Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Valiente, Manuel; Petrosyan, David

doi:10.1209/0295-5075/83/30007

Cited by 27 publications

(42 citation statements)

References 21 publications

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“…In the case of nonvanishing V T the single-particle eigenstates become qualitatively different [205][206][207][208]. They can be separated into two parts and some transient regime between those.…”

Section: Harmonic Trapmentioning

confidence: 99%

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: Harmonic Trapmentioning

confidence: 99%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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“…We expand the Hamiltonian parameters around the centre of the well and account for the hopping via an effective mass that is dependent on the hopping strength. Reference [71] considers a similar derivation for the case of a 1D Bose-Hubbard model. For a full derivation see appendix D. Following these approximations, we obtain the eigenstates to be of the form [71]…”

Section: High Filling Regimementioning

confidence: 99%

Mobile spin impurity in an optical lattice

et al. 2017

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We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impurity's spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.Recently, strongly-interacting trapped one-dimensional multicomponent systems, which suffer from huge ground state degeneracies, have been shown to be tractable by means of freezing the charge degrees of freedom and the reduction of the spin sector to an effective spin chain model [1][2][3]. With this development, there has been considerable theoretical work on strongly interacting one-dimensional systems in recent years [4][5][6][7][8][9][10][11][12][13][14][15][16], including for the case of a single spin impurity [17][18][19]. As a result in the last year, numerical methods have been developed to obtain the effective spin chain from an arbitrary confining potential [20,21]. At the same time, ultracold atom experimental techniques have been developed to reach the few-body limit in one-dimensional set-ups [22,23]. There have been several experimental realisations of the few-body limit with fermions [24-26], including for strong interactions [27], and bosons [28].The traditional notion of a polaron corresponds to a quasiparticle formed from the interactions between an impurity and its many-body surrounding medium, as first discussed by Landau and Pekar in 1948 [29]. Polaron physics plays, for instance, an important role in the theory of superconductors with strong interactions, where the carriers are small lattice polarons and bipolarons [30,31]. There is also strong evidence that polarons play a role in the mechanism for some high-temperature superconductors [31][32][33]. In magnetic systems, a spin polaron can be formed by the interaction of an impurity spin with the spins of the surrounding magnetic ions [33].It is well known that the definition of a quasipart...

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“…(9)]. This can be done with the help the Riemann-Lebesgue lemma which we state in the following form [42].…”

Section: Appendix A: Asymptotic Behavior Of S(rt)mentioning

confidence: 99%

“…After this experiment several theoretical works on the topic followed, most of them within the framework of the Bose-Hubbard model. Different two-body problems (with several trapping potentials and interactions) are investigated in [8][9][10][11][12][13][14][15]. Other authors study the effect using a larger ensemble of particles [16,17].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice

et al. 2012

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We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wave function at finite time. As initial condition we chose localized atoms that are separated by a distance of d lattice sites and carry a center-of-mass quasimomentum. An initially localized pair (d = 0) is found to be more stable as quantified by the pair probability (probability to find two atoms at the same lattice site) when the interaction and/or the center-of-mass quasimomentum is increased. For initially separated atoms (d = 0) there exists an optimal interaction strength for pair formation. Simple expressions for the wave function, the pair probability, and the optimal interaction strength for pair formation are computed in the limit of infinite time. Whereas the time-dependent wave function differs for values of the interaction strength that differ only by the sign, important observables such as the density and the pair probability do not. With a symmetry analysis this behavior is shown to extend to the N -particle level and to fermionic systems. Our results provide a complementary understanding of the recently observed [Winkler et al., Nature (London) 441, 853 (2006)] dynamical stability of atom pairs in a repulsively interacting lattice gas.

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Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Cited by 27 publications

References 21 publications

Ultracold bosons with short-range interaction in regular optical lattices

Ultracold bosons with short-range interaction in regular optical lattices

Mobile spin impurity in an optical lattice

Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice

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