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Interaction-induced localization of mobile impurities in ultracold systems.

Li J, An J, Ting CS - Sci Rep (2013)

Bottom Line: Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities.Based on our theory, we predict many intriguing phenomena in ultracold systems associated with the extended and localized impurities, including the formation of the impurity-molecules and impurity-lattices.We hope this investigation can open up a new avenue for the future studies on ultracold mobile impurities.

View Article: PubMed Central - PubMed

Affiliation: Texas Center for Superconductivity and Department of Physics, University of Houston, Houston, Texas 77204, USA.

ABSTRACT
The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different from those static impurities in a solid, the impurities realized in cold atomic systems are naturally mobile. Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities. Our theory reveals the interaction-induced transition between the extended and localized impurity states, and also explains the essential features obtained from several previous models in a unified way. Based on our theory, we predict many intriguing phenomena in ultracold systems associated with the extended and localized impurities, including the formation of the impurity-molecules and impurity-lattices. We hope this investigation can open up a new avenue for the future studies on ultracold mobile impurities.

No MeSH data available.


Related in: MedlinePlus

Two-impurity bonding energy and bonding length.(a), the background mediated impurity-impurity energy ET−2ES for two localized fermionic impurities as function of interimpurity distance in 1D, 2D and 3D (from left to right). (b), the bonding energy Ebond and the bonding length aB as function of dimensionless parameters in 1D, 2D and 3D (from left to right). Notice here Ebond is defined as the minimum ET − 2ES and aB is the equilibrium inter-impurity distance. The shadow region marks the parameter space of the formation of the bipolaron. For non-bonding states we have Ebond = 0 and the absence of aB. The numerical results give the critical value  at 1D and  at 2D. aB/λ decreases when the dimensionless parameters are increased in all dimensions, while Ebond shows a non-monotonic behavior in 1D, and at very large β′, Ebond approaches zero but still keeps negative, indicating that the bonding state is very weak in this case.
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f3: Two-impurity bonding energy and bonding length.(a), the background mediated impurity-impurity energy ET−2ES for two localized fermionic impurities as function of interimpurity distance in 1D, 2D and 3D (from left to right). (b), the bonding energy Ebond and the bonding length aB as function of dimensionless parameters in 1D, 2D and 3D (from left to right). Notice here Ebond is defined as the minimum ET − 2ES and aB is the equilibrium inter-impurity distance. The shadow region marks the parameter space of the formation of the bipolaron. For non-bonding states we have Ebond = 0 and the absence of aB. The numerical results give the critical value at 1D and at 2D. aB/λ decreases when the dimensionless parameters are increased in all dimensions, while Ebond shows a non-monotonic behavior in 1D, and at very large β′, Ebond approaches zero but still keeps negative, indicating that the bonding state is very weak in this case.

Mentions: Let us now turn our attention to the fermionic impurities. Two localized fermionic impurities are subject to indirect impurity-impurity interactions mediated by the background. This indirect interaction energy can be interpreted as ET – 2ES, where ES and ET are the energies for one impurity and two correlated impurities, respectively. By constructing a bonding and anti-bonding states of two localized wave functions(available in Supplementary Information) with distance between these two localized impurities a as the variational parameter, and considering ET − 2ES as function of a, transition between bonding and non-bonding states is found. As we can see from Fig. 3a, there is a critical value of the dimensionless parameter in 1D and 2D, above which two localized impurity can bond together at an equilibrium inter-impurity distance a = aB with the bonding energy Ebond < 0. In this case the total energy is lowered when two localized impurities bond together to share the same distortions of the background, and the bound pair can be viewed as an impurity bipolaron. Below the critical value two impurities are non-bonding and shortly repulsive to each other. In 3D bipolaron is always formed as long as the impurities are localized. The two-impurity behaviors in different dimensions, including the boundary between bipolaron and non-bonding state, and behaviors of aB and Ebond, are summarized in Fig. 3b.


