Slightly Imbalanced System of a Few Attractive Fermions in a One-Dimensional Harmonic Trap

Sowiński, Tomasz

doi:10.1007/s00601-015-1017-5

Cited by 12 publications

(12 citation statements)

References 21 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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“…Tunneling experiments in the few-body limit demonstrated single-atom control [6,7]. One has already observed the formation of a Fermi sea [8], as well as pair correlations in onedimensional (1D) few-body atomic gases [5] that have also been studied extensively theoretically [9][10][11][12][13]. The few-to many-body transition is arguably even more interesting in higher dimensions, where quantum phase transitions with varying degrees of broken symmetry are ubiquitous [14].…”

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confidence: 99%

“…is the angular momentum. This method has been extensively applied to attractive fermion systems, mainly in 1D [9][10][11][12][13] but also in 2D [31,32] Using a sparse representation of the resulting matrix, we find the eigenvectors using the implicitly restarted Arnoldi iteration method [36]. This generally allows for a significantly larger number of basis states, ∼ 10 7 , as compared to other available diagonalisation methods, which is crucial, since we need a very large basis set for an accurate calculation of the low-lying collective modes.…”

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confidence: 99%

Few-Body Precursor of the Higgs Mode in a Fermi Gas

2016

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We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalisation, the lowest monopole mode frequency is shown to depend non-monotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the fewbody analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using for instance a Feshbach resonance in cold atomic gases.The transition from few-body quantum physics to the thermodynamic limit with increasing particle number is a fundamental problem in science. A systematic investigation of this question is complicated by the fact that the few-body systems existing in nature, such as atoms and nuclei, have limited tunability. Artificially created clusters [1,2] or semiconductor quantum dots [3] offer more flexibility, but they are often strongly coupled to their surroundings making a study of pure quantum states difficult. The creation of highly controllable fewfermion systems using cold atoms in microtraps [4,5], however, has opened new perspectives. Tunneling experiments in the few-body limit demonstrated single-atom control [6,7]. One has already observed the formation of a Fermi sea [8], as well as pair correlations in onedimensional (1D) few-body atomic gases [5] that have also been studied extensively theoretically [9][10][11][12][13]. The few-to many-body transition is arguably even more interesting in higher dimensions, where quantum phase transitions with varying degrees of broken symmetry are ubiquitous [14]. A key question concerns the few-body fate of the order parameter, which describes a broken symmetry phase in the thermodynamic limit.Another fundamental problem concerns the properties of the Higgs mode, which corresponds to oscillations in the size of the order parameter for a given broken symmetry phase [15,16]. Elementary particles acquire their mass from the presence of a Higgs mode [17], which was famously observed at CERN [18,19]. The Higgs mode also leads to collective modes in condensed matter and nuclear systems [14,20]. Despite its fundamental importance, the list of table top systems where it has been observed is short, mainly because it is typically strongly damped, and because it couples only weakly to experimental probes [21][22][23]. Experimental evidence for the existence of a Higgs mode has been reported in disordered and niobium selenide superconductors [24][25][26][27]. Also, neutron scattering experiments for a quantum antiferromagnet [28] are consistent with the presence of a broad Higgs mode, and lattice experiments combined with theoretical models for bosonic atoms in an optical lattice, indicate that a threshold feature can be interpreted i...

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“…Quite a different approach to imbalanced fermionic mixtures was presented in [305], where systems with additional unpaired fermion were analyzed. Based on a description in the language of the reduced two-particle density matrix, it was shown that in the case studied, the pairing between fermions of opposite spins has completely different features that in the balanced case.…”

Section: H Attractive Forcesmentioning

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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Slightly Imbalanced System of a Few Attractive Fermions in a One-Dimensional Harmonic Trap

Cited by 12 publications

References 21 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

Few-Body Precursor of the Higgs Mode in a Fermi Gas

One-dimensional mixtures of several ultracold atoms: a review

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