Ramping fermions in optical lattices across a Feshbach resonance

Katzgraber, Helmut G.; Esposito, Aniello; Troyer, Matthias

doi:10.1103/physreva.74.043602

Cited by 13 publications

(19 citation statements)

References 32 publications

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“…A similar result for our experimental data was computed numerically in [8]. This value gives an upper limit to the temperature since it assumes adiabatic formation of molecules at all doubly occupied sites and a perfect 50:50 mixture of the spin states.…”

Section: Thermometry In the Optical Latticesupporting

confidence: 87%

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Strongly interacting atoms and molecules in a 3D optical lattice

Köhl¹,

Günter²,

Stöferle³

et al. 2006

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We report on the realization of a strongly interacting quantum degenerate gas of fermionic atoms in a three-dimensional optical lattice. We prepare a bandinsulating state for a two-component Fermi gas with one atom per spin state per lattice site. Using a Feshbach resonance, we induce strong interactions between the atoms. When sweeping the magnetic field from the repulsive side towards the attractive side of the Feshbach resonance we induce a coupling between Bloch bands leading to a transfer of atoms from the lowest band into higher bands. Sweeping the magnetic field across the Feshbach resonance from the attractive towards the repulsive side leads to two-particle bound states and ultimately to the formation of molecules. From the fraction of formed molecules we determine the temperature of the atoms in the lattice.

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Section: Thermometry In the Optical Latticesupporting

confidence: 87%

“…In this configuration approximative solutions of this model are feasible [5,6,7,8]. In the Hubbard model the interactions between particles are parametrized only by the parameter U regardless of the physical details of the interaction.…”

Section: Introductionmentioning

confidence: 99%

Strongly interacting atoms and molecules in a 3D optical lattice

Köhl¹,

Günter²,

Stöferle³

et al. 2006

J. Phys. B: At. Mol. Opt. Phys.

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“…So far, temperature has not been measured in a lattice since standard methods -such as observing the rounding-off of the Fermi surface -turned out to be dominated by the inhomogeneity of the trapping potential rather than by temperature [16]. However, we find that the occupancy of the lattice depends strongly on the temperature [17,18,19] and the conversion of pairs of atoms into molecules is a sensitive probe, similar to the case of harmonically trapped fermions [20].In a previous experiment, deeply bound molecules of bosonic atoms have been created in an optical lattice by photo-association and were detected by a loss of atoms [6,21]. There the binding energy is only determined by the atomic properties and does not depend on the external potential, nor can the scattering properties between the molecules be adjusted.…”

mentioning

confidence: 74%

Molecules of Fermionic Atoms in an Optical Lattice

et al. 2006

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We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunnelling, the individual wells can be regarded as independent threedimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.PACS numbers: 03.75. Ss, 05.30.Fk, 71.10.Fd Quantum degenerate atomic gases trapped in the periodic potential of an optical lattice form a quantum manybody system of unprecedented purity. The short-range interaction due to atom-atom collisions makes optical lattices ideal to experimentally realize Hubbard models [1,2]. Experimental studies of bosonic Mott insulators [3,4,5,6] and of a fermionic band insulator [7] have provided a first taste of this new approach to quantum many-body physics.In the vicinity of a Feshbach resonance the collisional interaction strength between two atoms is tunable over a wide range. For two fermionic atoms on one lattice site strong interactions change the properties of the system qualitatively and physics beyond the standard Hubbard model becomes accessible. Crossing the Feshbach resonance in one direction leads to an interaction induced coupling between Bloch bands which has been observed experimentally [7] and described theoretically [8].Crossing the resonance in the other direction converts fermionic atoms into bosonic molecules. These processes have no counterpart in standard condensed matter systems and demand novel approaches to understand the mixed world of fermions and bosons in optical lattices [9,10,11,12]. Descriptions based on multi-band Hubbard models are extremely difficult to handle and therefore the low-tunneling limit is often used as an approximation. In this limit the lattice is considered as an array of microscopic harmonic traps each occupied with two interacting atoms in different spin states.The harmonic oscillator with two interacting atoms has been studied theoretically and the eigenenergies have been calculated in various approximations [9,13,14,15]. Its physics is governed by several length scales. The shortest scale is the characteristic length of the vander-Waals interaction potential between the atoms. The next larger length scale is given by the s-wave scattering length characterizing low-energy atomic collisions. However, near the Feshbach resonance it may become much larger than the extension of the harmonic oscillator ground state. A precise understanding of the interactions in this elementary model is a prerequisite in order to comprehend the many-body physics occurring in optical lattice systems with resonantly enhanced interactions.In this paper we study a spin-mixture of fermionic atoms in an optical lattice and their conversion into molecules by means of a Feshbach resonance. The binding energy as a function of the s-wave scattering l...