Interaction-induced localization of mobile impurities in ultracold systems.

Li J, An J, Ting CS - Sci Rep (2013)

Two-impurity bonding energy and bonding length.(a), the background mediated impurity-impurity energy ET−2ES for two localized fermionic impurities as function of interimpurity distance in 1D, 2D and 3D (from left to right). (b), the bonding energy Ebond and the bonding length aB as function of dimensionless parameters in 1D, 2D and 3D (from left to right). Notice here Ebond is defined as the minimum ET − 2ES and aB is the equilibrium inter-impurity distance. The shadow region marks the parameter space of the formation of the bipolaron. For non-bonding states we have Ebond = 0 and the absence of aB. The numerical results give the critical value  at 1D and  at 2D. aB/λ decreases when the dimensionless parameters are increased in all dimensions, while Ebond shows a non-monotonic behavior in 1D, and at very large β′, Ebond approaches zero but still keeps negative, indicating that the bonding state is very weak in this case.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3818680&req=5

f3: Two-impurity bonding energy and bonding length.(a), the background mediated impurity-impurity energy ET−2ES for two localized fermionic impurities as function of interimpurity distance in 1D, 2D and 3D (from left to right). (b), the bonding energy Ebond and the bonding length aB as function of dimensionless parameters in 1D, 2D and 3D (from left to right). Notice here Ebond is defined as the minimum ET − 2ES and aB is the equilibrium inter-impurity distance. The shadow region marks the parameter space of the formation of the bipolaron. For non-bonding states we have Ebond = 0 and the absence of aB. The numerical results give the critical value at 1D and at 2D. aB/λ decreases when the dimensionless parameters are increased in all dimensions, while Ebond shows a non-monotonic behavior in 1D, and at very large β′, Ebond approaches zero but still keeps negative, indicating that the bonding state is very weak in this case.
Mentions: Let us now turn our attention to the fermionic impurities. Two localized fermionic impurities are subject to indirect impurity-impurity interactions mediated by the background. This indirect interaction energy can be interpreted as ET – 2ES, where ES and ET are the energies for one impurity and two correlated impurities, respectively. By constructing a bonding and anti-bonding states of two localized wave functions(available in Supplementary Information) with distance between these two localized impurities a as the variational parameter, and considering ET − 2ES as function of a, transition between bonding and non-bonding states is found. As we can see from Fig. 3a, there is a critical value of the dimensionless parameter in 1D and 2D, above which two localized impurity can bond together at an equilibrium inter-impurity distance a = aB with the bonding energy Ebond < 0. In this case the total energy is lowered when two localized impurities bond together to share the same distortions of the background, and the bound pair can be viewed as an impurity bipolaron. Below the critical value two impurities are non-bonding and shortly repulsive to each other. In 3D bipolaron is always formed as long as the impurities are localized. The two-impurity behaviors in different dimensions, including the boundary between bipolaron and non-bonding state, and behaviors of aB and Ebond, are summarized in Fig. 3b.

Bottom Line: Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities.Based on our theory, we predict many intriguing phenomena in ultracold systems associated with the extended and localized impurities, including the formation of the impurity-molecules and impurity-lattices.We hope this investigation can open up a new avenue for the future studies on ultracold mobile impurities.

View Article: PubMed Central - PubMed

Affiliation: Texas Center for Superconductivity and Department of Physics, University of Houston, Houston, Texas 77204, USA.

ABSTRACT
The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different from those static impurities in a solid, the impurities realized in cold atomic systems are naturally mobile. Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities. Our theory reveals the interaction-induced transition between the extended and localized impurity states, and also explains the essential features obtained from several previous models in a unified way. Based on our theory, we predict many intriguing phenomena in ultracold systems associated with the extended and localized impurities, including the formation of the impurity-molecules and impurity-lattices. We hope this investigation can open up a new avenue for the future studies on ultracold mobile impurities.

No MeSH data available.


Related in: MedlinePlus