We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of "superchemistry," in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finitetemperature "fermionization" through the measurement of the rates of two-body inelastic processes, such as photo-association. The knowledge of the exact solutions to the 1D models allows us to go far beyond the mean-field Bogoliubov approximation. In the current stage of studies of experimentally feasible 1D Bose gases, one of the most important issues that requires such an approach is understanding the correlation properties in the various regimes at finite temperatures.In this Letter we give an exact calculation of the finitetemperature two-particle local correlation for an interacting uniform 1D Bose gas,is the field operator and n = Ψ † (x)Ψ(x) is the linear (1D) density. As a result, we identify and classify various finite-temperature regimes of the 1D Bose gas. Aside from this, the pair correlations are responsible for the rates of inelastic collisional processes [9], and are of particular importance for the studies of coherence properties of atom "lasers" produced in 1D waveguides.At T = 0, the local two-and three-particle correlations of a uniform 1D Bose gas have recently been calculated in Ref. [10]. Here one has two well-known and physically distinct regimes of quantum degeneracy. For weak couplings or high densities, the gas is in a coherent or Gross-Pitaevskii (GP) regime with g (2) → 1. In this regime, long-range order is destroyed by longwavelength phase fluctuations [11] and the equilibrium state is a quasi-condensate characterized by suppressed density fluctuations. For strong couplings or low densities, the gas reaches the strongly interacting or TonksGirardeau (TG) regime and undergoes "fermionization" [3,4]: the wave function strongly decreases as particles approach each other, and g (2) → 0.At the non-zero temperatures studied here, one has to further extend the classification of different regimes. For strong enough couplings or low densities, we obtain the TG regime with g (2) → 0 not only at low temperatures, but also at high temperatures. In addition, and in contrast to previous T = 0 results, we find a weak-coupling or high-density regime in which fluctuations are enhanced. Asymptotically, they reach the non-interacting Bose gas level of g (2) → 2 (rather than g (2) → 1), for any finite temperature T .The emergence of this behavior at low temperatures implies that one can identify three physically distinct regimes of quantum degeneracy: the strong-coupling TG regime of "fermionization" with g (2) → 0, a coherent GP regime with g (2) ≃ 1 at intermediate coupling strength, and a fully decoherent quantum (DQ) regime with g (2) ≃ 2 at very weak couplings. In the GP regime, where the density fluctuations are suppresse...

We investigate the behavior of a weakly interacting nearly one-dimensional (1D) trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based on exact solutions obtained using the Yang-Yang thermodynamic formalism, in a regime where other, approximate theoretical approaches fail. We use Bose-gas focusing [Shvarchuck et al., Phys. Rev. Lett. 89, 270404 (2002)] to probe the axial momentum distribution of the gas, and find good agreement with the in situ results.PACS numbers: 03.75. Hh, 05.30.Jp, 05.70.Ce Reducing the dimensionality in a quantum system can have dramatic consequences. For example, the 1D Bose gas with repulsive delta-function interaction exhibits a surprisingly rich variety of physical regimes that is not present in 2D or 3D [1,2]. This 1D Bose gas model is of particular interest because exact solutions for the manybody eigenstates can be obtained using a Bethe ansatz [3]. Furthermore, the finite-temperature equilibrium can be studied using the Yang-Yang thermodynamic formalism [4,5,6], a method also known as the thermodynamic Bethe ansatz. This formalism is the unifying framework for the thermodynamics of a wide range of exactly solvable models. It yields solutions to a number of important interacting many-body quantum systems and as such provides critical benchmarks to condensed-matter physics and field theory [6]. The specific case of the 1D Bose gas as originally solved by Yang and Yang [4] is of particular interest because it is the simplest example of the formalism. The experimental achievement of ultracold atomic Bose gases in the 1D regime [7] has attracted renewed attention to the 1D Bose gas problem [8] and is now providing previously unattainable opportunities to test the Yang-Yang thermodynamics.In this paper, we present the first direct comparison between experiments and theory based on the Yang-Yang exact solutions. The comparison is done in the weakly interacting regime and covers a wide parameter range where conventional models fail to quantitatively describe in situ measured spatial density profiles. Furthermore, we use Bose-gas focusing [9] to probe the equilibrium momentum distribution of the 1D gas, which is difficult to obtain through other means.For a uniform 1D Bose gas, the key parameter is the dimensionless interaction strength γ = mg/ 2 n, where m is the mass of the particles, n is the 1D density, and g is the 1D coupling constant. At low densities or large coupling strength such that γ ≫ 1, the gas is in the strongly interacting or Tonks-Girardeau regime [10]. The opposite limit γ ≪ 1 corresponds to the weakly interacting gas. Here, for temperatures below the degeneracy temperature T d = 2 n 2 /2mk B , one distinguishes two regimes [11]. (i) For sufficiently low temperatures, T ≪ √ γT d , the equilibrium state is a quasi-condensate with suppressed density fluctuations. The system can be treated by the mean-field approach and by the Bogoliubov theory of excitations. The 1D c...

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEC, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupledcondensate soliton can form in three dimensions. This gives the possibility of an intense, stable atomlaser output. [S0031-9007(98) The coherently coupled atom-molecular condensate could provide a route to the observation of a localized threedimensional BEC soliton, even in the absence of a trap potential. A possible application is in the free propagation of a nondiverging atom-laser pulse, thus greatly increasing the intensity in an atom-laser beam. Even more than this would be the importance of observing the striking physical properties of this novel quantum field theory, and the corresponding Bose-enhanced chemical kinetics.The original solution for the parametric soliton was in a one-dimensional environment [6]. These classical solutions have been classified topologically [7], and are generic to the mean-field theories of parametric nonlinearities that convert one particle into two (and vice versa). The equations are nonintegrable, and are different to the usual integrable classes of soliton equations. A considerable advantage of these types of nonlinear equations is that they are capable of providing solutions in one, two, or three space dimensions, which does not occur in the usual Gross-Pitaevskii equations. Both classical [6][7][8] and quantum [9] solutions have been recently identified (including observation of classical solitons in experiment [10]), although these different types of soliton have strikingly different qualitative behavior.The purpose of this Letter is to point out the physical origin of these differences between the quantum and classical versions of the parametric field theory and to identify experimental requirements for observing these novel effects in Bose condensates. We consider the following basic Hamiltonian, to give a simple model of molecule formation:where the free and interacting Hamiltonians arê