Ultracold gases in optical lattices are of great interest, because these systems bear a great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a long-range dipole-dipole interaction, such as polar molecules. In an previous paper, the authors showed the preparation of a Mott-like state of molecules. The molecules are produced from an atomic Mott insulator 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. Remaining atoms can be removed with laser light. In this paper, the transport properties in the Mott-like state is studied. A molecule can tunnel with an amplitude Jmto an adjacent site. If there is already another molecule at that site the molecules can collide inelastically, leading to loss of both molecules from the sample. This loss occurs with a rate coefficient Gamma which is typically much faster than Jm/planck. The fast on-site loss leads to a suppression of tunneling. Loss from the initial state effectively occurs with a rate Gammaeffprop Jm2/Gamma . This effect is studied experimentally at different lattice depths and the results are compared with theoretical predictions.
Ultracold gases in optical lattices are of great interest, because these systems bear a great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a long-range dipole-dipole interaction, such as polar molecules. In an previous paper, the authors showed the preparation of a Mott-like state of molecules. The molecules are produced from an atomic Mott insulator 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. Remaining atoms can be removed with laser light. In this paper, the transport properties in the Mott-like state is studied. A molecule can tunnel with an amplitude Jmto an adjacent site. If there is already another molecule at that site the molecules can collide inelastically, leading to loss of both molecules from the sample. This loss occurs with a rate coefficient Gamma which is typically much faster than Jm/planck. The fast on-site loss leads to a suppression of tunneling. Loss from the initial state effectively occurs with a rate Gammaeffprop Jm2/Gamma . This effect is studied experimentally at different lattice depths and the results are compared with theoretical predictions.
We prepare a quantum state where each site of an optical lattice is occupied by exactly one molecule. This is the same quantum state as in a Mott insulator of molecules in the limit of negligible tunneling. Unlike previous Mott insulators, our system consists of molecules which can collide inelastically. In the absence of the optical lattice these collisions would lead to fast loss of the molecules from the sample. To prepare the state, we start from a Mott insulator of atomic 87Rb with a central region, where each lattice site is occupied by exactly two atoms. We then associate molecules using a Feshbach resonance. Remaining atoms can be removed using blast light. Our method does not rely on the molecule‐molecule interaction properties and is therefore applicable to many systems.
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.
This thesis describes the results of several experiments that studied the photoassociation of an ultracold atomic Rb gas. In the first experiment, we produced ultracold diatomic molecules from an atomic gas via single-color photoassociation. The molecules were detected with resonance-enhanced multiphoton ionization. Trapping of these molecules in a quadrupole magnetic trap, with lifetimes up to 20 seconds, was also demonstrated. In addition, the rate constant for inelastic collisions between the trapped molecules and atoms was determined from measurements of the atomic density dependence of the decay rate of the trapped molecules. In another experiment, stimulated Raman photoassociation of Rb atoms in a Mott insulator state was studied. A Bose-Einstein condensate (BEC) of 87Rb atoms was loaded into a three-dimensional optical lattice formed by the interference pattern of three orthogonal standing wave laser fields. This system constitutes a very good realization of the Bose-Hubbard model, which predicts a quantum phase transition between a superfluid state and a Mott insulator state at a particular lattice height. A time-of-flight imaging method was used to study the state of the atomic gas, and the quantum phase transition was observed at the predicted lattice height. The signature of the phase transition was the disappearance and reappearance of peaks in the image that arose from the interference of atoms originating from different lattice sites. Two coherent laser fields were applied to the gas in its Mott insulating state, and tuned close to a Raman photoassociation resonance, and this resulted in an observable loss of atoms due to the formation of molecules. This transition exhibited a double-peaked spectrum, with one of the peaks arising from photoassociation of atoms in sites containing only two atoms, and the other from sites containing three atoms. Also, the loss of atoms vs. the duration of the Raman photoassociation period was studied, with the lasers tuned to the peak corresponding to two atoms per site. It was found that a central core of the gas, containing about 40 percent of the atoms, exhibited a coherent oscillation between an atomic and molecular quantum gas.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
This thesis reports on experiments with ultracold atomic and molecular quantum gases. Magnetically tunable Feshbach resonances are used to associate diatomic molecules from atomic 87Rb in a three-dimensional optical lattice. In a first experiment, molecules are formed by a sudden jump of the magnetic field to the resonance. This induces coherent atom-molecule oscillations with large amplitude. In another experiment, a dissipative analog of the one-dimensional Tonks-Girardeau gas is realized with molecules in an optical lattice. Inelastic collisions between the molecules lead to particle loss. This interaction is so strong that the system reaches the strongly correlated regime, and the molecules, which are bosons, are forced to behave much like fermions. The strong correlations suppress the molecule loss rate by up to three orders of magnitude.
We present a theory for ultracold atomic gases in an optical lattice near a Feshbach resonance. In the single-band approximation the theory describes atoms and molecules that can both tunnel through the lattice. Moreover, an avoided crossing between the two-atom and the molecular states occurs at every site. We determine the microscopic parameters of the generalized Hubbard model that describes this physics, using the experimentally known parameters of the Feshbach resonance in the absence of the optical lattice. As an application we also calculate the zero-temperature phase diagram of an atomic Bose gas in an optical lattice.