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Journal of Nano- and Electronic Physics

Entanglement Properties of a Three-Mode Atom-Molecule Bose-Einstein Condensates System Considering the Interactions due to the s-wave Intramodal Elastic Scattering

S. K. Giri

Published Jan 1, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.21272/jnep.15(6).06003

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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.
An analytic operator solution of a generalized quantum mechanical Hamiltonian of two-mode Bose-Einstein condensates (BECs) is obtained for short-time dynamics and the same is used to investigate the nonclassical properties of the modes present in the system. Nonclassical characters are observed by means of single-mode and intermodal quadrature squeezing, single-mode and intermodal sub-Poissonian boson statistics, and intermodal entanglement. In addition to the traditionally studied lower-order nonclassical properties, signatures of higher-order nonclassical characters of two-mode BEC systems are also obtained by investigating the possibility of higher-order antibunching and higher-order entanglement. The mutual relation among the observed nonclassicalities and their evolution (variation) with time and the ratio of the single boson tunneling amplitude ($\ensuremath{\varepsilon}$) and the coupling constant for the intramodal interaction ($\ensuremath{\kappa}$) are also reported.
We investigate the conversion of a Bose-Einstein condensate (BEC) of a weakly interacting gas into a molecular BEC (MBEC) by Bose-stimulated Raman adiabatic passage (STIRAP). This method of producing an MBEC does not experience large spontaneous losses while the condensate is in an excited electronic state, and it is robust with respect to small changes in the physical parameters. We show that the atomic interactions affect the quantum statistics of the resulting field, although they do not interfere with the production of the MBEC. We demonstrate that STIRAP is still feasible when we include the spatial degrees of freedom that cause the Bose-enhanced coupling rate to vary across the condensate. The complete conversion is destroyed by spatial effects unless the time scale of the coupling is much faster than the propagation time, which in practice requires submillisecond conversion.
Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In particular, we study the entanglement between the atoms in the condensate as well as that between the two modes. The nature of the enhanced quantum correlations in TBEC is clarified by considering squeezing and entanglement both with and without the nonlinear interaction turned on; it is found that entanglement approaching maximal value can be achieved with the nonlinear interactions present. Somewhat counterintuitively, greater squeezing is found in the absence of nonlinear interactions. This is due to the collapses and revivals of the TBEC quantum state induced by the nonlinear interactions. In addition, results involving the self-trapping phase state of TBEC indicate potential for creating a dynamically stable, macroscopic entangled quantum state which is relatively robust with respect to atom number fluctuations.
The process of stimulated Raman adiabatic passage (STIRAP) provides a possible route for the generation of a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. We analyze this process in a three-dimensional mean-field theory, including atom-atom interactions and nonresonant intermediate levels. We find that the process is feasible, but at larger Rabi frequencies than anticipated from a crude single-mode lossless analysis, due to two-photon dephasing caused by the atomic interactions. We then identify optimal strategies in STIRAP allowing one to maintain high conversion efficiencies with smaller Rabi frequencies and under experimentally less demanding conditions.
We study coherent photoassociation, phenomena analogous to coherent optical transients in few-level systems, which may take place in photoassociation of an atomic Bose-Einstein condensate but not in a nondegenerate gas. We develop a second-quantized Hamiltonian to describe photoassociation, and apply the Hamiltonian both in the momentum representation and in the position representation (field theory). The solution of the two-mode problem, including only one mode each for the atomic and molecular condensates, displays analogs of Rabi oscillations and rapid adiabatic passage. 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 density fluctuations. Experimental complications, including spontaneous emission and unwanted ``rogue'' photodissociation from a photoassociated molecule, are analyzed. A two-color Raman scheme is studied as a method to set up an effective two-mode scheme with reduced spontaneous-emission losses. We discuss photoassociation rates and photoassociation Rabi frequencies for high-lying vibrational states in alkali dimers both on the basis of molecular-structure calculations, and by comparing with an experiment [Wynar et al., Science 287, 1016 (2000)].
Abstract Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a 87Rb BEC has been used to produce 87Rb2 molecules in a single rotational-vibrational state1, and ultracold molecules have also been formed2 through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work3, 4, 5, 6, 7. Here we make use of a time-varying magnetic field near a Feshbach resonance8, 9, 10, 11, 12 to produce coherent coupling between atoms and molecules in a 85Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules—two chemically different species.