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.

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound reachable by classical means [1]. This is known as the standard quantum limit, already defining the accuracy of the best available sensors for various quantities such as time [2] or position [3,4]. Many of these sensors are interferometers in which the standard quantum limit can be overcome by feeding their two input ports with quantum-entangled states, in particular spin squeezed states [5,6]. For atomic interferometers, Bose-Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles [7]. In this letter, we demonstrate their experimental realization by splitting a condensate in a few parts using a lattice potential. Site resolved detection of the atoms allows the measurement of the conjugated variables atom number difference and relative phase. The observed fluctuations imply entanglement between the particles [7,8,9], a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.Spin squeezing was one of the first quantum strategies proposed to overcome the standard quantum limit in a precision measurement [5,6] that triggered many experiments [10,11,12,13,14,15,16,17]. It applies to measurements where the final readout is done by counting the occupancy difference between two quantum states, as in interferometry or in spectroscopy. The name "spin squeezing" originates from the fact that the N particles used in the measurement can be described by a fictitious spin J = N/2. In an interferometric sequence, the spin undergoes a series of rotations where one of the rotation angles is the phase shift to be measured. A sufficient criterion for the input state allowing for quantum enhanced metrology is given by ξ S < 1 where ξis the squeezing parameter introduced in ref. [6]. The fluctuations of the spin in one direction have to be reduced below shot-noise ∆J 2 z < J/2, and the spin polarization in the orthogonal plane J x 2 + J y 2 has to be large enough to maintain the sensitivity of the interferometer. A pictorial representation of this condition is shown in figure 1b. The precision of such a quantum enhanced measurement is ξ S / √ N , whereas the standard quantum limit set by shot-noise is 1/ √ N . In this Letter, we report on the observation of entangled squeezed states in a Bose-Einstein condensate of 87 Rb atoms. The particles are distributed over a small number of lattice sites (between 2 and 6) in a one dimensional optical lattice (see figure 1a). The occupation number per site ranges from 100 to 1100 atoms. The two modes supporting the squeezing are two states of the external atomic motion corresponding to the condensate meanfield wave-functions in two adjacent lattice sites. These modes are spatially well separated and thus represent an ideal starting condition for a spatially split interferometer. Labeling a † and b † the creation o...

We report on the generation, subsequent oscillation and interaction of a pair of matter wave dark solitons. These are created by releasing a Bose-Einstein condensate from a double well potential into a harmonic trap in the crossover regime between one dimension (1D) and three dimensions (3D). Multiple oscillations and collisions of the solitons are observed, in quantitative agreement with simulations of the Gross-Pitaevskii equation. An effective particle picture is developed and confirms that the deviation of the observed oscillation frequencies from the asymptotic prediction νz/ √ 2, where νz is the longitudinal trapping frequency, results from the dimensionality of the system and the soliton interactions.

We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.

Multiparticle entanglement enables quantum simulations, quantum computing, and quantum-enhanced metrology. Yet, there are few methods to produce and measure such entanglement while maintaining single-qubit resolution as the number of qubits is scaled up. Using atom chips and fiber-optical cavities, we have developed a method based on nondestructive collective measurement and conditional evolution to create symmetric entangled states and perform their tomography. We demonstrate creation and analysis of entangled states with mean atom numbers up to 41 and experimentally prove multiparticle entanglement. Our method is independent of atom number and should allow generalization to other entangled states and other physical implementations, including circuit quantum electrodynamics.

We present a quantitative study of roughness in the magnitude of the magnetic field produced by a current carrying microwire, i.e. in the trapping potential for paramagnetic atoms. We show that this potential roughness arises from deviations in the wire current flow due to geometric fluctuations of the edges of the wire : a measurement of the potential using cold trapped atoms agrees with the potential computed from the measurement of the wire edge roughness by a scanning electron microscope.

A measurement necessarily changes the quantum state being measured, a phenomenon known as back-action. Real measurements, however, almost always cause a much stronger back-action than is required by the laws of quantum mechanics. Quantum non-demolition measurements have been devised that keep the additional back-action entirely within observables other than the one being measured. However, this back-action on other observables often imposes its own constraints. In particular, free-space optical detection methods for single atoms and ions (such as the shelving technique, a sensitive and well-developed method) inevitably require spontaneous scattering, even in the dispersive regime. This causes irreversible energy exchange (heating), which is a limitation in atom-based quantum information processing, where it obviates straightforward reuse of the qubit. No such energy exchange is required by quantum mechanics. Here we experimentally demonstrate optical detection of an atomic qubit with significantly less than one spontaneous scattering event. We measure the transmission and reflection of an optical cavity containing the atom. In addition to the qubit detection itself, we quantitatively measure how much spontaneous scattering has occurred. This allows us to relate the information gained to the amount of spontaneous emission, and we obtain a detection error below 10 per cent while scattering less than 0.2 photons on average. Furthermore, we perform a quantum Zeno-type experiment to quantify the measurement back-action, and find that every incident photon leads to an almost complete state collapse. Together, these results constitute a full experimental characterization of a quantum measurement in the 'energy exchange-free' regime below a single spontaneous emission event. Besides its fundamental interest, this approach could significantly simplify proposed neutral-atom quantum computation schemes, and may enable sensitive detection of molecules and atoms lacking closed transitions.

We have observed the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function g^{(2)}(t) of the microwave field inside one of the two resonators. The lowest measured value of g^{(2)}(0) is 0.4 for a resonator population of approximately 10^{-2} photons. The time evolution of g^{(2)}(t) exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade.