1Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch & Immanuel Bloch* Sektion Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4/III, D-80799 Munich, Germany & Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany. Entanglement lies at the heart of quantum mechanics and in recent years has been identified as an essential resource for quantum information processing and computation1-4. Creating highly entangled multi-particle states is therefore one of the most challenging goals of modern experimental quantum mechanics, touching fundamental questions as well as practical applications. Here we report on the experimental realization of controlled collisions between individual neighbouring neutral atoms trapped in the periodic potential of an optical lattice. These controlled interactions act as an array of quantum gates between neighbouring atoms in the lattice and their massively parallel operation allows the creation of highly entangled states in a single operational step, independent of the size of the system5,6. In the experiment, we observe a coherent entangling-disentangling evolution in the many-body system depending on the phase shift acquired during the collision between neighbouring atoms. This dynamics is indicative of highly entangled many-body states that present novel opportunities for theory and experiment.2During the last years, Bose-Einstein condensates have been loaded into the periodic dipole force potential of a standing wave laser field – a so-called optical lattice. In these new systems, it has been possible to probe fundamental many body quantum mechanics in an unprecedented way, with experiments ranging from Josephson junction tunnel arrays7,8 to the observation of a Mott insulating state of quantum gases9,10. Important applications for atoms in a Mott insulating state to quantum information processing have been envisaged early on. The Mott state itself, with one atom per lattice site, could act as a huge quantum memory, in which information would be stored in atoms at different lattice sites. Going far beyond these ideas, it has been suggested that controlled interactions between atoms on neighbouring lattice sites could be used to realise a massively parallel array of neutral atom quantum gates5,11-14, with which a large multi particle system could be highly entangled6 in a single operational step. Furthermore, the repeated application of the quantum gate array could form the basis for a universal quantum simulator along the original ideas of Feynman for a quantum computer as a simulator of quantum dynamics15-17. The basic requirement for such a unique control over the quantum state of a many body system including its entanglement is the precise microscopic control of the interactions between atoms on different lattice sites. In order to illustrate this, let us consider the case of two neighbouring atoms, initially in state 100jj+Ψ= placed on the jth and j+1th lattice site of the periodic potential in the spin-state 0 . First both atoms are brought into a superposition of two internal states 0 and 1 using a π/2 pulse such that ()()11010 1/2jj j j++Ψ= + +. Then a spin-dependent transport18 splits the3spatial wave packet of each atom such that the wave packet of the atom in state 0 moves to the left, whereas the wave packet of the atom in state 1 moves to the right. The two wave packets are separated by a distance ∆x=λ/2, such that now()12111200 01 1 0 1 1 /2jj jj j j j j++++++Ψ= + + + , where in the notation atoms in state 0 have retained their original lattice site index and λ is the wavelength of the laser forming the optical periodic potential. The collisional interaction between the atoms5,12,19 over a time thold will lead to a distinct phase shift 01/holdUtϕ= = , when both atoms occupy the same lattice site j+1 resulting in: ()12111200 01 1 0 1 1 /2ijj jj j j j je−ϕ++++++Ψ= + + + . Here U01 is the onsite-interaction matrix element that characterises the interaction energy when an atom in state 0 and an atom in state 1 are placed at the same lattice site and = is Planck’s constant divided by 2π. Alternatively a dipole-dipole interaction has been proposed11 for generating a state dependent phase shift ϕ. The final many body state after bringing the atoms back to their original site and applying a last π/2 pulse can be expressed as 11111 BELL22iijjee−ϕ −ϕ++−Ψ= + . Here BELL denotes the Bell-like state corresponding to ()()()11 1100 1 10 1 /2jj j jj j++ ++−+ + . This scheme can be generalised when more than two particles are placed next to each other, starting from a Mott insulating state of matter9,10. In such a Mott insulating state, atoms are localized to lattice sites, with a fixed number of atoms per site. For three4particles e.g. one can show that if ϕ=(2n+1) π (with n being an integer), so called maximally entangled Greenberger-Horne-Zeilinger (GHZ) states20 are realised. For a string of N>3 atoms, where each atom interacts with its left and right-hand neighbour (see Fig. 1), the entire string of atoms can be entangled to form so called cluster states in a single operational step5,6. The controlled interactions described above can be viewed as being equivalent to an ensemble of quantum gates acting in parallel3,5. The experimental setup used to load Bose-Einstein condensates into the three-dimensional optical lattice potential (see methods section) is similar to our previous work10,19. Briefly, we start with a quasi-pure Bose-Einstein condensate of 105 87Rb atoms in the 1, 1FFm==− state in a harmonic magnetic trapping potential with isotropic trapping frequencies of ω=2π×14 Hz. Here F and mF denote the total angular momentum and the magnetic quantum number of the atom’s hyperfine state. The three-dimensional periodic potential of an optical lattice is then ramped up over a period of 80 ms to a potential depth of 25 Er, such that the Bose-Einstein condensate is converted into a Mott insulating state. Here Er denotes the recoil energy Er==2k2/2m, with k=2π/λ being the wave vector of the laser light and m the mass of a single atom. For our experimental parameters of atom number and harmonic confinement, such a Mott insulator should consist mainly of a central core with n=1 atom per lattice site9,21,22. The magnetic trapping potential is then rapidly switched off, but