Observation of Microcanonical Atom Number Fluctuations in a Bose-Einstein Condensate.

Quantum systems are typically characterized by the inherent fluctuation of their physical observables. Despite this fundamental importance, the investigation of the fluctuations in interacting quantum systems at finite temperature continues to pose considerable theoretical and experimental challenges. Here we report the characterization of atom number fluctuations in weakly interacting Bose-Einstein condensates. Technical fluctuations are mitigated through a combination of nondestructive detection and active stabilization of the cooling sequence. We observe fluctuations reduced by 27% below the canonical expectation for a noninteracting gas, revealing the microcanonical nature of our system. The peak fluctuations have near linear scaling with atom number ΔN_{0,p}^{2}∝N^{1.134} in an experimentally accessible transition region outside the thermodynamic limit. Our experimental results thus set a benchmark for theoretical calculations under typical experimental conditions.

Observation of Atom Number Fluctuations in a Bose-Einstein Condensate.

Fluctuations are a key property of both classical and quantum systems. While the fluctuations are well understood for many quantum systems at zero temperature, the case of an interacting quantum system at finite temperature still poses numerous challenges. Despite intense theoretical investigations of atom number fluctuations in Bose-Einstein condensates, their amplitude in experimentally relevant interacting systems is still not fully understood. Moreover, technical limitations have prevented their experimental investigation to date. Here we report the observation of these fluctuations. Our experiments are based on a stabilization technique, which allows for the preparation of ultracold thermal clouds at the shot noise level, thereby eliminating numerous technical noise sources. Furthermore, we make use of the correlations established by the evaporative cooling process to precisely determine the fluctuations and the sample temperature. This allows us to observe a telltale signature: the sudden increase in fluctuations of the condensate atom number close to the critical temperature.

Universal Three-Body Physics in Ultracold KRb Mixtures.

Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected nonuniversal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of ^{39}K-^{87}Rb and ^{41}K-^{87}Rb and do not observe any signatures of Efimov resonances for accessible scattering lengths in either mixture. Our results show good agreement with our theoretical model for the scattering dependent three-body recombination coefficient and reestablish universality across isotopic mixtures.

A simple laser locking system based on a field-programmable gate array.

Frequency stabilization of laser light is crucial in both scientific and industrial applications. Technological developments now allow analog laser stabilization systems to be replaced with digital electronics such as field-programmable gate arrays, which have recently been utilized to develop such locking systems. We have developed a frequency stabilization system based on a field-programmable gate array, with emphasis on hardware simplicity, which offers a user-friendly alternative to commercial and previous home-built solutions. Frequency modulation, lock-in detection, and a proportional-integral-derivative controller are programmed on the field-programmable gate array and only minimal additional components are required to frequency stabilize a laser. The locking system is administered from a host-computer which provides comprehensive, long-distance control through a versatile interface. Various measurements were performed to characterize the system. The linewidth of the locked laser was measured to be 0.7 ± 0.1 MHz with a settling time of 10 ms. The system can thus fully match laser systems currently in use for atom trapping and cooling applications.

Preparation of Ultracold Atom Clouds at the Shot Noise Level.

We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼10^{6} is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN

Parametric amplification of vacuum fluctuations in a spinor condensate.

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 87Rb condensate. Interatomic interactions lead to correlated pair creation in the mF=±1 states from an initial mF=0 condensate, which acts as a vacuum for mF≠0. Although this pair creation from a pure mF=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial mF=±1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of nonclassical states of matter.

Spontaneous breaking of spatial and spin symmetry in spinor condensates.

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously formed patterns in the longitudinal magnetization.

Multiresonant spinor dynamics in a Bose-Einstein condensate.

We analyze the spinor dynamics of a 87Rb F=2 condensate initially prepared in the m(F) = 0 Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in m(F) = +/-1, presents an intriguing multiresonant magnetic-field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial m(F) = 0 condensate, showing that, in general, even a qualitative understanding of the pair-creation efficiency in a spinor condensate requires a careful consideration of the confinement.

Dynamics of F=2 spinor Bose-Einstein condensates.

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of 10(-12) cm(3) s(-1) for spin-changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10(-13) cm(3) s(-1) for hyperfine-changing collisions. We observe polar behavior in the F=2 ground state of 87Rb, while we find the F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.

Measurement of the spatial correlation function of phase fluctuating Bose-Einstein condensates.

We measure the intensity correlation function of two interfering spatially displaced copies of phase fluctuating Bose-Einstein condensates. It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated condensates. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.

Bose-Einstein condensation in dilute atomic gases.

Bose-Einstein condensation is one of the most curious and fascinating phenomena in physics. It lies at the heart of such intriguing processes as superfluidity and superconductivity. However, in most cases, only a small part of the sample is Bose-condensed and strong interactions are present. A weakly interacting, pure Bose-Einstein condensate (BEC) has therefore been called the "holy grail of atomic physics". In 1995 this grail was found by producing almost pure BECs in dilute atomic gases. We review the experimental development that led to the realization of BEC in these systems and explain how BECs are now routinely produced in about 25 laboratories worldwide. The tremendous experimental progress of the past few years is outlined and a number of recent experiments show the current status of the field. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00114-001-0277-8.

Observation of phase fluctuations in elongated Bose-Einstein condensates.

The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.