Long-Lived Feshbach Molecules in a Three-Dimensional Optical Lattice

Thalhammer, Gregor; Winkler, Klaus; Lang, Florian; Schmid, Stefan; Grimm, Rudolf; Denschlag, Johannes Hecker

doi:10.1103/physrevlett.96.050402

Cited by 167 publications

(203 citation statements)

References 19 publications

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“…For comparison, the thin solid lines show the analytically predicted momentum distribution n red,sp (K), Eq. (18). Note the log-log scale.…”

Section: Discussionmentioning

confidence: 99%

“…While the majority of investigations of the Efimov effect have focused on the three-body system, larger systems have attracted considerable attention recently from theoretical and experimental groups [4][5][6][7][8][9][10][11][12][13][14][15]. Second, small trapped atomic systems can be realized by loading an atomic gas into an optical lattice [16][17][18][19]. If the tunneling between lattice sites is small and if the interactions between neighboring sites can be neglected, then each lattice site provides a realization of a trapped few-body system.…”

Section: Introductionmentioning

confidence: 99%

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Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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We investigate small equal-mass two-component Fermi gases under external spherically symmetric confinement in which atoms with opposite spins interact through a short-range two-body model potential. We employ a non-perturbative microscopic framework, the stochastic variational approach, and determine the system properties as functions of the interspecies s-wave scattering length as, the orbital angular momentum L of the system, and the numbers N1 and N2 of spin-up and spin-down atoms (with N1 − N2 = 0 or 1 and N ≤ 6, where N = N1 + N2). At unitarity, we determine the energies of the five-and six-particle systems for various ranges r0 of the underlying two-body model potential and extrapolate to the zero-range limit. These energies serve as benchmark results that can be used to validate and assess other numerical approaches. We also present structural properties such as the pair distribution function and the radial density. Furthermore, we analyze the one-body and two-body density matrices. A measure for the molecular condensate fraction is proposed and applied. Our calculations show explicitly that the natural orbitals and the momentum distributions of atomic Fermi gases approach those characteristic for a molecular Bose gas if the s-wave scattering length as, as > 0, is sufficiently small.

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“…For comparison, the thin solid lines show the analytically predicted momentum distribution n red,sp (K), Eq. (18). Note the log-log scale.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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“…For lattice sites with n = 2 atoms, the association efficiency is above 80%, similar to ref. 15. The resulting molecular n = 1 state is sketched in Fig.…”

mentioning

confidence: 99%

“…The observed lifetime of the visibility is sufficient for many applications. For comparison, the measured lifetime of the molecule number is 160(20) ms, which is probably due to scattering of lattice photons 15 . This molecule loss sets an upper limit on the lifetime of the visibility, because the sites at which molecules are lost are randomly distributed across the lattice, thus gradually destroying the molecular n = 1 state.…”

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confidence: 99%

Preparation of a quantum state with one molecule at each site of an optical lattice

