Trapped one-dimensional Bose gas as a Luttinger liquid

Monien, H.; Linn, Marion; Elstner, N.

doi:10.1103/physreva.58.r3395

Cited by 58 publications

(52 citation statements)

References 23 publications

(39 reference statements)

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“…Our calculations predict that reactions (21) and (22) are both exothermic (∆U = −0.0541 and −0.3848 E h , respectively) and that reaction (22) is barrierless. It is interesting that the exothermicities of reactions (19) and (21) are close, and that the proton affinities (reactions (20) and (22)) are also broadly similar.…”

Section: Chemistry Of H +mentioning

confidence: 99%

Chemistry in one dimension

Loos

Ball

Gill

2015

Phys. Chem. Chem. Phys.

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We report benchmark results for one-dimensional (1D) atomic and molecular systems interacting via the Coulomb operator |x| −1 . Using various wavefunction-type approaches, such as Hartree-Fock theory, second-and third-order Møller-Plesset perturbation theory and explicitly correlated calculations, we study the ground state of atoms with up to ten electrons as well as small diatomic and triatomic molecules containing up to two electrons. A detailed analysis of the 1D helium-like ions is given and the expression of the high-density correlation energy is reported. We report the total energies, ionization energies, electron affinities and other interesting properties of the many-electron 1D atoms and, based on these results, we construct the 1D analog of Mendeleev's periodic table. We find that the 1D periodic table contains only two groups: the alkali metals and the noble gases. We also calculate the dissociation curves of various 1D diatomics and study the chemical bond in H + 2 , HeH 2+ , He 3+ 2 , H 2 , HeH + and He 2+ 2 . We find that, unlike their 3D counterparts, 1D molecules are primarily bound by one-electron bonds. Finally, we study the chemistry of H + 3 and we discuss the stability of the 1D polymer resulting from an infinite chain of hydrogen atoms.

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Section: Chemistry Of H +mentioning

confidence: 99%

Chemistry in one dimension

Loos

Ball

Gill

2015

Phys. Chem. Chem. Phys.

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“…Here we focus on the equilibrium state of a low-dimensional (1D and 2D) quantum gas [110,111,112,113,114,115,116,117] which is expected to show persistent phase fluctuations and similar effects in finite temperature condensates in very elongated 3D trapping geometries [118]. These fluctuations are connected to thermal excitations with energies below the lowest radial excitation energies but high enough to cause axial excitations.…”

Section: Phase Fluctuationsmentioning

confidence: 99%

Physics with coherent matter waves

Bongs¹,

Sengstock²

2004

Rep. Prog. Phys.

178

190

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Abstract. This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future. § To whom correspondence should be addressed (sengstock@physnet.uni-hamburg.de) Physics with coherent matter waves 2

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“…The Bose-Fermi mapping of the TG gas is a peculiar aspect of the universal low-energy properties which are exhibited by bosonic and fermionic gapless 1D quantum systems and are described by the Luttinger liquid model [3]. The concept of Luttinger liquid plays a central role in condensed matter physics and the prospect of a clean testing for its physical implications using ultracold gases confined in highly elongated traps is fascinating [4,5].…”

Section: Pacs Numbersmentioning

confidence: 99%

Beyond the Tonks-Girardeau Gas: Strongly Correlated Regime in Quasi-One-Dimensional Bose Gases

et al. 2005

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We consider a homogeneous 1D Bose gas with contact interactions and large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using a variational ansatz for the many-body wavefunction, we show that for small densities the gas-like state is stable and the corresponding equation of state is well described by a gas of hard rods. By calculating the compressibility of the system, we provide an estimate of the critical density at which the gas-like state becomes unstable against cluster formation. Within the hard-rod model we calculate the one-body density matrix and the static structure factor of the gas. The results show that in this regime the system is more strongly correlated than a Tonks-Girardeau gas. The frequency of the lowest breathing mode for harmonically trapped systems is also discussed as a function of the interaction strength. PACS numbers:The study of quasi-1D Bose gases in the quantumdegenerate regime has become a very active area of research. The role of correlations and of quantum fluctuations is greatly enhanced by the reduced dimensionality and 1D quantum gases constitute well suited systems to study beyond mean-field effects [1]. Among these, particularly intriguing is the fermionization of a 1D Bose gas in the strongly repulsive Tonks-Girardeau (TG) regime, where the system behaves as if it consisted of noninteracting spinless fermions [2]. The Bose-Fermi mapping of the TG gas is a peculiar aspect of the universal low-energy properties which are exhibited by bosonic and fermionic gapless 1D quantum systems and are described by the Luttinger liquid model [3]. The concept of Luttinger liquid plays a central role in condensed matter physics and the prospect of a clean testing for its physical implications using ultracold gases confined in highly elongated traps is fascinating [4,5].Bosonic gases in 1D configurations have been realized experimentally. Complete freezing of the transverse degrees of freedom and fully 1D kinematics has been reached for systems prepared in a deep 2D optical lattice [6,7]. The strongly interacting regime has been achieved by adding a longitudinal periodic potential and the transition from a 1D superfluid to a Mott insulator has been observed [8]. A different technique to increase the strength of the interactions, which is largely employed in both bosonic and fermionic 3D systems [9] but has not yet been applied to 1D configurations, consists in the use of a Feshbach resonance. With this method one can tune the effective 1D coupling constant g 1D to essentially any value, including ±∞, by exploiting a confinement induced resonance [10]. For large and positive values of g 1D the system is a TG gas of point-like impenetrable bosons. On the contrary, if g 1D is large and negative, we will show that a new gas-like regime is entered (super-Tonks) where the hard-core repulsion between particles becomes of finite range and correlations are stronger than in the TG...

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Trapped one-dimensional Bose gas as a Luttinger liquid

Cited by 58 publications

References 23 publications

Chemistry in one dimension

Chemistry in one dimension

Physics with coherent matter waves

Beyond the Tonks-Girardeau Gas: Strongly Correlated Regime in Quasi-One-Dimensional Bose Gases

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