Matter-wave interference experiments enable us to study matter at its most basic, quantum level and form the basis of high-precision sensors for applications such as inertial and gravitational field sensing. Success in both of these pursuits requires the development of atom-optical elements that can manipulate matter waves at the same time as preserving their coherence and phase. Here, we present an integrated interferometer based on a simple, coherent matter-wave beam splitter constructed on an atom chip. Through the use of radio-frequency-induced adiabatic double-well potentials, we demonstrate the splitting of Bose-Einstein condensates into two clouds separated by distances ranging from 3 to 80 microns, enabling access to both tunnelling and isolated regimes. Moreover, by analysing the interference patterns formed by combining two clouds of ultracold atoms originating from a single condensate, we measure the deterministic phase evolution throughout the splitting process. We show that we can control the relative phase between the two fully separated samples and that our beam splitter is phase-preserving

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering 1, 2 that is both of fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons [3][4][5] to strongly interacting atomic Rydberg states [6][7][8][9][10][11][12] in a cold, dense atomic gas 13 . Our approach opens the door for quantum-byquantum control of light fields, including single-photon switching 14 , all-optical deterministic 1 quantum logic 15 , and the realization of strongly correlated many-body states of light 16 .Recently, remarkable advances have been made towards optical systems that are nonlinear at the level of individual photons. The most promising approaches have used high-finesse optical cavities to enhance the atom-photon interaction probability 2,[17][18][19][20][21] . In contrast, our present method is cavity-free and is based on mapping photons onto atomic states with strong interactions in an extended atomic ensemble 13,14,22,23 . The central idea is illustrated in Fig. 1, where a quantum probe field incident onto a cold atomic gas is coupled to high-lying atomic states (Rydberg levels 24 ) by means of a second, stronger laser field (control field). For a single incident probe photon, the control field induces a transparency window in the otherwise opaque medium via Electromagnetically Induced Transparency (EIT), and the probe photon travels at much reduced speed in the form of a coupled excitation of light and matter (Rydberg polariton). However, in stark contrast to conventional EIT 5 , if two probe photons are incident onto the Rydberg EIT medium, the strong interaction between two Rydberg atoms tunes the EIT transition out of resonance, thereby destroying the EIT and leading to absorption 14,22,23, 25, 26 . The experimental demonstration of an extraordinary optical material exhibiting strong two-photon attenuation in combination with single-photon transmission is the central result of this work.The quantum nonlinearity can be viewed as a photon-photon blockade mechanism that prevents the transmission of any multi-photon state. It arises from the Rydberg excitation blockade 27 , which precludes the simultaneous excitation of two Rydberg atoms that are separated by less than a blockade radius r b (see Figure 1). During the optical excitation, an incident single photon is 2 converted, under the EIT conditions, into a Rydberg polariton inside the medium. However, due to the Rydberg blockade, a second polariton cannot travel within a blockade radius from the first one, and EIT is destroyed. Accordingly if the second photon approaches the single Rydberg polariton, it will be signific...

We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic hollow core of a single-mode photoniccrystal fiber and using quantum optical techniques for generating slow light propagation and large nonlinear interaction between light beams.