We report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly linked mesoscopic traps. We used the interference of atoms released from the traps as a sensitive probe of these statistics. By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeezed states and coherent states of the atom field. The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions.

We study the non-equilibrium evolution of the phase coherence of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice, as the lattice is suddenly quenched from an insulating to a superfluid state. We observe slowly damped phase coherence oscillations in the regime of large filling factor (∼100 bosons per site) at a frequency proportional to the generalized Josephson frequency. The truncated Wigner approximation (TWA) predicts the frequency of the observed oscillations.

Coherence properties of Bose-Einstein condensates offer the potential for improved interferometric phase contrast. However, decoherence effects due to the mean-field interaction shorten the coherence time, thus limiting potential sensitivity. In this work, we demonstrate increased coherence times with number squeezed states in an optical lattice using the decay of Bloch oscillations to probe the coherence time. We extend coherence times by a factor of 2 over those expected with coherent state BEC interferometry. We observe quantitative agreement with theory both for the degree of initial number squeezing as well as for prolonged coherence times.Experimental requirements for precision atom interferometry are well suited to many of the coherence properties of Bose-Einstein condensates [1,2,3,4,5]. BECs possess narrower momentum distributions than those of ultra-cold atomic gases, which removes the need for velocity selection during initial state preparation. The longer coherence length of a condensate improves phase contrast, and colder temperatures reduce ensemble expansion during long interferometer interrogation times. Furthermore, for confined atom-interferometers [6,7,8] which require spatial separation of a wavepacket in close proximity to a guiding surface, the superfluid properties of a BEC offer an additional advantage. The meanfield interaction energy in BECs provides an energy gap to external excitations, effectively decoupling the atomic proof-mass from the physical sensor.On the other hand, the coherence time for BEC interferometry can be significantly reduced with respect to cold atom sources. Prior to separation, two linked condensates have relative number fluctuations which support a well defined relative phase. However, when separated, the interplay of a large on-site mean-field interaction with large number variance causes rapid dephasing [9]. This concern has been addressed previously by using either dilute condensates [10] or alternatively, Fermi gases which do not suffer from density broadening mechanisms [11]. It is possible, however, to retain some of the benefits of BEC interferometry while minimizing mean-field induced decoherence. The generation of atom-number squeezed states from a BEC in an optical lattice [12,13] has offered the possibility to create states with reduced sensitivity to mean-field decay mechanisms.In this work, we study the characteristic time scale for which an array of BECs preserves relative phase information after becoming fragmented, and we observe prolonged coherence times for number squeezed states. The coherence time is probed through the decay time of a Bloch oscillation, and we find quantitative agreement with theoretical predictions.The theoretical treatment for a BEC in an optical lattice begins with the Bose-Hubbard Hamiltonian [14].where gβ represents the mean-field interaction energy and γ is the inter-well tunneling matrix element with both terms dependent on lattice depth. ε i denotes the external potential term andâ i andâ i † represent single particle ...

We report the observation of normal-mode splitting of the atom-cavity dressed states in both the fluorescence and transmission spectra for large atom number and observe subnatural linewidths in this regime. We also implement a method of utilizing the normal-mode splitting to observe Rabi oscillations on the 87 Rb ground state hyperfine clock transition. We demonstrate a large collective cooperativity, C = 1.2ϫ 10 4 , which, in combination with large atom number, N ϳ 2 ϫ 10 5 , offers the potential to realize an absolute phase sensitivity better than that achieved by state-of-the-art atomic fountain clocks or inertial sensors operating near the quantum projection noise limit.

We study the dynamics of Bose-Einstein condensed atoms in a 1-D optical lattice potential in a regime where the collective (Josephson) tunneling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross-Pitaevskii equations.1 Coherent control of the collective dynamics of macroscopic quantum systems is currently of great interest due to possible applications in quantum measurement and information science [1,2]. For example, coherent manipulation of superconducting currents in Josephson junction circuits has led to the realization of high-Q electronic qubits for quantum logic devices [3]. Similarly, manipulation of the superfluid properties in atomic systems, such as with BECs in optical lattices, may soon provide a realization of de Broglie wave interferometers which perform below the shot-noise limit [4].At zero temperature, the physical characteristics of coupled superconducting/superfluid reservoirs are determined by two competing energies: the kinetic energy associated with tunneling between sites (E J ), and the on-site interaction energy (E C ), resulting from (repulsive) inter-particle interactions [5,6]. Specifically, for a BEC in an optical lattice system E J ≡ Nγ, where N is the number of atoms in a lattice site and γ is the inter-site tunneling energy, and E C ≡ gβ, where gβ is the mean-field energy. The nature of the many-body ground state in the lattice array is governed by the ratio Γ ≡ E C /E J ≡ gβ/Nγ, which can be divided into three regimes. For Γ ≪ 1, the system exhibits global superfluidity and long-range phase order. As Γ approaches 1, interactions lead to a frustration of long-range phase order and a corresponding reduction of the single reservoir number variance δN, with δN ∼ (Nγ/gβ) 1/4 . When Γ ∼ 1, the system undergoes a transition to an insulating regime where number fluctuations are strongly suppressed (δN < 1) for commensurate filling. For translationally invariant lattice arrays, this defines the Mott-insulating regime (MI) [7,8].This system has been shown to map onto 1-D superconducting chains, which demonstrate a Kosterlitz-Thouless transition [9].Previously, interferometric techniques have been used to study the ground state properties of BECs in optical lattices forming 1-D arrays with high filling factor in the regime Γ > 1 [10]. This work demonstrated that, for the system studied, interferometric measurements do not have the specificity to reveal possible abrupt changes in the many-body state of the system as the Mott-insulating regime is reached [11]. However, recent theoretical work has ...