Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2408.06125 · Physical Review A

Engineering the Bogoliubov modes through geometry and interaction: From collective edge modes to flat-band excitations

Maryam Darvishi, Fatemeh Pouresmaeeli, Saeed H. Abedinpour

Published Jun 5, 2025• 1 citation
arXivHTMLPDF

Abstract

We propose a procedure to engineer solid-state lattice models with superlattices of interaction-coupled Bose-Einstein condensates. We show that the dynamical equation for the excitations of Bose-Einstein condensates at zero temperature can be expressed in an eigenvalue form that resembles the time-independent Schr{ö}dinger equation. The eigenvalues and eigenvectors of this equation correspond to the dispersions of the collective modes and the amplitudes of the density oscillations. This alikeness opens the way for the simulation of different tight-binding models with arrays of condensates. We demonstrate, in particular, how we can model a one-dimensional Su-Schrieffer-Heeger lattice supporting topological edge modes and a two-dimensional Lieb lattice with flat-band excitations with superlattices of Bose-Einstein condensates.

DOI
10.1103/6888-q2cd

Related papers

Excitation band topology and edge matter waves in Bose–Einstein condensates in optical lattices

Shunsuke Furukawa, Masahito Ueda

We show that Bose–Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose–Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.

arXiv:1506.04556•New Journal of Physics•Nov 27, 2015•49 citations

Optical-lattice-influenced geometry of quasi-two-dimensional binary condensates and quasiparticle spectra

Kuldeep Suthar, D. Angom

We explore the collective excitation of two-species Bose-Einstein condensates (TBECs) confined in quasi-two-dimensional optical lattices. For this we use a set of coupled discrete nonlinear Schr\"odinger equations to describe the system and we employ Hartree-Fock-Bogoliubov theory with the Popov approximation to analyze the quasiparticle spectra at zero temperature. The ground-state geometry, evolution of quasiparticle energies, structure of quasiparticle amplitudes, and dispersion relations are examined in detail. We observe that the TBEC acquires a side-by-side density profile when it is tuned from the miscible to the immiscible phase. In addition, the quasiparticle energies are softened as the system is tuned towards phase separation, but harden after phase separation and mode degeneracies are lifted. In terms of structure, in the miscible phase the quasiparticles have well-defined azimuthal quantum numbers, but that is not the case for the immiscible phase.

arXiv:1603.02455•Physical Review A•Jun 7, 2016•26 citations

Superfluid dynamics of a Bose–Einstein condensate in a one-dimensional optical superlattice

Aranya B. Bhattacherjee

We derive and study the Bloch and Bogoliubov spectrum of a Bose–Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with mode coupling. We show that a BEC in an optical superlattice experiences two different tunnelling parameters and hence behaves like a diatomic chain. We derive expressions for the tunnelling parameters as a function of the strength of the primary and secondary lattice. This gives rise to a gapped branch in addition to the gapless acoustical branch in the Bogoliubov spectrum. The spectrum strongly depends on the strength of the secondary lattice, the interaction parameter and the number density of atoms. The effective mass is found to increase as the depth of the secondary optical lattice increases, a property that was utilized in Paraedes et al (2004 Nature 429 277) to achieve the Tonks–Girardeau regime. The coupling between the inhomogeneous density in the radial plane and the density modulation along the optical lattice gives rise to a multibranch Bogoliubov spectrum.

arXiv:cond-mat/0603424•Journal of Physics B Atomic Molecular and Optical Physics•Dec 19, 2006•8 citations

\pi-flux Dirac bosons and Bogoliubov edge states of Bose-Einstein condensed atoms

Zhi-Fang Xu, Li You, Andreas Hemmerich +1 more

Topological edge states and Dirac fermions are fascinating phenomena known for fermionic systems. Whether similar phenomena can occur for interacting bosons is an open question in fundamental science. The recent observation of $^{87}$Rb chiral $p_x\pm ip_y$ condensates in a checkerboard optical lattice further raises the question whether a bosonic superfluid can be topological. Here we show that Dirac bosons experiencing a $\pi$ Berry flux emerge in the elementary excitation spectra of this experimentally realized Bose system. Tuning a population bias between the observed $p_x+ip_y$ and $p_x-ip_y$ condensate components opens an energy gap in the bulk, which results in Chern invariant and topologically protected Bogoliubov edge modes. Different from previous topological scenarios that employ the concept of engineered spin-orbit coupling or the equivalent in single-particle Bloch bands, spontaneous chiral orbital order driven by many-body interaction is a crucial ingredient in our finding.

