Coherence of bose condensates

Abstract

We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.     

Quantum dynamics of the phase of a Bose–Einstein condensate

Abstract

In this review we discuss the dynamics of the phase of trapped Bose–Einstein condensates. In particular we consider the phenomena of phase decoherence (termed also as phase collapse, or diffusion), and phase revival in systems of interacting atoms. We analyse the dependence of the collapse and revival times on the trap potential, dimensionality of the gas, atom number fluctuations, and on the coherent dynamics of the condensate. We show that in a class of experimentally relevant systems, the collapse time is relatively short, and in some cases vanishes in the limit of a large number of atoms, implying that the trapped Bose gas cannot sustain a well-defined quantum phase, and that the phase memory is lost on a relatively short time scale. Furthermore, we calculate the relative atom number fluctuations or a model of two interacting condensates, and show that the fluctuations are generically sub-Poissonian.     

Coherence properties of a continuous atom laser

Abstract

We investigate the coherence properties of an atomic beam evaporatively cooled in a magnetic guide, assuming thermal equilibrium in the quantum degenerate regime. The gas experiences two-dimensional, transverse Bose-Einstein condensation rather than a full three-dimensional condensation because of the very elongated geometry of the magnetic guide. First order and second order correlation functions of the atomic field are used to characterize the coherence properties of the gas along the axis of the guide. The coherence length of the gas is found to be much larger than the thermal de Broglie wavelength in the strongly quantum degenerate regime. Large intensity fluctuations present in the ideal Bose gas model are found to be strongly reduced by repulsive atomic interactions; this conclusion is obtained with a one-dimensional classical field approximation valid when the temperature of the gas is much higher than its chemical potential, k _B T » |μ|.     

Controlled simultaneous rotation of multiple optically trapped particles

Abstract

We present a method for the controlled alignment or rotation of birefringent particles trapped in multiple optical trap sites of an interference pattern between two Laguerre—Gaussian laser modes. Controlled spin or alignment of the particles within each individual trap site is achieved independently of the lateral or rotational motion of the interference pattern as a whole. This technique may lead to driving arrays of micro-machines and micro-fluidic studies and can be used in combination with dynamically generated trapping arrays for uniformly distributed stirring throughout microscopic volumes of fluid.     

Particle number fluctuations in an ideal Bose gas

Abstract

We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.     

Quasi 1 and 2d Dilute Bose Gas in Magnetic Traps: Existence of Off-Diagonal Order and Anomalous Quantum Fluctuations

Current magnetic traps can be made so anisotropic that dilute Bose gases confined in these traps will occupy the lowest quantum state in the tightly confining direction, while still in the Thomas-Fermi limit in the loosely confining direction. As a result, the trapped Bose gas behaves like a quasi one or two dimensional systems. Unlike the homogeneous case, quantum phase fluctuations do not destroy macroscopic off-diagonal order of trapped Bose gases in d2 because they are suppressed by the the trapping potential. In the dilute limit, quantum fluctuations increase, remain constant, and decrease with size for 3, 2, 1 d respectively. These behaviors are due to the combination of a finite gap and the universal spectrum of the collective mode.     

Theory for double beam interference microscopes with coherence effects and verification using the linnik microscope

Abstract

A theoretical model for the interferogram from double beam interference microscopes, which takes into account the coherence effects, is presented. The model is based on the general imaging theory of a lens in defocus. For the case of zero relative lateral displacements between the reference and object beams a simplified expression is found for the defocus and path length dependence of the interferogram. Based on this expression the characteristics of the interferogram are studied and special attention is devoted to explaining the dependence of the fringe size on the objective numerical aperture, and the effect of the spatial and temporal coherence. For the Linnik microscope in which two objectives and a beam splitter cube are used, the effect of the mismatch between chromatic aberrations of the two objectives, and the effect of glass dispersions and misalignment of the beam splitter cube are investigated. Experimental results using the Linnik microscope are presented and they confirm the proposed model.     

Spatial coherence wavelets

Abstract

It is shown that the cross-spectral density at a plane in the Fresnel—Fraunhofer domain can be expressed as a certain diffraction pattern, which is generated by the superposition of second-order spatial coherence wavelets that emerge from the aperture. The amplitude of each coherence wavelet exhibits units of power density (average energy) and the power spectrum at the far zone plane will be the summation of the amplitudes of such wavelets. Thus, the spatial coherence wavelet constitutes a vehicle for both correlation and energy transport in free space. Some simulation results are discussed to illustrate these ideas.     

Role of Bose enhancement in photoassociation

Abstract

We discuss the role of Bose enhancement of the dipole matrix element in photoassociation, using stimulated Raman adiabatic passage as an example. In a non-degenerate gas the time scale for coherent optical transients tends to infinity in the thermodynamic limit, whereas Bose enhancement keeps this time scale finite in a condensate. Coherent transients are therefore absent in photoassociation of a thermal non-degenerate gas, but are feasible if the gas is a condensate.     

Classification of Phase Transitions for an Ideal Bose Gas in a d-Dimensional Quartic Potential

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number N of particles trapped in a d-dimensional quartic potential. We find that the presence and nature of phase transition depend on the dimensionality of the quartic potential. Proposing three different definitions of transition temperature, we discuss either N or d dependence of transition temperature for the ideal Bose condensate in the d-dimensional quartic potential.     

