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BoseEinstein condensation of atomic hydrogen, Phys
 Rev. Lett
, 1998
"... We report observation of BoseEinstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by twophoton spectroscopy of the 1S2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The c ..."
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Cited by 35 (1 self)
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We report observation of BoseEinstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by twophoton spectroscopy of the 1S2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is 4.8 6 1.1 3 10 15 cm 23 , corresponding to a condensate population of 10 9 atoms. The BEC transition occurs at about T 50 mK and n 1. Silvera and Walraven [3]. Subsequent attempts to achieve BEC were thwarted by recombination on the walls of the confinement cell Hydrogen condensates share many characteristics with condensates of alkali metal atoms, but there are several notable differences. Owing to hydrogen's simplicity, properties such as interatomic potentials and spin relaxation rates are well understood theoretically. Compared to those of other atoms, the swave scattering length, a, and threebody loss rate are anomalously low. As a result the condensate density is high, even for small condensate fractions, and the elastic collision rate is low, which retards evaporative cooling. Because of hydrogen's small mass, the BEC transition occurs at higher temperatures than previously observed. The cryogenic trap loading technique used for H allows orders of magnitude more atoms to be trapped, providing condensates that are much larger than yet achieved in other systems. Finally, high resolution twophoton spectroscopy provides a new tool for studying condensates. The starting point for the observations reported here is described in the accompanying Letter [10]: a gas of atomic hydrogen, confined in a cylindrically symmetric magnetic trap, and cooled to 120 mK by evaporation over a magnetic field saddlepoint at one end of the trap To overcome this problem, we turned to a different ejection technique, based on spin resonance We measure the temperature and density distribution of the gas by twophoton spectroscopy of the 1S2S transition
SECONDORDER CORRECTIONS TO MEAN FIELD EVOLUTION OF WEAKLY INTERACTING BOSONS. II.
"... Abstract. We study the evolution of a Nbody weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a secondorder correction to a meanfield evolution law for coherent states in the presence of small interaction potential. Here, we remove ..."
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Cited by 33 (2 self)
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Abstract. We study the evolution of a Nbody weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a secondorder correction to a meanfield evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the secondorder correction. This implies an improved Fockspace estimate for our approximation of the Nbody state. 1.
Laser cooling and trapping of neutral atoms
 Rev. Mod. Phys
, 1998
"... In 1978, while I was a postdoctoral fellow at MIT, I ..."
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Cited by 31 (0 self)
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In 1978, while I was a postdoctoral fellow at MIT, I
Mathematical theory and numerical methods for BoseEinstein condensation
 Kinet. Relat. Models
"... Abstract. In this paper, we mainly review recent results on mathematical theory and numerical methods for BoseEinstein condensation (BEC), based on the GrossPitaevskii equation (GPE). Starting from the simplest case with onecomponent BEC of the weakly interacting bosons, we study the reduction of ..."
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Cited by 28 (14 self)
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Abstract. In this paper, we mainly review recent results on mathematical theory and numerical methods for BoseEinstein condensation (BEC), based on the GrossPitaevskii equation (GPE). Starting from the simplest case with onecomponent BEC of the weakly interacting bosons, we study the reduction of GPE to lower dimensions, the ground states of BEC including the existence and uniqueness as well as nonexistence results, and the dynamics of GPE including dynamical laws, wellposedness of the Cauchy problem as well as the finite time blowup. To compute the ground state, the gradient flow with discrete normalization (or imaginary time) method is reviewed and various full discretization methods are presented and compared. To simulate the dynamics, both finitedifference methods andtimesplitting spectralmethods arereviewed, and their error estimates are briefly outlined. When the GPE has symmetric properties, we show how to simplify the numerical methods. Then we compare two widely used scalings, i.e. physical scaling (commonly used) and semiclassical scaling, for BEC in strong repulsive interaction regime (ThomasFermi
Making, probing and understanding ultracold fermi gases
"... 1. 1. State of the field................................. 5 1. 2. Strongly correlated fermions a gift of nature?................ 6 1. 3. Some remarks on the history of fermionic superfluidity........... 7 1. 3.1. BCS superfluidity............................ 7 ..."
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Cited by 24 (0 self)
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1. 1. State of the field................................. 5 1. 2. Strongly correlated fermions a gift of nature?................ 6 1. 3. Some remarks on the history of fermionic superfluidity........... 7 1. 3.1. BCS superfluidity............................ 7
Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of BoseEinstein Condensates
, 1996
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Quantum particles as conceptual entities. A possible explanatory framework for quantum theory
 Foundations of Science
, 2009
"... We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, ..."
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Cited by 21 (19 self)
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We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses,..., in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and nonlocality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many ’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter. 1
Optimal error estimates of finite difference methods for the GrossPitaevskii equation with angular momentum rotation
 Math. Comp
"... Abstract. We analyze finite difference methods for the GrossPitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative CrankNicolson finite difference (CNFD) method and semiimplicit finite difference (SIFD) ..."
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Cited by 19 (12 self)
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Abstract. We analyze finite difference methods for the GrossPitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative CrankNicolson finite difference (CNFD) method and semiimplicit finite difference (SIFD) method, at the order of O(h 2 + τ 2)inthel 2norm and discrete H 1norm with time step τ and mesh size h. Besides the standard techniques of the energy method, the key technique in the analysis for the SIFD method is to use the mathematical induction, and resp., for the CNFD method is to obtain apriori bound of the numerical solution in the l ∞norm by using the inverse inequality and the l 2norm error estimate. In addition, for the SIFD method, we also derive error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts, respectively, which are at the same order of the convergence rate as that of the numerical solution itself. Finally, numerical results are reported to confirm our error estimates of the numerical methods. 1.
BoseEinstein condensates in spatially periodic potentials
 Phys. Rev. A
, 1998
"... Introduction BoseEinstein condensation in trapped dilute gases 1, 2, 3 was observed only recently. Nevertheless, the experimental developments in this field have advanced rapidly, and the properties of condensates in different circumstances have become a matter of practical interest. In this wor ..."
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Cited by 16 (0 self)
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Introduction BoseEinstein condensation in trapped dilute gases 1, 2, 3 was observed only recently. Nevertheless, the experimental developments in this field have advanced rapidly, and the properties of condensates in different circumstances have become a matter of practical interest. In this work we study the influence of a spatially periodic external potential on the properties of a BoseEinstein condensate, as reported elsewhere in more detail 4 . Such a periodic potential may be induced by a faroff resonant laser field, and with present trapped condensates it is possible to have a condensate extending over many periods of such a field. The proposed periodic potential could be realized by a simple rearrangement of the laser field in the experiments with an optically trapped condensate 5 . The present study of condensates in periodic potentials both serves to generalize studies of single atom behaviour in such periodic potentials<F4