Two peaks in the momentum distribution of bosons in a weakly frustrated two-leg optical ladder

Cha, Min-Chul; Shin, Jong-Geun

doi:10.1103/physreva.83.055602

Cited by 27 publications

(25 citation statements)

References 26 publications

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“…(We set t = 1 here.) As noted previously [7,15], the boson momentum distribution n(k) in the presence of π-flux exhibits two peaks; for our gauge choice, these peaks are located at k = 0, π. In the CSF state, which is a Luttinger liquid [26] on the ladder, we have a singular momentum distribution n(k → 0) ∼ |k| −(1−K/2) , with K > 0 being an interaction dependent Luttinger parameter [22].…”

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confidence: 76%

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

et al. 2012

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Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the "fully frustrated" Bose-Hubbard (FFBH) model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a 2-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.The simplest model to understand strongly correlated bosons is the Bose-Hubbard (BH) model [1] which describes bosons hopping on a lattice and interacting via a local repulsive interaction. With increasing repulsion, at integer filling, its ground state undergoes a superfluid to Mott insulator quantum phase transition which has been studied using ultracold atoms in an optical lattice [2].Remarkably, recent experiments have used two-photon Raman transitions to create a uniform or staggered "synthetic magnetic field" for neutral atoms [3], permitting one to access large magnetic fields for lattice bosons. The multiple degenerate minima in the resulting Hofstadter spectrum can be populated by non-interacting bosons in many ways. Repulsive interactions quench this "kinetic frustration", leading to unconventional superfluids [4][5][6][7], or quantum Hall liquids [8]. Tuning the sign of the atom hopping amplitude or populating higher bands also leads to such frustrated bosonic fluids [4]. These developments motivate us to study the interplay of strong correlations and frustration in the fully frustrated BoseHubbard (FFBH), with half a "magnetic flux" quantum per plaquette [5][6][7]. At large integer filling, the FFBH is also the simplest quantum variant of the classical fully frustrated XY (FFXY) model [9, 10] of Josephson junction arrays (JJAs) [11].Here, we obtain the phase diagram shown in Fig. 1 of the FFBH model at integer filling on a 2-leg ladder using the density matrix renormalization group (DMRG) method [12] and Monte Carlo (MC) simulations. Our key result is that the ground state of the FFBH and quantum FFXY models at intermediate Hubbard repulsion is a chiral Mott Insulator (CMI). The CMI has a nonzero charge gap, and simultaneously supports staggered loop currents that spontaneously break time reversal symmetry. With increasing repulsion, the CMI undergoes an Ising transition into an ordinary Mott insulator (MI) where the loop currents vanish. Weakening the repulsion leads to a Berezinskii-Kosterlitz-Thouless (BKT) [13] transition out of the CMI into a previously studied

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confidence: 76%

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

et al. 2012

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“…Bosons on a ladder subjected to gauge fields have been the topic of previous theoretical work [37][38][39][40][41][42][43][44] (see also [45,46] for 2D lattices), yet complete quantitative phase diagrams are lacking. In our work, we use DMRG to systematically explore the full dependence on J ⊥ , φ, and filling and, as a main result, we observe both gapped and gapless Meissner and vortex phases for stronglyinteracting bosons.…”

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Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

et al. 2015

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We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Introduction. The quantum states of interacting electrons in the presence of spin-orbit coupling and magnetic fields are attracting significant attention in condensed matter physics because of their connection to Quantum Hall physics [1], topological insulators [2-4] and the emergence of unusual excitations in low dimensions [5,6]. Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed.

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“…The possibility to mimic the bosonic flux ladder by using ultracold atoms in optical lattices, that was brought to reality in the laboratory experiment [1], has renewed the theoretical interest to this unordinary quantum system [2][3][4][5][6][7]. By definition, the ladder consists of two coupled one-dimensional lattices where the quantum particle hops along the ladder legs with the rate J/h and along the ladder rungs with the rate J ⊥ /h.…”

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confidence: 99%

Bogoliubov depletion of the fragmented condensate in the bosonic flux ladder

Kolovsky

2017

Phys. Rev. A

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We theoretically analyze the ground state of weakly interacting bosons in the flux ladder -the system that has been recently realized by means of ultacold atoms in the specially designed optical lattice [M. Atala, et al., Nat. Phys. 10, 588 (2014)]. It is argued that, for the system parameters corresponding to the so-called 'vortex phase', the ground state is a fragmented condensate. We study the Bogoliubov depletion of this condensate and discuss the role of boundary conditions.

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Two peaks in the momentum distribution of bosons in a weakly frustrated two-leg optical ladder

Cited by 27 publications

References 26 publications

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

Bogoliubov depletion of the fragmented condensate in the bosonic flux ladder

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