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 ˆ H k , each one associated to momentum modes ± k . Each ˆ 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 nontrivial 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.

Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations / Penna, V.; Richaud, A.. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - STAMPA. - 96:(2017). [10.1103/PhysRevA.96.053631]

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

Penna, V.;Richaud , A.
2017

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 ˆ H k , each one associated to momentum modes ± k . Each ˆ 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 nontrivial 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.
File in questo prodotto:
File Dimensione Formato  
PRA96_053631pr.pdf

non disponibili

Descrizione: PRA96_053631pr.pdf
Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 1.05 MB
Formato Adobe PDF
1.05 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2693854
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo