We study one-dimensional trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum of the one-dimensional gas in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of quantum depletion. In the Mott insulating phase a discrete spectrum is measured. The excitation spectra of both phases are compared to the three-dimensional situation and to the crossover regime from one to three dimensions. The coherence length and coherent fraction of the gas in all configurations are measured quantitatively. We observe signatures for increased fluctuations which are characteristic for 1D systems. Furthermore, ceasing collective oscillations near the transition to the Mott insulator phase are found.PACS numbers: 05.30. Jp, 03.75.Kk, 03.75.Lm, 73.43.Nq Quantum gases trapped in the periodic potential of an optical lattice have opened a new experimental window on many-particle quantum physics. The recent observation of the quantum phase transition from a superfluid to a Mott insulating phase in a Bose gas [1] has offered a first glimpse on the physics which is now becoming experimentally accessible. However, the full wealth of possibilities has yet to be explored. Besides controlling the effect of interactions in the trapped gas, it is conceivable to induce disorder, to change the dimensionality of the system, or to trap Fermi gases or Bose-Fermi mixtures. The realization of these systems is expected to provide a deeper understanding of general concepts related to superfluidity and superconductivity.Here we use the optical lattice to realize a strongly interacting Bose gas in one spatial dimension and to study the crossover to three dimensions. Emphasis is put on the measurement of excitation spectra which characterize the transition from the superfluid [2,3] to the Mott insulating state [1,4,5]. Several features observed in the spectra go beyond the description of current theoretical models.Degenerate Bose gases trapped in the lowest band of an optical lattice can be modelled using the Bose-Hubbard Hamiltonian [6,7,8,9], in which the hopping of atoms between neighboring lattice sites is characterized by the tunnelling matrix element J, while the interaction energy for two atoms occupying the same site is given by U . The physics of this model is governed by the ratio between U and J, i.e. between interaction and kinetic energy. This parameter can be controlled by changing the depth of the lattice potential. If the ratio U/J is below a critical value the atoms are superfluid. Above this value the system becomes Mott insulating. We access the one-dimensional regime [6, 10, 11] using an anisotropic optical lattice consisting of three mutually perpendicular standing waves. By choosing large potential depths in two axes we can selectively s...

Strong interactions between electrons in a solid material can lead to surprising properties. A prime example is the Mott insulator, in which suppression of conductivity occurs as a result of interactions rather than a filled Bloch band. Proximity to the Mott insulating phase in fermionic systems is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. The Hubbard model, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice. It is therefore now possible to access this regime with tools developed in atomic physics. However, an atomic Mott insulator has so far been realized only with a gas of bosons, which lack the rich and peculiar nature of fermions. Here we report the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is identified by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to an increase in atom number, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating regime and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin-ordering and ultimately the question of d-wave superfluidity.

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.

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...