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arXiv:cond-mat/0504336 · Physical Review A

Coherent population trapping and dynamical instability in coupled atom-molecule condensates

Hong Yuan Ling, P. Maenner, Han Pu

Published Jul 18, 2005• 13 citations
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Abstract

Coherent population trapping (CPT) is an important concept in many subfields of physics and chemistry. Here we analyze the collective excitation spectrum of the CPT states in a coupled atom-molecule condensate system. We find that collisions between particles can cause the CPT state to be dynamically unstable, which is a unique feature of the nonlinear system. We obtain a set of analytical criteria for determining the stability properties of the CPT state in the long-wavelength limit. We construct stability diagrams and provide a systematic classification of various instabilities according to collisional interaction strengths.

DOI
10.1103/physreva.72.013608

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Coherent population trapping (CPT) is an important concept in many subfields of physics and chemistry. Here we analyze the collective excitation spectrum of the CPT states in a coupled atom-molecule condensate system. We find that collisions between particles can cause the CPT state to be dynamically unstable, which is a unique feature of the nonlinear system. We obtain a set of analytical criteria for determining the stability properties of the CPT state in the long-wavelength limit. We construct stability diagrams and provide a systematic classification of various instabilities according to collisional interaction strengths.
A study of coherent photoassociation is presented for the case of an atomic Bose-Einstein condensate. It is shown that the phenomenon is analogous to coherent optical transient in a few-level system, with a difference that the participating levels have Bose enhanced populations. A second-quantized Hamiltonian in momentum and position representation is developed to describe photoassociation. A classical version of the field theory for atoms and molecules is used to demonstrate that in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of the density fluctuations. ^ A simple mean-field model of atom-molecule Bose-Einstein condensate is constructed and it is shown that in the model there is no collapse, irrespective of the sign of the effective atom-atom scattering length. The properties of the two most important eigenstates, the ground state and the twin state, are determined for different values of the system parameters δ and K, the detuning and the atom-molecule coupling, respectively. It is shown that in a coupled atom-molecule system a collapse is replaced by a dynamical instability. The lines in the parameter space where these instabilities occur are in fact fractures where the underlying eigenstates discontinuously change. The features of instability are in good qualitative agreement with the experimental observations of collapse. ^
The emergence of standing-wave states and modulational instability in a system of coupled nonlocal nonlinear Hartree equations is considered. Such equations naturally arise in the mean-field description of two-component Bose-Einstein condensates and in nonlinear optical media with long-range interactions. By analytical stability analysis, applying a Lens-type transformation, we determine the modulational instability gain spectrum and identify the conditions under which uniform (steady) states become unstable. We consider a quadratic external potential of the form Vj(x) = λjx2, where the parameter λj may take positive, negative, or zero values, allowing us to explore trapping, expulsive, and homogeneous configurations for all types of atomic interactions. Numerical simulations reveal rich dynamical behavior characterized by the onset of phase segregation and overlapping patterns in the unstable regime. The interplay between strong nonlinearity and nonlocal coupling drives spontaneous structure formation and collective excitation modes in coupled nonlocal systems.
Coherent population trapping (CPT) is a technique in ultrahigh-resolution spectroscopy, developed in recent years. It relies on the nonlinear coherent interaction between an atomic system and incident electromagnetic radiation and is followed by an analysis of the fine structure of the response to this interaction, which contains information about the spectral characteristics of the quantum system. The basic physics of CPT are reviewed, and the effects of level relaxation and structure, and of external factors, on CPT dynamics and characteristics are examined. Experimental results confirming the validity of theoretical ideas on CPT are presented. Possible applications of CPT to frequency stabilization, laser cooling of atoms, and so on are discussed.
We investigate the relationship between stability, adiabaticity and transfer efficiency in a Λ-type atom-molecule coupling system via a nonlinear stimulated Raman adiabatic passage. We find that only when the pump and control lasers overlap in time domain, the coherent population trapping (CPT) state could become unstable. If the overlapping time of the two lasers is short so that unstable growth of the deviation from the CPT state is negligible, then good adiabaticity of the CPT state could be maintained even in the unstable region. In this case, a high atom-molecule transfer efficiency could be obtained by chirping applied laser pulses to elegantly compensate the frequency shift induced by intra-atomic collision. Our results could be useful for efficiently photoassociating ground-state molecules from a cold atomic gas with strong atom-atom collisional interaction.
We investigate the relationship between stability, adiabaticity and transfer efficiency in a \Lambda-type atom-molecule coupling system via a nonlinear stimulated Raman adiabatic passage. We find that only when the pump and control lasers overlap in time domain, the coherent population trapping (CPT) state could become unstable. If the overlapping time of the two lasers is short so that unstable growth of the deviation from the CPT state is negligible, then good adiabaticity of the CPT state could be maintained even in the unstable region. In this case, a high atom-molecule transfer efficiency could be obtained by chirping applied laser pulses to elegantly compensate the frequency shift induced by intra-atomic collision. Our results could be useful for efficiently photoassociating ground-state molecules from a cold atomic gas with strong atom-atom collisional interaction.