Feshbach resonances in an optical lattice

Dickerscheid, D. B. M.; Khawaja, U. Al; Oosten, D. van; Stoof, H. T. C.

doi:10.1103/physreva.71.043604

Cited by 81 publications

(130 citation statements)

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“…A similar problem also appears when replacing the interaction potential by the delta-like Fermi-Huang pseudo-potential [18]. Also within analytical treatments of FRs in harmonic traps that use non-interacting basis states the eigenenergies do not converge [10,19]. In this case, after an infinite summation, the diverging terms can be absorbed by introducing a renormalized boundstate energy.…”

Section: Introductionmentioning

confidence: 99%

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Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Schneider

Sáenz

2013

Phys. Rev. A

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Based on the analytic model of Feshbach resonances in harmonic traps described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced that provides an accurate description of two atoms in an optical lattice at a Feshbach resonance with only a small number of Bloch bands. The approach circumvents the problem that the eigenenergies in the presence of a delta-like coupling do not converge to the correct energies, if an uncorrelated basis is used. The predictions of the BoseHubbard model are compared to non-perturbative calculations for both the stationary states and the time-dependent wavefunction during an acceleration of the lattice potential. For this purpose, a square-well interaction potential is introduced, which allows for a realistic description of Feshbach resonances within non-perturbative single-channel calculations.

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Section: Introductionmentioning

confidence: 99%

“…In this situation the resonant bound state must be explicitly included into the BH model. Several different kinds of these extended models have been introduced and debated [9][10][11][12] and applied to map out the phase diagramm [10,13,14] or to investigate lattice solitons [15].…”

Section: Introductionmentioning

confidence: 99%

Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Schneider

Sáenz

2013

Phys. Rev. A

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“…It is natural to consider combination of these two techniques, and indeed, significant efforts have been put forward towards this direction [5,6,7,8,9].…”

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confidence: 99%

“…For these developments, two experimental control techniques play the critical role: one is the Feshbach resonance to control the interaction magnitude between the atoms [3], and the other is the optical lattice to introduce diverse interaction configurations [4]. It is natural to consider combination of these two techniques, and indeed, significant efforts have been put forward towards this direction [5,6,7,8,9].A fundamental problem along this direction is to derive an appropriate Hamiltonian for this strongly interacting system which can serve as the starting point for further investigations. A number of generalizations of the Hubbard model have been proposed to describe this system by including the on-site atom-molecule coupling, typically ignoring the upper-band occupations [5,6] (see the comment in Ref.…”

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Effective Hamiltonian for Fermions in an Optical Lattice across a Feshbach Resonance

Duan

2005

Phys. Rev. Lett.

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We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective singleband model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.PACS numbers: 03.75. Fi, 32.80.Pj, 39.25+k Recently, there are many exciting advances in the ultracold atoms physics [1,2]. For these developments, two experimental control techniques play the critical role: one is the Feshbach resonance to control the interaction magnitude between the atoms [3], and the other is the optical lattice to introduce diverse interaction configurations [4]. It is natural to consider combination of these two techniques, and indeed, significant efforts have been put forward towards this direction [5,6,7,8,9].A fundamental problem along this direction is to derive an appropriate Hamiltonian for this strongly interacting system which can serve as the starting point for further investigations. A number of generalizations of the Hubbard model have been proposed to describe this system by including the on-site atom-molecule coupling, typically ignoring the upper-band occupations [5,6] (see the comment in Ref. [7]). These generalizations may model physics associated with a very narrow resonance, however, they are not adequate to describe typical broad Feshbach resonance, such as for 40 K or 6 Li. For the latter case, first, one needs to include all the multiband coupling terms even if the system temperature is well below the band gap. The reason is that the strong atom-molecule coupling results in population of the upper bands (the on-site coupling rate is typically larger than the band gap) [7]. Second, one also needs to include the atommolecule coupling from the neighboring sites which has been ignored in all the previous works. We will see that off-site atom-molecule coupling is typically larger than the atom tunnelling rate, and inclusion of these off-site interactions leads to qualitatively different physics.In this paper we rigorously derive the interaction Hamiltonian for fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband couplings and off-site interactions. The strong on-site interaction between the atoms make them first form local dressed molecules. Under typical experimental conditions, we then derive an effective single-band Hamiltonian, describing the resonant interaction between the local dressed molecules and the valence bonds (singlets) of fermions at neighboring sites [10...

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Quantum Phase Transitions in Cold Atoms and Low Temperature Solids

Hazzard¹

2011

Springer Theses

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This thesis describes how to create and probe novel phases of matter and exotic (non-quasiparticle) behavior in cold atomic gases. It focuses on situations whose physics is relevant to condensed matter systems, and where open questions about these latter systems can be addressed. It also attempts to better understand several experimental anomalies in condensed matter systems.The thesis is divided into five parts. The first section or chapter of each part gives an introduction to the motivation and background for the physics of that part; the last section or chapter gives an outlook for future studies. Parts 1-4 (Chapters 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15) introduce and show different facets of how to learn about novel physics relevant to condensed matter using cold atomic systems. Part 5 ( Chapters 16, 17, 18, and 19) constrains explanations of several ill-understood phenomena occurring in low-temperature quantum solids and condensed matter systems and attempts to construct mechanisms for their behavior.Part 1 (Chapters 1 and 2) generally motivates and introduces condensed matter, cold atoms, and many-body physics. Part 2 (Chapters 3, 4, 5, 6, and 7) introduces optical lattice physics and describes ways of spectroscopically probing many-body physics, especially dynamics, near quantum phase transitions in these systems. Part 3 (Chapters 8, 9, 10, 11, and 12) discusses the effects of rotation and how this can create exotic states, as well as alternative methods of creating exotic states. This leads us to study optical lattices where particles possess non-trivial correlations between particles even within a site in Chapters 10 and 11. Part 4 (Chapters 13, 14, and 15) introduces another route to studying exotic physics in cold atoms: examining finite temperature behavior near second order quantum phase transitions. In the "quantum critical regime" occurring near these transitions, non-quasiparticle behavior generically manifests. This behavior has been hidden in previous analyses of data, but Chapter 14 introduces a set of tools required to extract universal quantum critical behavior from standard observables in cold atoms experiments. Chapter 15 discusses near-term opportunities to use these tools to impact fundamental, open questions in condensed matter physics.Part 5 (Chapters 16, 17, 18, and 19) introduces several anomalous or interesting experimental results from low-temperature and solid state physics, constrains possible explanations, and attempts to construct mechanisms for their behavior.Chapter 17 shows that collisional properties between quasi-two-dimensional spinpolarized hydrogen atoms are dramatically modified by the presence of a helium film, on which they are invariably adsorbed in present experiments. Chapter 18 constrains theories regarding recent observations on atomic hydrogen defects in molecular hydrogen quantum solids. Finally, Chapter 19 proposes a mechanism for supersolidity that could account for the experimental observations at that time.Since then, it probably has been...

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Feshbach resonances in an optical lattice

Cited by 81 publications

References 13 publications

Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

Effective Hamiltonian for Fermions in an Optical Lattice across a Feshbach Resonance

Quantum Phase Transitions in Cold Atoms and Low Temperature Solids

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