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...

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We prepare a Bose-Einstein condensed gas in a three-dimensional optical lattice and study the excitation spectrum of the superfluid phase for different interaction strengths. We probe the response of the system by modulating the depth of the optical lattice along one axis. The interactions can be controlled independently by varying the tunnel coupling along the other two lattice axes. In the weakly interacting regime we observe a small susceptibility of the superfluid to excitations, while for stronger interactions an unexpected resonance appears in the excitation spectrum. In addition we measure the coherent fraction of the atomic gas, which determines the depletion of the condensate.

We report the observation of nonclassical quantum correlations of continuous light variables from an altogether different type of source. It is a frequency nondegenerate optical parametric oscillator below threshold, where signal and idler fields are separated by 740 MHz corresponding to two free spectrum ranges of the parametric oscillator cavity. The degree of entanglement observed, Ϫ3.8 dB, is the highest to date for a narrow-band tunable source suitable for atomic quantum memory and other applications in atomic physics. Finally we use the latter to visualize the Einstein-Podolsky-Rosen paradox.

We report an experiment on mapping a quantum state of light onto the ground state spin of an ensemble of Cs atoms with the lifetime of 2 ms. Recording of one of the two quadrature phase operators of light is demonstrated with vacuum and squeezed states of light. The sensitivity of the mapping procedure at the level of approximately 1 photon/sec per Hz is shown. The results pave the road towards complete (storing both quadrature phase observables) quantum memory for Gaussian states of light. The experiment also sheds new light on fundamental limits of sensitivity of the magneto-optical resonance method.

We report on the study of the momentum distribution of a one-dimensional Bose gas in an optical lattice. From the momentum distribution we extract the condensed fraction of the gas and thereby measure the depletion of the condensate and compare it with a theorical estimate. We have measured the coherence length of the gas for systems with average occupationn > 1 andn < 1 per lattice site.1 The one-dimensional Bose gas in an optical lattice A one-dimensional gas can be created in a trap when the confining potential restricts the motion of the particles to one dimension with the transverse motional degrees of freedom being frozen out. A cigar shaped harmonic trapping geometry is characterized by the frequencies ω ⊥ in the two strongly confining axes and ω ax in the weakly confining axis. A kinematically one-dimensional situation is achieved when all particles occupy only the ground state in the radial directions, which implies that both the thermal energy k B T and the interaction energy µ have to be much smaller than the transverse energy level spacing. In general, one-dimensional systems exhibit increased quantum fluctuations of the phase, such that for a homogeneous 1D gas Bose-Einstein condensation is prevented. For trapped low-dimensional gases the cross-over to a Bose-Einstein condensate takes place at a finite temperature k B T 1D = Nhω ax / ln(2N ), where N is the number of particles in the 1D system [1,2]. The fluctuating phase alters the properties of the gas [3,4,5,6,7]. One-dimensional quantum systems exhibit a wealth of fascinating phenomena whose explanations go beyond the mean-field description [8].One-dimensional trapped Bose-Einstein condensates were recently created and studied [9] using an optical lattice consisting of two mutually perpendicular standing wave laser fields. In this geometry the optical lattice forms an array of one-dimensional tubes, each filled with a Bose-Einstein condensate. This experiment revealed the distinctively different excitation spectrum of a onedimensional quantum system as compared to its three dimensional counterpart [10]. In a previous experiment a Bose condensates was loaded into a two-dimensional optical lattices to study the coherence between the tubes. In that experiment the tunnel-coupling between adjacent tubes was larger than the axial oscillation frequency, thereby an array of strongly coupled tubes was created [11]. Very recently the lifetime of one-dimensional gases created in an optical lattice were studied [12]. In elongated magnetic and optical traps a regime was accessed where a Bose condensate with µ ≤hω ⊥ coexisted with a three-dimensional thermal cloud [13,14]. In similar elongated traps studies of solitons [15] and of enhanced phase fluctuations have been performed [16,17].When the one-dimensional Bose gas is exposed to an additional optical lattice potential in axial direction the bosons may become localized in the minima of a periodic potential and the system can be described by the BoseHubbard Hamiltonian [18,19]:J denotes the hopping...

We have created one-, two-, and three-dimensional quantum gases and study the superfluid to Mott insulator transition. Measurements of the transition using Bragg spectroscopy show that the excitation spectra of the lowdimensional superfluids differ significantly from the three-dimensional case.

We describe a radio-frequency (RF) discriminator, or frequency-to-voltage converter, based on a voltage-controlled oscillator phase-locked to the signal under test, which has been developed to analyze the frequency noise properties of an RF signal, e.g., a heterodyne optical beat signal between two lasers or between a laser and an optical frequency comb. We present a detailed characterization of the properties of this discriminator and we compare it to three other commercially available discriminators. Owing to its large linear frequency range of 7 MHz, its bandwidth of 200 kHz and its noise floor below 0.01 Hz 2 /Hz in a significant part of the spectrum, our frequency discriminator is able to fully characterize the frequency noise of a beat signal with a linewidth ranging from a couple of megahertz down to a few hertz. As an example of application, we present measurements of the frequency noise of the carrier envelope offset beat in a low-noise optical frequency comb.