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“…While number distributions have been analyzed for bosonic [65,203,[205][206][207] and fermionic systems [116,204], this method has been extensively evaluated, specifically for thermometry, in fermionic systems where the number of atoms per site is limited to zero, one, and two [116,204]. The number of doubly occupied sites as a function of temperature in the Fermi-Hubbard model can be calculated from theory with relative accuracy in certain limits [116,184,204,208]. A comparison of QMC, DMFT, and series approximations demonstrated that simple series approximations give almost identical results to the more complex computational calculations in the parameter range of current experiments [116].…”

Section: In-situ Imagingmentioning

confidence: 99%

Cooling in strongly correlated optical lattices: prospects and challenges

2011

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Optical lattices have emerged as ideal simulators for Hubbard models of strongly correlated materials, such as the high-temperature superconducting cuprates. In optical lattice experiments, microscopic parameters such as the interaction strength between particles are well known and easily tunable. Unfortunately, this benefit of using optical lattices to study Hubbard models comes with one clear disadvantage: the energy scales in atomic systems are typically nanoKelvin compared with Kelvin in solids, with a correspondingly miniscule temperature scale required to observe exotic phases such as d-wave superconductivity. The ultra-low temperatures necessary to reach the regime in which optical lattice simulation can have an impact-the domain in which our theoretical understanding fails-have been a barrier to progress in this field. To move forward, a concerted effort is required to develop new techniques for cooling and, by extension, techniques to measure even lower temperatures. This article will be devoted to discussing the concepts of cooling and thermometry, fundamental sources of heat in optical lattice experiments, and a review of proposed and implemented thermometry and cooling techniques. 4 of the simplest FH model, cool to low temperature, and search for d-wave superfluidity (the analog of SC for neutral atoms). If the simplest FH model is insufficient to generate d-wave SF, then we can add in long-range interactions, disorder, and other features, and determine the impact on the phase diagram. Ultimately, the hope is to use optical lattices to measure the FH phase diagram.Experimental and theoretical work on optical lattice simulation has not been focused solely on the FH model. An in-depth review of proposals can be found in Ref. [9]; here, we mention a few areas that lattices are primed to impact. Bosonic atoms trapped in a lattice realize the Bose-Hubbard (BH) model [26]. In the simplest, spinless BH model, particles tunnel between sites and interact if they are on the same site, just as in the FH model. The primary difference with the FH model are that the particles obey Bose statistics, and therefore particles in the same spin state can interact. While the ground state phase diagram of the BH model is well understood (see , for example), dynamics are not, and lattice experiments are beginning to have an impact on that front [30][31][32][33][34][35][36]. Adding disorder to bosonic particles in an optical lattice is a method for studying the disordered Bose-Hubbard (DBH) model [9,37,38], which has been used as a paradigm for granular superconductors and superfluids in porous media. In the DBH model, the characteristic physical parameters, such as the tunneling energy, vary from site-to-site. Experiments are starting to influence our understanding of the DBH model [39], about which there remain some disputes. Finally, ultra-cold atoms in a lattice can be used to study a variety of interacting spin models that involve magnetic interactions between spins pinned to a lattice (see, for example, Refs. [40][41][...

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Ramping fermions in optical lattices across a Feshbach resonance

Cited by 13 publications

References 32 publications

Strongly interacting atoms and molecules in a 3D optical lattice

Strongly interacting atoms and molecules in a 3D optical lattice

Molecules of Fermionic Atoms in an Optical Lattice

Cooling in strongly correlated optical lattices: prospects and challenges

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