Fermionized Dipolar Bosons Trapped in a Harmonic Trap

Kościk, Przemysław

doi:10.1007/s00601-017-1229-y

Cited by 8 publications

(5 citation statements)

References 12 publications

(21 reference statements)

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“…where K 0 = Ψ 0 |H ab |Ψ 0 /g. For a given K ∞ opt we can now find a new value of Ψ 0 |Ψ ∞ , which can be inserted in the expression for the optimized energy (11). In this way one obtains much better estimation of the groundstate energy.…”

Section: Final Remarksmentioning

confidence: 99%

“…One-dimensional systems of few quantum particles have attracted a lot of attention in the past few years due to the amazing experimental progress in studying such systems. At last, it becomes possible not only to test and improve theoretical description of such systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], but also to test all these theoretical ideas experimentally [17][18][19][20][21][22][23][24][25][26][27]. New experiments of an extremely high accuracy have challenged theoreticians to serve predictions with incredible precision and as a consequence to audit previous rough approximations made to describe properties of few quantum bodies [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach

et al. 2017

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Detailed analysis of the system of four interacting ultra-cold fermions confined in a onedimensional harmonic trap is performed. The analysis is done in the framework of a simple variational ansatz for the many-body ground state and its predictions are confronted with the results of numerically exact diagonalization of the many-body Hamiltonian. Short discussion on the role of the quantum statistics, i.e. Bose-Bose and Bose-Fermi mixtures is also presented. It is concluded that the variational ansatz, although seemed to be oversimplified, gives surprisingly good predictions of many different quantities for mixtures of equal as well as different mass systems. The result may have some experimental importance since it gives quite simple and validated method for describing experimental outputs. arXiv:1703.08720v2 [cond-mat.quant-gas]

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Section: Final Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach

et al. 2017

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“…and the leading term has the typical form for dipolar interactions, 1/ξ 3 . This observation opens a route to a simplified description of the system in the crystallization limit (similarly as done for ultracold ions [358]), i.e., when particles are spatially well-separated [359][360][361]. Note that the general form of the one-dimensional dipolar potential (68) can be very unstable from the numerical point of view if calculated straightforwardly.…”

Section: B Dipolar Interactionsmentioning

confidence: 99%

One-dimensional mixtures of several ultracold atoms: a review

Sowiński¹,

2019

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Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two-and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higherspin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification. :1903.12189v3 [cond-mat.quant-gas] CONTENTS arXiv

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“…[24][25][26] In the context of variational approaches applied to few-body problems, some effort was devoted recently to construct an appropriate variational trial wave function for particles confined in traps being close to parabolic shape. [27][28][29] Starting from the well-known exact solution for two interacting particles, 30 following the Jastrow idea, 31 there were proposed reasonable many-body wave functions for bosons 32,33 as well as fermions. 34 Some sort of generalization to multi-component systems was also given.…”

Section: Introductionmentioning

confidence: 99%

Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

Kościk,

Kuroś,

Pieprzycki

et al. 2021

Preprint

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We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

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Fermionized Dipolar Bosons Trapped in a Harmonic Trap

Cited by 8 publications

References 12 publications

Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach

Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach

One-dimensional mixtures of several ultracold atoms: a review

Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

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