et al. 2006

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U ltracold gases in optical lattices are of great interest, because these systems bear great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a longrange dipole-dipole interaction, such as polar molecules 1-5 . Here we show the preparation of a quantum state with exactly one molecule at each site of an optical lattice. The molecules are produced from an atomic Mott insulator 6 with a density profile chosen such that the central region of the gas contains two atoms per lattice site. A Feshbach resonance is used to associate the atom pairs to molecules 7-14 . The remaining atoms can be removed with blast light 13,15 . The technique does not rely on the moleculemolecule interaction properties and is therefore applicable to many systems.A variety of interesting proposals for quantum information processing and quantum simulations 1-5 require as a prerequisite a quantum state of ultracold polar molecules in an optical lattice, where each lattice site is occupied by exactly one molecule. A promising strategy for the creation of such molecules is based on the association of ultracold atoms using a Feshbach resonance, or photoassociation and subsequent transfer to a much lower rovibrational level using Raman transitions 16 . If the moleculemolecule interactions are predominantly elastic and effectively repulsive, then a state with one molecule per lattice site can finally be obtained using a quantum phase transition from a superfluid to a Mott insulator by ramping up the depth of an optical lattice 6 . However, many molecular species do not have such convenient interaction properties, so alternative strategies are needed. Here, we demonstrate a technique that is independent of the molecule-molecule interaction properties. The technique relies on first forming an atomic Mott insulator and then associating molecules. Several previous experiments 15,17-20 associated molecules in an optical lattice, but none of them demonstrated the production of a quantum state with exactly one molecule per lattice site. Another interesting perspective of the state prepared here is that after Raman transitions to the rovibrational ground state, the lattice potential can be lowered to obtain a Bose-Einstein condensate (BEC) of molecules in the rovibrational ground state 21,22 . Figure 1 Schematic diagram of the molecular n = 1 state. In the core of the cloud, each lattice site is occupied by exactly n = 1 molecule (shown in green). In the surrounding shell, each site is occupied by exactly one atom (shown in red). The atoms can be removed with a blast laser. In the experiment, the number of occupied lattice sites is much larger than shown here.The behaviour of bosons in an optical lattice is described by the Bose-Hubbard hamiltonian 23 . The relevant parameters are the amplitude J for tunnelling between neighbouring lattice sites and the on-site interaction matrix element U. We create a Mott insulator 6 of atomic 87 Rb starting from an atomic BEC in an optical dipol...

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“…The atom pairs reside in the motional ground state at each well and are then associated 20 with 94(1)% probability to Cs 2 Feshbach molecules, which are subsequently transferred to the weakly bound level |1 , the starting level for the optical transfer (see the Methods section) 15,21,22 . Atoms at singly occupied sites are removed by a combination of microwave and optical excitation 20 . We now have a pure molecular sample with a high occupation of about 85(3)% in the central region of the lattice (see the Methods section).…”

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confidence: 99%

An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice

et al. 2010

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Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry 1,2 . In particular, samples of ground-state molecules at ultralow temperatures and high number densities will facilitate new quantum-gas studies 3 and future applications in quantum information science 4 . However, high phase-space densities for molecular samples are not readily attainable because efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zero-temperature atomic Mott-insulator state 5 with optimized double-site occupancy 6 , weakly bound dimer molecules are efficiently associated on a Feshbach resonance 7 and subsequently transferred to the rovibronic ground state by a stimulated four-photon process with >50% efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose-Einstein condensation of groundstate molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantumgas phases in optical lattices [8][9][10] .Recent years have seen spectacular advances in the field of atomic quantum gases. Ultracold atomic samples have been loaded into optical lattice potentials, enabling the realization of strongly correlated many-body systems and the direct observation of quantum phase transitions with full control over the entire parameter space 5 . Molecules with their higher level of complexity are expected to have a crucial role in future-generation quantumgas studies. For example, the long-range dipole-dipole force between polar molecules gives rise to nearest-neighbour and next-nearest-neighbour interaction terms in the extended BoseHubbard Hamiltonian and should thus lead to unusual many-body states in optical lattices in the form of striped, checkerboard and supersolid phases [8][9][10] .An important prerequisite for all proposed molecular quantumgas experiments is the capability to fully control all internal and external quantum degrees of freedom of the molecules. For radiative and collisional stability, the molecules need to be prepared in their rovibronic ground state, that is, the lowest vibrational and rotational level of the lowest electronic state, and preferably in its energetically lowest hyperfine sublevel. As a starting point for the realization of new quantum phases, the molecular ensemble should be in the ground state of the many-body system. Such state control is possible only at ultralow temperatures and sufficiently high particle densities. Although versatile non-optical cooling and slowing techniques have recently been developed for molecular ensembles 11 and photo-association experiments with atoms in magneto-optical traps have reached the rovibrational ground sta...

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Long-Lived Feshbach Molecules in a Three-Dimensional Optical Lattice

Cited by 167 publications

References 19 publications

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Preparation of a quantum state with one molecule at each site of an optical lattice

An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice

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