Multiband bosons in optical lattices

Larson, Jonas; Collin, A.; Martikainen, Jani-Petri

doi:10.1103/physreva.79.033603

Cited by 55 publications

(68 citation statements)

References 31 publications

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“…where J k = 2dJ − k with k being the energy of a free particle (140). This system is valid for both phases and generalizes the Bogoliubov-de Gennes (BdG) equations previously derived for coherent states [381,382].…”

Section: Excitationsmentioning

confidence: 58%

“…which can be also obtained from the well-known expression for the ideal Bose gas in a homogeneous continuous space [188] replacing the mass M by the effective mass (93) which follows from the dispersion relation of non-interacting particles in a lattice (140). In the opposite limit, n l 1, T c is large and the sum in Eq.…”

Section: Critical Temperature For the Condensationmentioning

confidence: 99%

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Ultracold bosons with short-range interaction in regular optical lattices

2016

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During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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Section: Excitationsmentioning

confidence: 58%

Section: Critical Temperature For the Condensationmentioning

confidence: 99%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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“…More recently, progress in controlling and stabilizing atoms in the excited bands of an optical lattice [5][6][7][8] has given rise to the exciting possibility of simulating multiband condensed matter Hamiltonians, which involve a nontrivial interplay of spin, charge, and orbital degrees of freedom. These achievements have precipitated a variety of theoretical investigations into the new physics made possible by the orbital degrees of freedom in an optical lattice [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the bosonic Kondo-Hubbard model

Foss‐Feig

Rey

2011

Phys. Rev. A

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We study a bosonic version of the Kondo lattice model with an on-site repulsion in the conduction band, implemented with alkali atoms in two bands of an optical lattice. Using both weak and strongcoupling perturbation theory, we find that at unit filling of the conduction bosons the superfluid to Mott insulator transition should be accompanied by a magnetic transition from a ferromagnet (in the superfluid) to a paramagnet (in the Mott insulator). Furthermore, an analytic treatment of Gutzwiller mean-field theory reveals that quantum spin fluctuations induced by the Kondo exchange cause the otherwise continuous superfluid to Mott-insulator phase transition to be first order. We show that lattice separability imposes a serious constraint on proposals to exploit excited bands for quantum simulations, and discuss a way to overcome this constraint in the context of our model by using an experimentally realized non-separable lattice. A method to probe the first-order nature of the transition based on collapses and revivals of the matter-wave field is also discussed.

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“…This extra energy shift of order µ for high momentum states is a consequence of exchange interactions with the zero-momentum condensate. Indeed, the modification of the energy-momentum dispersion results not from momentum-dependent collisional interactions, but rather from the quantum statistics of the identical bosons in distinguishable motional states [25][26][27]. This is analogous to the effective magnetic interactions of electrons in condensed matter that result from spin-independent Coulomb interactions and exchange statistics.…”

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confidence: 99%

Correlated Dynamics in a Synthetic Lattice of Momentum States

Meier

Ang’ong’a

et al. 2018

Phys. Rev. Lett.

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We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven atomic transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the distinguishability of the discrete momentum states coupled in MSLs gives rise to an added exchange energy between condensate atoms in different momentum orders, relating to an effectively attractive, finite-ranged interaction in momentum space. We explore the types of phenomena that can result from this interaction, including the formation of chiral self-bound states in topological MSLs. We also discuss the prospects for creating squeezed states in momentum-space double wells.Quantum simulation with ultracold atoms [1,2] has been a powerful tool in the study of many-body physics and nonequilibrium dynamics. There has been recent interest in extending quantum simulation studies from real-space potentials to synthetic lattice systems composed of discrete internal [3,4] or external [5] states. These synthetic dimensions enable many unique capabilities for quantum simulation, including new approaches to engineering nontrivial topology [4,6], access to higher dimensions [3], and potential insensitivity to finite motional temperature.The recent development of momentum-space lattices (MSLs), based on the use of discrete momentum states as effective sites, has introduced a fully synthetic approach to simulating lattice dynamics [7][8][9][10][11]. As compared to partially synthetic systems [12,13], fully synthetic lattices offer complete microscopic control of system parameters. While this level of control is analogous to that found in photonic simulators [14,15], matter waves of atoms can interact strongly with one another.However, fully synthetic systems also present apparent challenges for studying nontrivial atomic interactions. Synthetic systems based purely on internal states suffer from limited state spaces, sensitivity to external noise for generic, field-sensitive states [16], and possible collisional relaxation [17] and three-body losses [18]. Furthermore, for isotropic scattering lengths as in 87 Rb [16] and alkaline earth atoms [19], interactions in the synthetic dimension are nearly all-to-all. Similarly, s-wave contact interactions relate to nearly infinite-ranged momentumspace interactions at low energy, and should naively be decoupled from particle dynamics in MSLs.Here, we investigate the role of atomic interactions in MSLs, showing that finite-ranged interactions in momentum space result from the exchange energy of bosonic condensate atoms in distinguishable momentum states. We explore potential interaction-driven phenomena that can be studied in topological MSLs, showing that chiral propagating bound states can emerge in the presence of an artificial magnetic flux. We additionally discuss the use of momentum-space double wells for the gener...

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Multiband bosons in optical lattices

Cited by 55 publications

References 31 publications

Ultracold bosons with short-range interaction in regular optical lattices

Ultracold bosons with short-range interaction in regular optical lattices

Phase diagram of the bosonic Kondo-Hubbard model

Correlated Dynamics in a Synthetic Lattice of Momentum States

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