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:cond-mat/0403236 · Journal of Physics B Atomic Molecular and Optical Physics

From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates

Pierfrancesco Buonsante, Roberto Franzosi, Vittorio Penna

Published Mar 24, 2004• 8 citations
arXivHTMLPDF

Abstract

We consider a system formed by an array of Bose–Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose–Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid–Mott transition in Bose–Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.

DOI
10.1088/0953-4075/37/7/065

Related papers

Nonclassical dynamics of Bose-Einstein condensates in an optical lattice in the superfluid regime

Roberto Franzosi

A condensate in an optical lattice, prepared in the ground state of the superfluid regime, is stimulated first by suddenly increasing the optical lattice amplitude and then, after a waiting time, by abruptly decreasing this amplitude to its initial value. Thus the system is first taken to the Mott regime and then back to the initial superfluid regime. We show that, as a consequence of this nonadiabatic process, the system falls into a configuration far from equilibrium whose superfluid order parameter is described in terms of a particular superposition of Glauber coherent states that we derive. We also show that the classical equations of motion describing the time evolution of this system are inequivalent to the standard discrete nonlinear Schr\"odinger equations. By numerically integrating such equations with several initial conditions, we show that the system loses coherence, becoming insulating.

arXiv:0706.2078•Physical Review A•May 24, 2007•4 citations

Superfluid current disruption in a chain of weakly coupled Bose–Einstein condensates

F. S. Cataliotti, L. Fallani, Francesca Ferlaino +3 more

We report the experimental observation of the disruption of the superfluid atomic current flowing through an array of weakly linked Bose–Einstein condensates. The condensates are trapped in an optical lattice superimposed on a harmonic magnetic potential. The dynamical response of the system to a change of the magnetic potential minimum along the optical lattice axis goes from a coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('classical' insulator regime). The localization occurs when the initial displacement is larger than a critical value or, equivalently, when the velocity of the wavepacket's centre of mass is larger than a critical velocity dependent on the rate of tunnelling between adjacent sites.

arXiv:cond-mat/0311410•New Journal of Physics•Jun 13, 2003•197 citations

Dynamics of a trapped Bose Einstein condensate in the presence of a one-dimensional optical lattice

F. S. Cataliotti, L. Fallani, Francesca Ferlaino +3 more

We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.

Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•15 citations

Cold Bosonic Atoms in Optical Lattices

Dieter Jaksch, Christoph Bruder, J. I. Cirac +2 more

The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.

arXiv:cond-mat/9805329•Physical Review Letters•Oct 12, 1998•3,677 citations

Bose–Hubbard model with occupation-dependent parameters

Omjyoti Dutta, André Eckardt, Philipp Hauke +2 more

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.

arXiv:1009.1313•New Journal of Physics•Feb 9, 2011•59 citations

Superfluid State of Strongly-Correlated Bose–Fermi Mixtures on Optical Lattices at Commensurate Filling

Sota Tsukada, Akiko Masaki, 弘之 森

Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites:

Journal of the Physical Society of Japan•Feb 10, 2009•0 citations
We consider a system formed by an array of Bose–Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose–Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid–Mott transition in Bose–Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.
A condensate in an optical lattice, prepared in the ground state of the superfluid regime, is stimulated first by suddenly increasing the optical lattice amplitude and then, after a waiting time, by abruptly decreasing this amplitude to its initial value. Thus the system is first taken to the Mott regime and then back to the initial superfluid regime. We show that, as a consequence of this nonadiabatic process, the system falls into a configuration far from equilibrium whose superfluid order parameter is described in terms of a particular superposition of Glauber coherent states that we derive. We also show that the classical equations of motion describing the time evolution of this system are inequivalent to the standard discrete nonlinear Schr\"odinger equations. By numerically integrating such equations with several initial conditions, we show that the system loses coherence, becoming insulating.
We report the experimental observation of the disruption of the superfluid atomic current flowing through an array of weakly linked Bose–Einstein condensates. The condensates are trapped in an optical lattice superimposed on a harmonic magnetic potential. The dynamical response of the system to a change of the magnetic potential minimum along the optical lattice axis goes from a coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('classical' insulator regime). The localization occurs when the initial displacement is larger than a critical value or, equivalently, when the velocity of the wavepacket's centre of mass is larger than a critical velocity dependent on the rate of tunnelling between adjacent sites.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites: