An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.

Feb 6, 20066 citations

Optical control of a magnetic Feshbach resonance in an ultracold Fermi gas

Zhengkun Fu, Pengjun Wang, Lianghui Huang +3 more

We use laser light near resonant with a molecular bound-to-bound transition to control a magnetic Feshbach resonance in ultracold Fermi gases of ${}^{40}$ K atoms. The spectrum of excited molecular states is measured by applying a laser field that couples the ground Feshbach molecular state to electronically excited molecular states. Nine strong bound-to-bound resonances are observed below the ${}^{2}{P}_{1/2}+{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ threshold. We use radio-frequency spectroscopy to characterize the laser-dressed bound state near a specific bound-to-bound resonance and show clearly the shift of the magnetic Feshbach resonance using light. The demonstrated technology could be used to modify interatomic interactions with high spatial and temporal resolutions in the crossover regime from a Bose-Einstein condensate to a Bardeen-Cooper-Schrieffer superfluid.We use laser light near resonant with a molecular bound-to-bound transition to control a magnetic Feshbach resonance in ultracold Fermi gases of ${}^{40}$K atoms. The spectrum of excited molecular states is measured by applying a laser field that couples the ground Feshbach molecular state to electronically excited molecular states. Nine strong bound-to-bound resonances are observed below the ${}^{2}{P}_{1/2}+{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ threshold. We use radio-frequency spectroscopy to characterize the laser-dressed bound state near a specific bound-to-bound resonance and show clearly the shift of the magnetic Feshbach resonance using light. The demonstrated technology could be used to modify interatomic interactions with high spatial and temporal resolutions in the crossover regime from a Bose-Einstein condensate to a Bardeen-Cooper-Schrieffer superfluid.

arXiv:1306.0395Physical Review AOct 9, 201336 citations

Observation of Feshbach resonances in a Bose–Einstein condensate

S. Inouye, Michael R. Andrews, J. Stenger +3 more

NatureMar 1, 19982,094 citations

We use laser light near resonant with a molecular bound-to-bound transition to control a magnetic Feshbach resonance in ultracold Fermi gases of

{}^{40}

K atoms. The spectrum of excited molecular states is measured by applying a laser field that couples the ground Feshbach molecular state to electronically excited molecular states. Nine strong bound-to-bound resonances are observed below the

{}^{2}{P}_{1/2}+{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

threshold. We use radio-frequency spectroscopy to characterize the laser-dressed bound state near a specific bound-to-bound resonance and show clearly the shift of the magnetic Feshbach resonance using light. The demonstrated technology could be used to modify interatomic interactions with high spatial and temporal resolutions in the crossover regime from a Bose-Einstein condensate to a Bardeen-Cooper-Schrieffer superfluid.