NDLI: Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results

Content Provider	Springer Nature Link
Author	Marchukov, Oleksandr V. Eriksen, Emil H. Midtgaard, Jonatan M. Kalaee, Alex A.S. Fedorov, Dmitri V. Jensen, Aksel S. Zinner, Nikolaj T.
Copyright Year	2016
Abstract	One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining potentials the local exchanges are given by highly non-trivial geometric factors that depend solely on the geometry of the confinement through the single-particle eigenstates of the external potential. To obtain accurate effective Hamiltonians to describe such systems one needs to be able to compute these geometric factors with high precision which is difficult due to the computational complexity of the high-dimensional integrals involved. An approach using the local density approximation would therefore be a most welcome approximation due to its simplicity. Here we assess the accuracy of the local density approximation by going beyond the simple harmonic oscillator that has been the focus of previous studies and consider some double-wells of current experimental interest. We find that the local density approximation works quite well as long as the potentials resemble harmonic wells but break down for larger barriers. In order to explore the consequences of applying the local density approximation in a concrete setup we consider quantum state transfer in the effective spin models that one obtains. Here we find that even minute deviations in the local exchange coefficients between the exact and the local density approximation can induce large deviations in the fidelity of state transfer for four, five, and six particles.
Starting Page	1
Ending Page	12
Page Count	12
File Format	PDF
ISSN	14346060
Journal	The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics
Volume Number	70
Issue Number	2
e-ISSN	14346079
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-02-09
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cold Matter and Quantum Gas Atomic, Molecular, Optical and Plasma Physics Physical Chemistry Quantum Physics Quantum Information Technology, Spintronics Spectroscopy/Spectrometry Nonlinear Dynamics
Content Type	Text
Resource Type	Article
Subject	Atomic and Molecular Physics, and Optics

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