics. The stability of toroidal solitons is shown to have a topological nature. We examine different methods of generating a nonlinear contribution to the Lagrangian in order to insure stability of the torus to collapse. Using the Faddeev and Skyrme models, we analyze the toroidal ordering in Bose-Einstein condensates of ²³Na, ³⁹K, and ⁸⁷Rb alkali-metal atoms, the toroidal structures recently found in the magnetic oxides BiFeO₃ and GaFeO₃, and potential applications of such structures in spintronics. In addition, we address several critical issues in the chemistry and physics of solitons with high topological charges.     

Resistors for precision low-temperature measurements

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 9–11, January, 1993.     

Atoms in precision electromagnetic measurements

Past, present, and future roles of atoms in precision electromagnetic measurements are discussed. In particular, atomic frequency standards, the current definition of the meter, the Josephson voltage, and the quantized Hall resistance are reviewed. Laser cooling and trapping of atoms are discussed with emphasis on a proposal of further cooling the atoms to a temperature of microkelvins and nanokelvins by utilizing the dipole force rather than the scattering force     

Cryogenic microwave amplifiers for precision measurements

The noise performance of two cryogenic HEMT amplifiers has been studied. The effective noise temperature for each amplifier is shown to be close to the 6 K thermodynamic temperature before a power threshold of about -70 dBm is achieved.     

Calculable coaxial resistors for precision measurements

Coaxial straight-wire resistors have been constructed with the purpose of improving comparisons between resistors, capacitors, and inductors in the audio-frequency range. The design is based on the principle that a coaxial line with a cylindrical shield can be described by relatively simple equations for the real and imaginary parts of the impedance. The resistors, with values at and above 100 Ω will be used as transfer standards for characterization of the frequency dependence of standard resistors and of the quantum Hall resistance in the audio frequency range     

Investigating the precision of linear dimension measurements

Conclusions It is necessary to oblige the Committee of Standards'laboratories and institutes to supervise systematically the level of errors in production measurements, to generalize the results thus obtained, and to provide industry with information on the accumulated data. It is necessary to improve the qualifications of the personnel engaged in measurements and, in raising the wage scales of workers, to consider without fail their metrological qualifications.Translated from Izmeritel'naya Tekhnika, No. 5, pp. 33–34, May, 1968.