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arXiv:quant-ph/0512234

Spatially Separated and Correlated Atom-molecule Lasers from a Bose Condensate

Hui Jing, Wei Hua Cai, Jingjun Xu, Mingsheng Zhan

Published Dec 26, 2005• 0 citations
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Abstract

We propose a feasible scheme to create two spatially separated atomic and molecular beams from an atomic Bose-Einstein condensate by combining the Raman-type atom laser output and the two-color photo-association processes. We examine the quantum dynamics and statistical properties of the system under short-time limits, especially the quadrature-squeezed and mode-correlated behaviors of two output beams for different initial state of the condensate. The possibility to generate the entangled atom-molecule lasers by an optical technique was also discussed.

DOI
10.48550/arxiv.quant-ph/0512234

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Ultracold atoms in the atomic Bose-Einstein condensate (ABEC) state can form molecular Bose-Einstein condensate (MBEC) through photoassociation.In the atom-molecule Bose-Einstein condensates (BECs), two or more atoms in the ABEC can combine to form a molecule in the MBEC and again a molecule from a MBEC can decompose to atoms in the ABEC.The Bose-stimulated Raman adiabatic passage is an efficient mechanism for conversion of an atomic BEC to a molecular BEC.A three-mode atom-molecule Bose-Einstein condensates system can be prepared through the photoassociative Bose-stimulated Raman adiabatic passage.In our system, three modes are one ABEC, one excited MBEC, and one stable MBEC.The intramodal interactions due to the  (3) nonlinearity is present in all three BEC modes along with ABEC-excited MBEC and excited MBEC-stable MBEC intermodal couplings.The quantum mechanical Hamiltonian of the system is constructed considering all three intraspecies interactions and intermodal couplings among the modes.The Hamiltonian of the system is solved analytically using a special intuitive approach which is more general and gives more accurate result than the well-known short time approximation method.The correctness of the solution is verified through the equal time commutation relation.Staring from a three-mode composite coherent state we compute the time evolution of the field annihilation operators of all three modes in presence of all possible interactions and couplings.Using these solutions, we investigate the quantum entanglement properties of the system for all three two-mode combinations.Entanglement is found for two combinations of modes, where as one combination is always separable.Also, we study the dependence of the entanglement properties of the system with the interaction and coupling constants.
A method to create paired-atom laser beams from a metastable helium atom laser via four-wave mixing is demonstrated. Radio-frequency outcoupling is used to extract atoms from a Bose-Einstein condensate near the center of the condensate and initiate scattering between trapped and untrapped atoms. The unequal strengths of the interactions for different internal states allows an energy-momentum resonance which leads to the creation of pairs of atoms scattered from the zero-velocity condensate. The resulting scattered beams are well separated from the main atom laser in the two-dimensional transverse atom laser profile. Numerical simulations of the system are in good agreement with the observed atom laser spatial profiles and indicate that the scattered beams are generated by a four-wave mixing process, suggesting that the beams are correlated.
We have studied the characteristics of an atom laser created by removing atoms from a Bose-Einstein condensate (BEC) via a two-photon Raman process. In contrast with outcoupling by RF transitions, Raman outcoupling offers spatial selectivity within the condensate and delivers significant momentum transfer to the outcoupled atoms. We develop a version of zero-temperature mean-field theory for BECs which includes the internal state of the atom and the effect of laser fields focused into the cloud. For a model condensate we find that the outcoupled matter wave develops sharp peaks at spatial positions where the two-photon Raman process is resonant with the hyperfine splitting of the atomic ground state. As time proceeds the width of the outcoupled wave expands and a steady stream of matter waves travels outside the condensate volume.
We propose a direct, coherent coupling scheme that can create massively entangled states of Bose-Einstein-condensed atoms. Our idea is based on an effective interaction between two atoms from coherent Raman processes through a (two-atom) molecular intermediate state. We compare our scheme with other recent proposals for generation of massive entanglement of Bose-Einstein-condensed atoms. We also present explicit calculations that support the possibility of detecting maximally entangled states without requiring single-atom resolved measurements.