Measurement of the spatial coherence of superluminescent diodes

Abstract

In recent years, superluminescent diodes (SLDs) have gained increasing importance as light sources for partial coherence interferometry and optical coherence tomography. The requirements of SLDs are high spatial coherence, low temporal coherence, and, for some applications, high power. Since there might be a trade-off between these properties we built an instrument for measuring the spatial coherence of SLDs. This instrument consists of a hybrid bulk optic-fibre optic Mach-Zehnder interferometer. The special advantages of the instrument are the ability to measure the spatial coherence between arbitrary points within the light beam and to observe directly the measurement points within the beam which facilitates the alignment. We used this instrument to evaluate the spatial coherence of several commercially available SLDs. As expected, a single mode fibre pigtailed SLD shows the best spatial coherence. If free-space emitting SLDs are considered, those with a more complicated chip structure have a somewhat poorer spatial coherence, however, their temporal coherence is considerably better than that of a SLD which is only antireflection coated.     

Switching and self-trapping dynamics of bose-Einstein solitons

Abstract

We investigate the dynamics of two weakly coupled Bose condensates in long cigar-shaped traps. The Bose condensates are characterized by attractive mean-field interaction and consequently can be studied in terms of bright solitons. We exploit the analogy with directional fibre couplers in nonlinear fibre optics to uncover interesting dynamical regimes like switching of condensates from one trap to another and self-trapping of condensates. We also discuss the analogy between two weakly coupled Bose condensates and the Josephson junction in superfluids and superconductors.     

Experimental demonstration of the spectral interference between two linearly polarized modes at the output of a fibre waveguide excited by a low-coherence source

Abstract

The mutual interference of two linearly polarized (LP) modes in the frequency domain has been demonstrated experimentally at the output of a fibre waveguide excited by a low-coherence source when the optical path difference between both LP modes exceeds the coherence length of the source. The spectral interference between two LP modes, which shows up a periodic modulation of the source spectrum, serves as an illustration of the experimental verification of conclusions we have made in previous theoretical works. Consequently, the feasibility of a novel experimental method utilizing a high-resolution spectrometer in the evaluation of the group-delay time difference between both LP modes has been confirmed.     

Theory of Ultra-high-resolution Optical Raman Ramsey Spectroscopy

A non-perturbative theoretical analysis of Ramsey interference lineshapes in three-level lambda systems excited by laser fields has been developed for the general case of several interaction regions. In conventional Ramsey excitation, two laser fields excite the lambda system each in two separate spatial interaction regions. Here we examine how increasing the number of interaction regions or altering the interaction times change and improve the lineshape characteristics such as fringe visibility. For short interaction times the fringe pattern is strongly dependent on the number of interaction regions, with the n = 2 sinusoidal fringes replaced by sharper fringes of greater visibility. With larger interaction times, the fringe pattern is virtually unchanged on increasing the number of interaction regions. The optimum fringe pattern is obtained with short interaction times and a larger (n a 9) number of regions.     

Finite-temperature Effect in Phase Transition to Superfluidity for Bose–Einstein Condensates in a 1-D Optical Lattice

We experimentally study the phase transition of ⁸⁷Rb Bose–Einstein condensates adiabatically loaded to a combined trap of a 1D optical lattice and a magnetic trap. The phase coherence property of this system is probed by recording the interference pattern of the expanded atomic cloud suddenly released from the combined trap. We show that as the temperature is sufficiently low (below the critical temperature T _C ), an interference pattern has a “peak on a peak” feature which is a true signature of macroscopic superfluid states. The normal gas only contributes to the broad background and three wide peaks in an interference pattern. These observations qualitatively agree with the recent theoretical predictions (Diener et al. in Phys. Rev. Lett. 98:180404, 2007; Kato et al. in Nat. Phys. 4:617, 2008). We also computed both the critical temperature and the interference pattern for a practical combined trap as ours in the tight-binding limit, and the numerical results are consistent with our experimental observations.     

Development of a digital astronomical intensity interferometer: laboratory results with thermal light

Abstract

We present measurements of the second-order spatial coherence function of thermal light sources using Hanbury-Brown and Twiss interferometry with a digital correlator. We demonstrate that intensity fluctuations between orthogonal polarizations, or at detector separations greater than the spatial coherence length of the source, are uncorrelated but can be used to reduce systematic noise. The work performed here can readily be applied to existing and future Imaging Air-Cherenkov Telescopes used as star light collectors for stellar intensity interferometry to measure spatial properties of astronomical objects.     

Visualization of the spatial distribution of current densities in a photographic system with a semiconductor photodetector

Abstract

This paper studies the visualization of the spatial distribution pattern of current density in a semiconductor photographic system with a gallium arsenide semiconductor photodetector. The spatial distribution of the current in the filaments was determined by photometric analysis of the gas discharge light emission when a current was passed through a photographic cell. This method ensured spatial resolution of ~ 10/mm and made it possible to describe quantitatively the distributions involving a drop in current density of ? 10². Transformation of the profile and amplitude of the current density of the filaments in the different regions of the current-voltage characteristic (CVC) has been studied. The filamentation (i.e. an inhomogencous distribution of the current density) was primarily due to the formation of a space charge of positive ions in the discharge gap between the photodetector and a transparent anode plate that changed the discharge from the Townsend type to the glow type.     

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

No Heading We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.PACS numbers: 03.75.Hh, 05.30.Jp, 05.70 Fh, 32.80.Pj