QUROPE Quantum Information Processing and Communication in Europe

A. Physical approach and perspective

Neutral atoms and molecules provide a promising test bed for the development of scalable general purpose quantum processors, and for quantum simulators as special purpose quantum computers involving a very large number of qubits. As in the case of ions, qubits can be represented by long-lived internal atomic and molecular states in electronic ground states (hyperfine levels, rotational states), or in metastable excited electronic states, which can be manipulated by optical and microwave fields. The unique promises of neutral atom quantum computing rest in particular on the well developed cooling and trapping techniques, as exemplified by laser cooling, realization of Bose Einstein condensates and quantum degenerate Fermi gases, in combination with optical, magnetic and electric traps, realized in free space or in cavities or on atom chips. Such techniques provide an ideal starting point to build and prepare large scale quantum registers with high fidelity. At present these trapping and cooling techniques are being extended to molecules, including, for example, electric on-chip traps for polar molecules. The scenarios of quantum computing with neutral atoms are directly linked to the development of specific trapping techniques. First, traps can be developed allowing the independent manipulation of the centre-of-mass degrees of freedom of individual atoms and molecules, including the addressing of single qubits, which is a necessary requirement for general purpose quantum computing; and massively parallel, identical manipulations of large number of qubits, as realized for example in optical lattices, are relevant in the context of quantum simulators of translation invariant condensed matter systems.

Entanglement of neutral atom or molecule qubits is based on the following physical mechanisms

• Controlled qubit-dependent two-particle interactions, as for example in cold coherent collisions, cavity-assisted collisions, or dipole-dipole interactions between highly excited atomic states (Rydberg states); this kind of approach essentially provide deterministic entanglement and quantum gates;
• Entanglement between distant qubits generated via photon exchange, which plays the role of a quantum data bus; this approach is most often related to the idea of entanglement swapping, and it is usually probabilistic: a measurement must be successful for the entangled state to be generated.

Both scenarios can be played either in free space, or by using cavity QED techniques, where the atomic or molecular qubit is strongly coupled to a high-Q cavity. This can be done in the optical domain by coupling to an electronic excitation, or in the microwave regime for a transition between Rydberg states or rotational states of a polar molecule. Two-qubit gates between distant qubits can be achieved via photon exchange as quantum data bus, in close formal analogy to the phonon data bus of collective oscillation modes in trapped ions. These cavity QED setups also provide a natural interface to quantum communication with photons.

Atoms and molecules can be stored in optical lattices, corresponding to an array of microtraps generated by counterpropagating laser fields. The dynamics of cold atoms loaded into optical lattices can be described by a Hubbard model, with atoms hopping between lattice sites, and interacting via collisions. Thus cold atoms in optical lattices provide a direct way to simulating condensed matter systems with a large number of bosons or fermions. In addition, loading an optical lattice from an atomic Bose Einstein condensate provides via the superfluid-Mott insulator transition the preparation of a Mott phase with exactly one atom per lattice site, and thus the preparation of a very large number of atomic qubits. These atoms can be entangled in parallel operations with qubit-dependent controllable 2-particle interactions, provided, for example, by coherent collisional interactions in combination with movable qubit (spin) dependent optical lattices. This provides the basis for a digital quantum simulator, for example of a spin lattice system, where the time evolution generated by the Hamiltonian is decomposed into a series of single and two-qubit gates performed in parallel on all qubits (spins).

A major recent development is the possibility to image and (at least partially) address individual atoms in optical lattices. When coupled to atom-atom interactions using either cold collisions or Rydberg dipole-dipole interactions, this opens the way to performing nearly individual measurements on large arrays of entangled atoms, which would be a crucial steps towards quantum simulators and even quantum computers.

For single atoms strongly coupled to an optical cavity, single photons for the purpose of exchanging quantum information between remote locations can be generated on demand and with high quantum efficiency. Protocols for generating a stream of photons with entanglement mediated and controlled by a single intracavity atom have been proposed. In addition to these deterministic mechanisms for entanglement, probabilistic protocols can be developed which are based on free space atoms emitting photons where entanglement is achieved by appropriate photon detection.

Currently, quantum computing with neutral atoms is investigated experimentally in several dozen laboratories worldwide, with half of them located in Europe. The European groups working with a controllable number of atoms include I. Bloch (Munich, DE), T. Esslinger (Zurich, CH), P. Grangier (Palaiseau, FR), S. Haroche (Paris, FR), D. Meschede (Bonn, DE), G. Rempe (Garching, DE), and H. Weinfurter (Munich, DE). Related experiments, sometimes done in an AMO context broader than QIP only, are also performed by W. Ertmer (Hannover, DE), E. Hinds (London, UK), J. Reichel (Paris, FR), and J. Schmiedmayer (Vienna, AT). The experimental program is strongly supported by implementation-oriented theory groups like H. Briegel (Innsbruck, AT), K. Burnett (Oxford, UK), J. I. Cirac (Garching, DE), A. Ekert (Cambridge, UK), P. L. Knight (London, UK), M. Lewenstein (Barcelona, ES), K. Mølmer (Aarhus, DK), M. B. Plenio (London, UK), W. Schleich (Ulm, DE), P. Tombesi (Camerino, IT), R. Werner (Braunschweig, DE), M. Wilkens (Potsdam, DE), & P. Zoller (Innsbruck, AT). In fact, European theory groups have played a crucial role in the development of QIPC science from the very beginning. The close collaboration between experiment and theory in Europe is unique, largely thanks to the support provided by the European Union.

