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Physical Review A

Nonclassical Bose-Einstein condensate

Heping Zeng, Weiping Zhang, Fucheng Lin

Published Sep 1, 1995• 29 citations
Publisher

Abstract

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, ${\mathit{M}}_{\mathit{F}}$=\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}${\mathit{g}}_{+}$〉.

DOI
10.1103/physreva.52.2155

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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}g\ifmmode±\else\textpm\fi,0{\mathit{g}}_{\ifmmode\pm\else\textpm\fi{},0}g\ifmmode±\else\textpm\fi,0​〉). Initially, the atomic condensate is assumed to be prepared in a hyperfine sublevel \ensuremath{\Vert}g\ensuremath−{\mathit{g}}_{\mathrm{\ensuremath{-}}}g\ensuremath−​〉. By effective two-photon excitations with two classical (\ensuremathσ\ensuremath−{\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}\ensuremathσ\ensuremath−) and quantum (\ensuremathσ+{\mathrm{\ensuremath{\sigma}}}^{+}\ensuremathσ+) 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+​〉.
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.
In this paper, we study quantum statistical properties of atoms and photons in interaction of -atomic Bose–Einstein condensate in the ground-state hyperfine sublevels with laser fields. We investigate not only quantum conversions between atoms in the condensate and photons in the quantized laser field, but also transfer of nonclassical characteristics of atoms and photons between input states and output states when the atom field is initially in a number state and the quantized laser field is in the even coherent state and the odd coherent state, respectively. We find various conditions to realize these quantum conversions. We also study atom-photon quantum correlations and their input-output conversions. It is indicated that there are atom-field nonclassical correlations.
We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy-Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.``
Quantum manipulation of polaritonic band gaps of two coherently coupled BosendashndashndashEinstein condensates confined in an optical lattice
We have investigated quantum statistical behaviors of photons and atoms in interaction of an atomic Bose–Einstein condensate with quantized laser field. When the quantized laser field is initially prepared in a superposition state which exhibits holes in its photon-number distribution, while the atomic field is initially in a Fock state, it is found that there is energy exchange between photons and atoms. For the input and output states, the photons and atoms may exhibit the sub-Poissonian distribution. The input and output laser fields may exhibit quadrature squeezing, but for the atomic field, only the output state exhibits quadrature squeezing. It is shown that there exists the violation of the Cauchy–Schwartz inequality, which means that the correlation between photons and atoms is nonclassical.
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.