Quantum rings for beginners II: Bosons versus fermions

Manninen, M.; Viefers, S.; Reimann, S. M.

doi:10.1016/j.physe.2012.09.013

Cited by 29 publications

(21 citation statements)

References 99 publications

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“…This is particularly striking for a bosonic system, which does not display parity effects in other observables e.g. in the persistent currents [38,39]. When the barrier potential is not placed at the center of the harmonic trap, the parity effect is still present, but it is modulated by the position of the barrier, see Fig.…”

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Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

2015

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We consider an interacting, one-dimensional Bose gas confined in a split trap, obtained by an harmonic potential with a localized barrier at its center. We address its quantum-transport properties through the study of dipolar oscillations, which are induced by a sudden quench of the position of the center of the trap. We find that the dipole-mode frequency strongly depends on the interaction strength between the particles, yielding information on the classical screening of the barrier and on its renormalization due to quantum fluctuations. Furthermore, we predict a parity effect which becomes most prominent in the strongly correlated regime.PACS numbers: 05.30. Jp, 67.10.Jn, 03.75.Kk The study of elementary excitations is a fundamental aspect of many-body theories. For neutral quantum fluids, these excitations at low energy correspond to sound waves for homogeneous systems and to inhomogeneous collective modes with discrete frequencies for confined ones. The analysis of the latter in ultracold quantum gases has been the subject of intense experimental [1][2][3][4][5][6][7][8] and theoretical [9][10][11][12][13][14] activity in the last decades. A variety of different excitation modes has been characterized, as the monopole (breathing), dipole (sloshing), quadrupole, and scissor modes, to cite the best known. An unprecedented precision has been reached in the measurement of their frequencies, becoming one of the most reliable tests for theoretical models and tools to investigate many-body phases and beyond-mean field effects [2,[15][16][17]. One of the most interesting aspects of these excitations is that their frequencies depend on the microscopic properties of the system, yielding information e.g. on the equation of state or on its superfluid properties.The analysis of collective modes allows in particular to investigate the interplay between strong interactions and confinement in low-dimensional geometries [18][19][20][21]. In this work, we show that by using a specific confining geometry, i.e. a localized barrier at the center of a quasionedimensional harmonic trap, one can directly access the effect of quantum fluctuations, which play a major role in low dimensions. Effectively one-dimensional systems have been realized in ultracold-atoms experiments, by employing optical lattices to create arrays of tubes or by creating a single atomic waveguide on an atom chip [22][23][24][25]. Strongly correlated phases are more accessible in one-dimensional gases [26], where interparticle interactions may be tuned by confinement-induced resonances, and because, counterintuitively, in one dimension the interactions become dominant in the low-density regime where particle losses and three-body recombination effects are reduced. The demonstration of the peculiar fermionized Tonks-Girardeau phase constitutes a beautiful example [27,28].We focus on the dipolar excitation mode of a onedimensional (1D) ultracold Bose gas, i.e. on a periodic oscillation of the center of mass of the atomic cloud. In ultracold-gas experiments, ...

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confidence: 97%

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

2015

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“…Cross-dimensional effects have been observed [17,18] and also theoretically studied [8,19]. These phenomena in lowdimensional systems have recently been reviewed by [20][21][22][23][24].After achieving success in creating reduced-dimensional systems, physicists began to explore the scattering properties of atoms, hoping to find additional tunability of interactions in ultracold gases. The confinement-induced resonance (CIR) is one such useful tunability of particular interest.…”

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Quasi-one-dimensional scattering with general transverse two-dimensional confinement

Zhang

Greene

2013

Phys. Rev. A

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Confinement-induced resonances (CIR) in quasi-one-dimensional (quasi-1D) systems have been theoretically predicted and observed in various ultracold atomic gases. Here a regularized local frame transformation method is developed to treat CIR in a quasi-1D system that has an arbitrary transverse trap shape in general. The method is applied to predict the CIR position in a system having a square transverse geometry with hard walls. PACS number(s): 03.65.Nk, 68.65.−k, 67.85.−d I. INTRODUCTIONQuantum systems in reduced dimensions have attracted extensive interest dating back at least to the 1950s. Since then, striking predictions have been made for the behavior of quantum gases in reduced dimensions. In both manybody [1-5] and few-body physics [6][7][8], predictions exist that quantum states in reduced dimensional systems will show qualitatively different behavior from isotropic threedimensional (3D) systems, both in the zero-temperature limit and in the thermodynamic limit. Many of these conclusions can be connected to theoretical explorations from the mathematics community into the nature of scattering in a space of arbitrary dimensions [9], dating even farther back in time. However, for a long time, the creation and observation of reduced dimensional systems were hampered by limits on existing experimental techniques. Later, after laser cooling and trapping techniques were developed for ultracold atomic gases [10], many experimental quasi-one-dimensional (quasi-1D) and quasi-twodimensional (quasi-2D) [11][12][13][14] quantum systems were realized and a number of theoretically predicted novel behaviors were observed. In quasi-1D fermionic 40 K [15,16] and bosonic 87 Rb [12], various properties from pure-1D theory have been confirmed. By tuning the ratio(s) of trapping frequencies in different directions (ω ρ /ω z , e.g.), the shape of an ultracold gas can be engineered and varied continuously from a nearly isotropic 3D geometry to a quasi-1D or quasi-2D geometry. Cross-dimensional effects have been observed [17,18] and also theoretically studied [8,19]. These phenomena in lowdimensional systems have recently been reviewed by [20][21][22][23][24].After achieving success in creating reduced-dimensional systems, physicists began to explore the scattering properties of atoms, hoping to find additional tunability of interactions in ultracold gases. The confinement-induced resonance (CIR) is one such useful tunability of particular interest. From an experimental point of view, the CIR adds another way to manipulate and control low-dimensional systems. Dunjko et al. [21] has reviewed developments related to CIR for a variety of systems. The CIR is unique in the sense that the system exhibits the unitarity limit at a nonresonant value of the 3D scattering parameters (i.e., the scattering length for s-wave, and the scattering volume for p wave).The CIR in a harmonically transverse-confined quasi-1D system was predicted theoretically by Olshanii [25], and later extended to fermions by Granger and Blume [26]. In realistic a...

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“…Such behaviour has been derived for bosonic particles featuring an infinity repulsive interaction when confined in a 1D ring. 47 However, we remark that our outcome is issued from highly accurate full quantum calculations and not a theoretical model.…”

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confidence: 94%

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of ³He, ⁴He, and para-H₂

Lara‐Castells

Mitrushchenkov

2021

Phys. Chem. Chem. Phys.

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Quantum rings for beginners II: Bosons versus fermions

Cited by 29 publications

References 99 publications

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Quasi-one-dimensional scattering with general transverse two-dimensional confinement

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of ³He, ⁴He, and para-H₂

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Quantum rings for beginners II: Bosons versus fermions

Cited by 29 publications

References 99 publications

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Quasi-one-dimensional scattering with general transverse two-dimensional confinement

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2

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A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of ³He, ⁴He, and para-H₂