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...

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement which we confirm by Bayesian phase estimation with sub shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems. [14,15]. The production of these fragile states in large systems remains a challenge and efficient methods for characterization are necessary because full state reconstruction becomes intractable. Here, we generate a class of non-Gaussian many-particle entangled states and reveal their quantum properties by studying the distinguishability of experimental probability distributions.A measure of the distinguishability with respect to small phase changes of the state is provided by the Fisher information F [16]. It is related to the highest attainable interferometric phase sensitivity by the Cramer-Rao bound ∆θ CR = 1/ √ F [17]. This limit follows from general statistical arguments for a measurement device with fluctuating output [18]. The Fisher information is limited by quantum fluctuations of the input state as well as the performance of the device. Even in the absence of technical noise, the Fisher information of a classical input state is F ≤ N because of the intrinsic granularity of N independent particles which translates into the shot-noise limit ∆θ ≥ 1/ √ N for phase estimation. This classical bound can be surpassed with a reduction of the input fluctuations by introducing entanglement between the N particles [5]. These states, known as squeezed states, are fully characterized by mean and variance of the observable and already employed in precision measurements [19][20][21]. In contrast, non-Gaussian quantum states can have increased fluctuations of the observable but nevertheless allow surpassing shot-noise limited performance. A textbook example is the Schrödinger cat state characterized by macroscopic fluctuations but achieving the best interferometric performance allowed by quantum mechanics, i.e. at the fundamental Heisenberg limit F = N . The initial coherent spin state (green) ideally evolves into a squeezed state (orange) followed by non-Gaussian states at later evolution times (violet). Edges of shaded areas are contours of the Husimi distribution for N = 380 at 1/e 2 of its maximum. (C) Experimental absorption picture, showing the site-and state-resolved optical lattice after a Stern-Gerlach separation. Shaded boxes indicate the sites with a total atom number in the range 380 ± 15, which are sele...

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.