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Chinese Physics Letters

Nonclassical Bose-Einstein Condensate

Zeng Heping, Lin Fucheng

Published Oct 1, 1995• 2 citations
Publisher

Abstract

A scheme for the generation of a nonclassical Bose-Einstein condensate is proposed in a J g = 1 → J e = 0 system where ultracold atoms are populated in one ground-state sublevel | g -⟩ and form a Bose-Einstein condensate. By coupling the condensate to copropagating classical (σ - ) and quantum (σ + ) non-resonant travelling-wave laser fields, effective two-photon excitations between two ground-state sublevels | g -⟩ and | g +⟩ create a new condensate in | g +⟩. For an appropriate selection of the interaction time and atom-field coupling strengths, the quantum features of the quantized laser field, which may be prepared in a certain nonclassical state, can be exchanged with those of the quantum density field of the generated condensate.

DOI
10.1088/0256-307x/12/10/005

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A scheme for the generation of a nonclassical Bose-Einstein condensate is proposed in a J g = 1 → J e = 0 system where ultracold atoms are populated in one ground-state sublevel | g -⟩ and form a Bose-Einstein condensate. By coupling the condensate to copropagating classical (σ - ) and quantum (σ + ) non-resonant travelling-wave laser fields, effective two-photon excitations between two ground-state sublevels | g -⟩ and | g +⟩ create a new condensate in | g +⟩. For an appropriate selection of the interaction time and atom-field coupling strengths, the quantum features of the quantized laser field, which may be prepared in a certain nonclassical state, can be exchanged with those of the quantum density field of the generated condensate.
A scheme is proposed to manipulate the quantum-statistical properties of a neutral atomic Bose-Einstein condensate in an ultracold alkali-atom-trap system with atoms in the ground hyperfine F=1, MF{\mathit{M}}_{\mathit{F}}MF​=\ifmmode\pm\else\textpm\fi{}1,0 states (labeled respectively as \ensuremath{\Vert}${\mathit{g}}_{\ifmmode\pm\else\textpm\fi{},0}$〉). Initially, the atomic condensate is assumed to be prepared in a hyperfine sublevel \ensuremath{\Vert}${\mathit{g}}_{\mathrm{\ensuremath{-}}}$〉. By effective two-photon excitations with two classical (${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$) and quantum (${\mathrm{\ensuremath{\sigma}}}^{+}$) nonresonant copropagating traveling-wave light fields, we show that the atomic system can be settled into a coherent superposition of two atomic Bose-Einstein condensates corresponding to different ground hyperfine sublevels and different quantum statistics. Furthermore, with an appropriate choice of interaction time, atom-field coupling strengths, and quantum features of the quantized laser field, a nonclassical condensate can be prepared in the hyperfine sublevel \ensuremath{\Vert}g+{\mathit{g}}_{+}g+​〉.
In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser, and a strong classical coupling laser, which form a three-level $\ensuremath{\Lambda}$-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and interatomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.
We discuss a method to launch gap solitonlike structures in atomic Bose-Einstein condensates confined in optical traps. Bright vector solitons consisting of a superposition of two hyperfine Zeeman sublevels can be created for both attractive and repulsive interactions between the atoms. Their formation relies on the dynamics of the atomic internal ground states in two far-off-resonance counterpropagating $({\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}})$-polarized laser beams that form the optical trap. Numerical simulations show that these solitons can be prepared from a one-component state provided with an initial velocity.
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. ^