Few interacting fermions in a one-dimensional harmonic trap

Sowiński, Tomasz; Graß, Tobias; Dutta, Omjyoti; Lewenstein, Maciej

doi:10.1103/physreva.88.033607

Cited by 87 publications

(135 citation statements)

References 24 publications

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“…Recently, the method has been successfully used for equal mass fermions confined in a harmonic trap [13,62,63] as well as for fermions of different masses [42]. First we decompose the field operatorsΨ σ (x) into the basis of the eigenfunctions of the corresponding single-particle Hamiltonians…”

Section: Exact Diagonalization Approachmentioning

confidence: 99%

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

Pęcak

Sowiński

2016

Phys. Rev. A

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The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.

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Section: Exact Diagonalization Approachmentioning

confidence: 99%

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

Pęcak

Sowiński

2016

Phys. Rev. A

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“…In the pioneering works in this topic, the energy spectra of two trapped atoms was obtained analytically [7,8]. This research was recently followed by the study of the energy spectra of three atoms in a trap in three and reduced dimensions [9][10][11][12][13][14]. Systems of few atoms permit us to study microscopically many interesting phenomena, like the Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate (BCS-BEC) crossover [15].…”

Section: Introductionmentioning

confidence: 99%

Distinguishability, degeneracy, and correlations in three harmonically trapped bosons in one dimension

et al. 2014

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We study a system of two bosons of one species and a third atom of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter-and intraspecies interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical Ansätze gaining physical insight over the numerically obtained wave functions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wave function when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the interspecies and/or the intraspecies interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit us to build up different correlations in the system and lead to different spatial distributions of the three atoms.

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“…(21). In order to obtain the same energy functional as (23), the only way is to consider the following effective Hamiltonian…”

Section: Spin-1/2 Fermionsmentioning

confidence: 99%

“…Recently, taking advantage of the high controllability of a few particles in the trapped ultra-cold systems [20], a number of studies have revealed the energy spectra and correlation effects for a few spin-1/2 fermions by numerical simulations [21][22][23][24]. In the strong coupling regime, an effective Heisenberg spin-chain model has also been deduced [25][26][27][28].…”

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confidence: 99%

Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

Yang

Cui

2016

Phys. Rev. A

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We present a general form of the effective spin-chain model for strongly interacting atomic gases with an arbitrary spin in the one-dimensional(1D) traps. In particular, for high-spin systems the atoms can collide in multiple scattering channels, and we find that the resulted form of spin-chain model generically follows the same structure as that of the interaction potentials. This is a unified form working for any spin, statistics (Bose or Fermi) and confinement potentials. We adopt the spinchain model to reveal both the ferromagnetic(FM) and anti-ferromagnetic(AFM) magnetic orders for strongly interacting spin-1 bosons in 1D traps. We further show that by adding the spin-orbit coupling, the FM/AFM orders can be gradually destroyed and eventually the ground state exhibits universal spin structure and contacts that are independent of the strength of spin-orbit coupling.

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Few interacting fermions in a one-dimensional harmonic trap

Cited by 87 publications

References 24 publications

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

Distinguishability, degeneracy, and correlations in three harmonically trapped bosons in one dimension

Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

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