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.

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 develop a theory of quantum fluctuations and squeezing in a three-dimensional Bose-Einstein condensate atom interferometer with nonlinear losses. We use stochastic equations in a truncated Wigner representation to treat quantum noise. Our approach includes the multi-mode spatial evolution of spinor components and describes the many-body dynamics of a mesoscopic quantum system. PACS numbers: 03.75. Gg, 03.75.Dg, 67.85.Fg, 67.85.De Atom interferometry is an important quantum technology at the heart of many proposed future applications of ultra-cold atomic physics. Bose-Einstein condensates (BECs) or atom lasers are macroscopic quantum objects and have potential advantages as interferometric detectors and sensors, provided one can precisely extract atomic phase information. However, unlike photons, atoms can interact strongly, causing dephasing and loss of interference fringes. An intimate understanding of quantum many-body dynamics is the key to calculating interaction-induced dephasing in the measurement process. This is essential for a quantitative theory of atom interferometry.In this Letter we present a simple, yet quantitatively accurate theoretical approach to simulating the dynamics and evaluating limits of atom interferometry at large atom number, using a truncated Wigner representation [1][2][3]. This method extends the conventional Gross-Pitaevskii equations describing a Bose condensate to include quantum noise effects, including noise due to linear and nonlinear losses. The theory allows the accurate inclusion of quantum fluctuations due to nonlinear losses, which is a dominant effect when atom numbers are increased to improve fringe visibility.Importantly, we can clearly demonstrate where fringe visibility is driven by quantum fluctuations, and where it is driven by trap inhomogeneity and dynamical effects, in order to choose optimal conditions for quantum noise reduction and spin squeezing. These calculations are a first step towards understanding mesoscopic superpositions and entanglement in ultra-cold atomic gases. An advantage of our method compared to the variational approaches used elsewhere [4,5] is that it allows us to treat a large number of independent field modes and particles, thus including degrees of freedom that are excited due to collisional and nonlinear loss dynamics [6,7]. Our theory can be readily extended to include finite temperature initial conditions [2,8], which will be treated elsewhere. Nonlinear losses and finite temperature effects can be also described within the confines of the variational approach [9,10].Quantum phase-diffusion is defined as the phase noise induced by number fluctuations which are conjugate to phase. This is a fundamental feature of BEC interferometry, and can only be removed when there are no interactions. However, there are other reasons for decoherence, which are also important. The approach used here captures all three significant features of atom interferometry that can result in decoherence: phase-diffusion, losses, and trap inhomogeneity effe...