Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states. Extending quantum interferometry to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the 'one-axis-twisting' scheme and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11-15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms.

We report on the experimental realization of an internal bosonic Josephson junction in a Rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted π-phase modes and quantitatively confirms analytical predictions, revealing a classical bifurcation. Our results suggest that this system is a model system which can be tuned from classical to the quantum regime and thus is an important step towards the experimental investigation of entanglement generation close to critical points.PACS numbers: 03.75.Lm,03.75.Mn Bifurcation occurs when a small smooth parameter change in a dynamical system leads to a sudden qualitative or topological change in its behavior. In classical nonlinear systems bifurcations are frequently encountered and are strongly related to critical phenomena and chaotic behavior [1]. This relation is less obvious in the quantum regime due to the intrinsic uncertainty of the quantum states. However, macroscopic quantum systems exist which can be well described by classical theories exhibiting bifurcation phenomena [2][3][4][5][6]. It has been theoretically shown that such a bifurcation can be used for the creation of highly entangled and nontrivial quantum states [3,[7][8][9]]. An exemplary system with these characteristics is the bosonic Josephson Junction [10-14] which has so far been observed in weakly linked reservoirs of Helium [15] and Bose-Einstein condensates [16][17][18].We report on the realization of a Josephson Junction in a Bose-Einstein condensate with internal i.e. spin degrees of freedom [19] allowing the access of parameter regimes around the bifurcation point which have not been experimentally addressable yet. Since the experimental control of the tunneling coupling is realized via electromagnetic radiation the well developed techniques of precision spectroscopy can be employed to map out the full phase space i.e. dynamics of canonical conjugate variables, with high accuracy.An internal Josephson junction is realized by N particles coherently distributed between two internal states |a and |b . These states are linearly coupled with resonant two-photon radiofrequency-microwave radiation and experience coherent nonlinear interaction due to s-wave scattering between the atoms (see Fig. 1). Assuming that both states are in the same spatial mode the dynamics is well described in the N particle two mode model with the Hamiltonian H = χĴ 2 z − ΩĴ x , whereˆ J is the Schwinger pseudo spin representation of the N atom system.Ĵ z describes quantum mechanically the population difference between the two modes andĴ x andĴ y are corresponding coherences. Since the time evolution is given only by rotations in configuration space with the total number of particles conserved the dynamics can be visualized on a generalized Bloch sphere [20] (see Fig. 1b). (color online) Interacting many particle system as a model system for bifurcation physics. (a) 87 Rb offers two hyperfine states |a (blue), |b (red) wh...

Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution, the realization of quantum teleportation and quantum memories, or the demonstration of the Einstein-Podolsky-Rosen paradox. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose-Einstein condensate reveals continuous-variable entanglement, as well as the twin-atom character of the state. Our results provide a rare example of continuous-variable entanglement of massive particles. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles.

We experimentally investigate the mixing/demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena. PACS numbers: 32.80.Qk, 03.75.Kk, 03.75.Mn Critical phenomena appear in many areas of physics including phase transitions [1] and nonlinear dynamical systems [2]. Their experimental study requires a high level of control in order to quantitatively compare with theoretical predictions.Multi-component Bose gases featuring miscibilityimmiscibility transitions are prototypical systems for the investigation of critical phenomena due to unprecedented experimental control of the relevant parameters. Early experiments with Bose-Einstein condensates revealed demixing as well as mixing dynamics of two [3] and three-component [4] quantum fluids. In the latter, even spontaneous symmetry breaking and the corresponding pattern formation has been observed [5,6]. While these experiments have been performed with fixed interaction between the components, atomic systems also allow for the control of the interspecies interaction strength via a Feshbach resonance. This has enabled experiments, that clearly demonstrate miscibilityimmiscibility transitions [7] and study the two-component dynamics in detail [8][9][10]. An alternative approach for the control of interaction properties and the corresponding dynamics in one-dimensional systems has been demonstrated using state-selective transversal confinement [11]. Recently it has been shown, that the miscibility characteristics of spinor gases can be changed using Raman coupling [12].In the present letter, we experimentally investigate the theoretically predicted miscibility properties of two spin states in a Bose-Einstein condensate in the presence of linear coupling [13][14][15]. We report on the experimental observation of the demixing dynamics of the relevant spin states, i.e. dressed states. The (im)miscibility of the system manifests itself in the amplitude of the Rabi oscillations, which is given by the spatial overlap of the corresponding dressed states. Employing both sides of an interspecies Feshbach resonance, the miscible and immiscible regime of the uncoupled two-component system is accessible allowing to contrast the mixing/demixing dynamics to the coupled situation. As shown in the right panel of Fig. 1 the amplitude of the Rabi oscillations drops in the miscible regime (top) and remains close to unity for immiscible parameters (bottom). These observations indicate...