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arXiv:cond-mat/0112365 · Physical Review A

Formation of a two-component Bose condensate during the chemical-potential curve crossing

M. Amin Kayali, Nikolai A. Sinitsyn

Published Apr 28, 2003• 12 citations
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Abstract

In this paper, we study the coherent dissociation of a molecular condensate into a multiple-mode atomic condensate during the chemical-potential curve crossing beyond the mean-field approximation. We show that the problem can be reduced to the dissociation of a molecular condensate into a two-mode atomic one. We employ the time-dependent Landau-Zener theory and derive analytical expression for the transition amplitudes. We calculate the number of produced atoms and show that they exist in squeezed state. We also study the formation of multiple-mode atomic condensate by inelastic scatterings of atoms in a single-mode atomic condensate. We show that the problem is also a Landau-Zener-like and exact solution can be found by imposing an additional symmetry.

DOI
10.1103/physreva.67.045603

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In this paper, we study the coherent dissociation of a molecular condensate into a multiple-mode atomic condensate during the chemical-potential curve crossing beyond the mean-field approximation. We show that the problem can be reduced to the dissociation of a molecular condensate into a two-mode atomic one. We employ the time-dependent Landau-Zener theory and derive analytical expression for the transition amplitudes. We calculate the number of produced atoms and show that they exist in squeezed state. We also study the formation of multiple-mode atomic condensate by inelastic scatterings of atoms in a single-mode atomic condensate. We show that the problem is also a Landau-Zener-like and exact solution can be found by imposing an additional symmetry.
Formation of atomic pairs by the dissociation of a molecular condensate or by inelastic collisions in an atomic condensate due to a time-dependent curve crossing process is studied beyond the mean-field approximation. The number of atoms formed by the spontaneous process is described by a Landau-Zener formula multiplied by an exponential amplification factor due to quantum many-body effects. Correlated atomic pairs are formed in squeezed states. The rate of stimulated processes depends on the relative phase of the two fields.
Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.
We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory. Large-amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as N/lnN\sqrt{N}/\mathrm{ln}NN​/lnN with the total number of atoms N, rather than the expected pure N\sqrt{N}N​ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean-field theory is an initially nonexponential ``spontaneous'' dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (superexponential) rate observed for the entangled state formed by spontaneous dissociation.
Association in an atomic Bose‐Einstein condensate, and the subsequent dissociation of the resulting molecular condensate, due to Feshbach resonance in a time‐dependent magnetic field, are analyzed, incorporating non‐mean‐field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long‐lived molecular condensate (with lifetimes of 10 ms and longer), if the magnetic field is temporally changed one way. Entangled atoms in two‐mode squeezed states (with noise reduction of about 30 dB) are formed by molecular dissociation when the field is changed the other way.
We provide a framework to solve generic models describing the dissociation of multiple molecular Bose-Einstein condensates in a nonadiabatic regime. The competition between individual chemical reactions can lead to nontrivial dependence on critical components such as path interference and symmetries, thus, affecting the final distribution of atomic population. We find an analytical solution for an illustrative example model involving four atomic modes. When the system parameters satisfy CPTCPTCPT symmetry, where CCC is the charge conjugation, PPP is parity, and TTT is time-reversal symmetry, our solution predicts a population imbalance between atomic modes that is exponentially sensitive to system parameters. However, a weakly broken symmetry alters the population in each atomic mode and can reverse the population imbalance. Our solution also demonstrates a strong quantum correlation between atomic modes that leads to the spontaneous production of atoms in a multimode squeezed state. Moreover, in our framework, a time-dependent non-Hermitian quantum mechanics naturally manifests, which can alternatively be realized experimentally in photonic systems.
In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69 , 043612 (2004); J. Phys. A 38 , 3505 (2005)] by order of magnitude.