•Feb 15, 2016•0 citations

Doublons, topology and interactions in a one-dimensional lattice

Pablo Martínez-Azcona, Charles Andrew Downing

We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.

arXiv:2105.04406•Scientific Reports•Jun 15, 2021•19 citations

Quantum Geometry and Flat Band Bose-Einstein Condensation

Aleksi Julku, Georg M. Bruun, Päivi Törmä

We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.

arXiv:2104.14257•Physical Review Letters•Oct 21, 2021•61 citations
We propose a procedure to engineer solid-state lattice models with superlattices of interaction-coupled Bose-Einstein condensates. We show that the dynamical equation for the excitations of Bose-Einstein condensates at zero temperature can be expressed in an eigenvalue form that resembles the time-independent Schr{ö}dinger equation. The eigenvalues and eigenvectors of this equation correspond to the dispersions of the collective modes and the amplitudes of the density oscillations. This alikeness opens the way for the simulation of different tight-binding models with arrays of condensates. We demonstrate, in particular, how we can model a one-dimensional Su-Schrieffer-Heeger lattice supporting topological edge modes and a two-dimensional Lieb lattice with flat-band excitations with superlattices of Bose-Einstein condensates.
We show that Bose–Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose–Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.
We explore the collective excitation of two-species Bose-Einstein condensates (TBECs) confined in quasi-two-dimensional optical lattices. For this we use a set of coupled discrete nonlinear Schr\"odinger equations to describe the system and we employ Hartree-Fock-Bogoliubov theory with the Popov approximation to analyze the quasiparticle spectra at zero temperature. The ground-state geometry, evolution of quasiparticle energies, structure of quasiparticle amplitudes, and dispersion relations are examined in detail. We observe that the TBEC acquires a side-by-side density profile when it is tuned from the miscible to the immiscible phase. In addition, the quasiparticle energies are softened as the system is tuned towards phase separation, but harden after phase separation and mode degeneracies are lifted. In terms of structure, in the miscible phase the quasiparticles have well-defined azimuthal quantum numbers, but that is not the case for the immiscible phase.
We derive and study the Bloch and Bogoliubov spectrum of a Bose–Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with mode coupling. We show that a BEC in an optical superlattice experiences two different tunnelling parameters and hence behaves like a diatomic chain. We derive expressions for the tunnelling parameters as a function of the strength of the primary and secondary lattice. This gives rise to a gapped branch in addition to the gapless acoustical branch in the Bogoliubov spectrum. The spectrum strongly depends on the strength of the secondary lattice, the interaction parameter and the number density of atoms. The effective mass is found to increase as the depth of the secondary optical lattice increases, a property that was utilized in Paraedes et al (2004 Nature 429 277) to achieve the Tonks–Girardeau regime. The coupling between the inhomogeneous density in the radial plane and the density modulation along the optical lattice gives rise to a multibranch Bogoliubov spectrum.
Topological edge states and Dirac fermions are fascinating phenomena known for fermionic systems. Whether similar phenomena can occur for interacting bosons is an open question in fundamental science. The recent observation of 87^{87}87Rb chiral px±ipyp_x\pm ip_ypx​±ipy​ condensates in a checkerboard optical lattice further raises the question whether a bosonic superfluid can be topological. Here we show that Dirac bosons experiencing a π\piπ Berry flux emerge in the elementary excitation spectra of this experimentally realized Bose system. Tuning a population bias between the observed px+ipyp_x+ip_ypx​+ipy​ and px−ipyp_x-ip_ypx​−ipy​ condensate components opens an energy gap in the bulk, which results in Chern invariant and topologically protected Bogoliubov edge modes. Different from previous topological scenarios that employ the concept of engineered spin-orbit coupling or the equivalent in single-particle Bloch bands, spontaneous chiral orbital order driven by many-body interaction is a crucial ingredient in our finding.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.