Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations

Abstract

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians ${\hat{H}}_k$, each one associated to momentum modes $\pm k$. Each ${\hat{H}}_k$ is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but still very interesting closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly-populated vortices, is investigated considering different choices of the initial conditions, and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

arXiv comment11 pages, 7 figures

References in corpus (27)

• Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
• Phase diagram of two-component bosons on an optical lattice
• Quantum many particle systems in ring-shaped optical lattices
• Degenerate Bose-Bose mixture in a three-dimensional optical lattice
• Superfluidity of Interacting Bosonic Mixtures in Optical Lattices
• Superfluid-insulator transitions of two-species Bosons in an optical lattice
• Phase Separation and Dynamics of two-component Bose-Einstein condensates
• Bogoliubov approach to superfluidity of atoms in an optical lattice
• Symmetry-Breaking and Symmetry-Restoring Dynamics of a Mixture of Bose-Einstein Condensates in a Double Well
• Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices
• Mixtures of strongly interacting bosons in optical lattices
• Effective dynamics of cold atoms flowing in two ring shaped optical potentials with tunable tunneling
• Atomic Josephson junction with two bosonic species
• Demixing Effects in Mixtures of Two Bosonic Species
• Superfluidity and Chaos in low dimensional circuits
• Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
• Bose-Hubbard model with attractive interactions
• Quantum signatures of self-trapping transition in attractive lattice bosons
• Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species
• Optical lattice influenced geometry of quasi-2D binary condensates and quasiparticle spectra
• Variational Polaron Method for Bose-Bose Mixtures
• Coherent Quantum Phase Slip in two-component bosonic Atomtronic Circuits
• Delocalization effects, entanglement entropy and spectral collapse of boson mixtures in a double well
• Quantum properties of a binary bosonic mixture in a double well
• Ehrenfest breakdown of the mean-field dynamics of Bose gases
• Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer
• A continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

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• Pathway toward the formation of supermixed states in ultracold boson mixtures loaded in ring lattices
• The phase-separation mechanism of a binary mixture in a ring trimer
• Residual entropy and critical behavior of two interacting boson species in a double well
• Massive-vortex realization of a Bosonic Josephson Junction
• Correlations in few two-component quantum walkers on a tilted lattice
• Persistent currents in Bose-Bose mixtures after an interspecies interaction quench
• Spatial Phase Separation of a Binary Mixture in a Ring Trimer
• Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons
• Instabilities of a Bose-Einstein condensate with mixed nonlinear and linear lattices
• Quantum-granularity effect in the formation of supermixed solitons in ring lattices
• The Quantum Dynamics of Two-component Bose-Einstein Condensate: an $Sp(4,R)$ Symmetry Approach
• Quantum Echo in Two-Component Bose-Einstein Condensates
• Patterning by dynamically unstable spin-orbit-coupled Bose-Einstein condensates
• Supercurrents and tunneling in massive many-vortex necklaces and star-lattices
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems
• Ground-state phase diagram of two-component interacting bosons on a two-leg ladder