We use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of 87 Rb atoms prepared in the internal states |1 ≡ |F = 1, mF = −1 and |2 ≡ |F = 2, mF = 1 for the precision measurement of the interspecies scattering length a12 with a relative uncertainty of 1.6 × 10 −4 . We show that in a cigar-shaped trap the three-dimensional (3D) dynamics of a component with a small relative population can be conveniently described by a one-dimensional (1D) Schrödinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio a12/a11, where a11 is the intraspecies scattering length of a highly populated component 1, and is largely decoupled from the scattering length a22, the total atom number and loss terms. By fitting numerical simulations of the coupled Gross-Pitaevskii equations to the recorded temporal evolution of the axial width we obtain the value a12 = 98.006(16) a0, where a0 is the Bohr radius. Our reported value is in a reasonable agreement with the theoretical prediction a12 = 98.13(10) a0 but deviates significantly from the previously measured value a12 = 97.66 a0 [1] which is commonly used in the characterisation of spin dynamics in degenerate 87 Rb atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length a22 = 95.44(7) a0 which also deviates from the previously reported value a22 = 95.0 a0 [1]. We characterise two-body losses for the component 2 and obtain the loss coefficients γ12 = 1.51(18) × 10 −14 cm 3 /s and γ22 = 8.1(3) × 10 −14 cm 3 /s.

Abstract. We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having nonzero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths (∼0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.

We investigate frequency up-conversion of low power cw resonant radiation in Rb vapour as a function of various experimental parameters. We present evidence that the process of four wave mixing is responsible for unidirectional blue light generation and that the phase matching conditions along a light-induced waveguide determine the direction and divergence of the blue light. Velocity-selective excitation to the 5D level via step-wise and two-photon processes results in a Doppler-free dependence on the frequency detuning of the applied laser fields from the respective dipole-allowed transitions. Possible schemes for ultraviolet generation are discussed.

We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to 0.75 at the evolution time of 1.5 s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of 2.8 s for a trapped condensate of 5.5 × 10 4 interacting atoms.

We report on the expansion of an ultracold Fermi-Fermi mixture of 6 Li and 40 K under conditions of strong interactions controlled via an interspecies Feshbach resonance. We study the expansion of the mixture after release from the trap and, in a narrow magnetic field range, we observe two phenomena related to hydrodynamic behavior. The common inversion of the aspect ratio is found to be accompanied by a collective effect where both species stick together and expand jointly despite of their widely different masses. Our work constitutes a major experimental step for a controlled investigation of the many-body physics of this novel strongly interacting quantum system. Since the first observations of strongly interacting Fermi gases [1, 2] the field has produced many exciting results and provided important new insights into the manybody behavior of strongly interacting quantum matter [3][4][5]. The general interest cuts across different branches of physics, ranging from strongly correlated condensedmatter systems to neutron stars and the quark-gluon plasma.

Quantum decay of a relativistic scalar field from a false vacuum is a fundamental idea in quantum field theory. It is relevant to models of the early Universe, where the nucleation of bubbles gives rise to an inflationary universe and the creation of matter. Here we propose a laboratory test using an experimental model of an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated radiofrequency coupling of the spin components. Numerical simulations demonstrate the spontaneous formation of true vacuum bubbles with realistic parameters and time-scales.As proposed by Coleman in a seminal paper [1], the false vacuum is a metastable state of the relativistic scalar field that can decay by quantum tunneling, locally forming bubbles of true vacuum that expand at the speed of light. It has a close analogy with the ubiquitous phenomenon of bubble nucleation during a first order phase transition in condensed matter [2], e.g. the spontaneous creation of vapor bubbles in superheated water [3]. Applied to a quantum field such as the inflaton or Higgs field, bubble nucleation is an event of cosmological significance in some early universe models. Indeed, the Coleman decay scenario of the inflaton field features prominently in the theory of eternal inflation [4,5], where bubbles continuously nucleating from a false vacuum grow into separate universes, each subsequently undergoing exponential growth of space [6]. This scenario, which could potentially explain the value of the cosmological constant by the anthropic principle, is currently being tested against observational evidence in astrophysical experiments [7,8]. For an observer inside the bubble, the tunneling event -occurring in the observer's past -appears like a cosmological "big-bang", prior to inflation.From a theoretical point of view, quantum tunneling from a false vacuum is a problem that can only be solved approximately [1,9] (except for simplified models [10]) due to the exponential complexity of quantum field dynamics. This motivates the search for an analog quantum system that is accessible to experimental scrutiny, to test these models. The utility of such experiments, which complement astrophysical investigations, is that they would provide data that allow verification of widely used approximations inherent in current theories [11].Here we demonstrate how to use an ultra-cold atomic two-component Bose-Einstein condensate (BEC) as a quantum simulator that generates a decaying, relativistic false vacuum. Quantum field dynamics occurs for the relative phase of two spin components that are linearly coupled by a radio-frequency field. In this proposal the speed of sound in the condensate models the speed of light, and the "universe" is less than a millimeter across. Domains of true vacuum are observable using interferometric techniques [12] over millisecond time-scales with realistic parameters.Modulating the radio-frequency coupling in time allows one to cr...

We investigate the spatially dependent relative phase evolution of an elongated two-component Bose-Einstein condensate. The pseudospin-1 2 system is comprised of the |F = 1, mF = −1 and |F = 2, mF = +1 hyperfine ground states of 87 Rb , which we magnetically trap and interrogate with radio-frequency and microwave fields. We probe the relative phase evolution with Ramsey interferometry and observe a temporal decay of the interferometric contrast well described by a mean-field formalism. Inhomogeneity of the collective relative phase dominates the loss of interferometric contrast, rather than decoherence or phase diffusion. We demonstrate a technique to simultaneously image each state, yielding subpercent variations in the measured relative number while preserving the spatial mode of each component. In addition, we propose a spatially sensitive interferometric technique to image the relative phase.

The quantum decay of a relativistic scalar field from a metastable state ("false vacuum decay") is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal [EPL 110, 56001 (2015)] for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component 7 Li or 41 K bosonic condensates in one-dimensional traps of ∼ 100 µm size. arXiv:1607.01460v4 [cond-mat.quant-gas]