B. State of the art

I. Quantum memories: The strength of using neutral atoms for QIPC is their relative insensitivity against environmental perturbations. Their weakness comes from the fact that only shallow trapping potentials are available. This disadvantage is compensated by cooling the atoms to very low temperatures. So far, several different experimental techniques for trapping and manipulating neutral atoms have been developed:

Optical tweezers and arrays of optical traps allow for the preparation of a well-defined quantum state of atomic motion, as can be achieved by either cooling single atoms into the ground state of the trapping potential, or by loading a Bose-Einstein condensate into an optical lattice. Given recent developments, both approaches have the potential for individual atom manipulations, and for massive parallelism, with many pairs of atoms colliding at once. The landmark results attained are:

• Single atoms were trapped with a large aperture lens, thus providing a three-dimensional sub-wavelength confinement.
• Single atoms were also loaded into the antinodes of a one-dimensional standing wave, and excited into a quantum superposition of internal states.
• This superposition was preserved under transportation of the atoms; coherent write and read operations on individual qubits were performed.
• A small number of atoms were loaded into a two-dimensional array of movable dipole traps made with a microlens array.
• Single atoms were loaded into the antinodes of a three-dimensional optical lattice, by starting from a Bose-Einstein condensate and using a Mott transition.
• Various imaging techniques (using large aperture lenses, or even electron beams) were developed to see individual sites and even individual atoms in planar (two-dimensional) optical lattices.

Atom chips: The ability to magnetically trap and cool atoms close to a surface of a micro-fabricated substrate (for example using micro-magnetic potential wells produced by micron-sized current carrying wires or microscopic permanent magnets) has led to an explosive development of atom chips in the past few years. Such devices are very promising building blocks for quantum logic gates due to their small size, intrinsic robustness, strong confinement, and potential scalability. The main accomplishments they have attained include: Cooling of atoms to quantum degeneracy (Bose-Einstein condensation). Transport of an ensemble of atoms using a magnetic conveyor belt. Very long coherence times by using appropriate qubit states. Multilayer atom chips with sub-µm resolution and smooth magnetic potentials. On-chip single-qubit rotation via two-photon transitions on hyperfine qubits. Single-atom detection using various techniques, including Fabry-Perot cavities. Advanced atom interferometry techniques using BEC on chips. Traps for polar molecules at the individual level have recently been proposed, based on microwave or electric fields, and are the subject of growing experimental investigation. On the experimental side, cold polar molecules at millikelvin temperatures have been produced by several different techniques, including deceleration of supersonic molecules, filtering of slow molecules from a thermal ensemble, Helium buffer gas cooling in a cryogenic environment, and more recently by direct photoassociation. ensembles of cold polar molecules have been stored in magnetic or electric bottles. Techniques using atomic ensembles either in vapour cells, optical traps, or cryo-cooled rare-earth doped crystals. These methods are extensively discussed under the "Quantum communications" heading, and we refer the reader to sections 4.1.3, 4.1.4, 4.1.5 for details. We note that studies related to quantum repeaters, involving both quantum memories and some data processing, are currently establishing a strong bridge between quantum communications and quantum computing, under the general goal of achieving efficient quantum information processing. II. Entangling gates: a variety of schemes have been proposed theoretically, based on interatomic interactions which may be either direct (for instance collisional, possibly enhanced by Feshbach resonances, or between dipoles of Rydberg excited atoms) or mediated by a quantum data bus, i.e. a different degree of freedom (for instance photons, freely propagating or within a high-finesse cavity mode). Optical tweezers and arrays of optical traps are ideal to perform collisional gates, which require the preparation of a well-defined quantum state of atomic motion. With optical lattices, highly parallelized quantum gates were implemented by state-selectively moving the atoms, and making them interact using cold collisions. This landmark experiment has pioneered a new route towards large-scale massive entanglement and quantum simulators with neutral atoms. With single atoms in optical tweezers, a series of experiments in 2009-2010 were able to obtain fast atom-atom entanglement and quantum gates using the Rydberg blockade mechanism, as initially proposed in 2000. This scheme is very promising for neutral atoms, because it is very fast (sub-microsecond), does not require to move the atoms, and is relatively insensitive to the thermal motion of the trapped atoms. Cavity QED, possibly in combination with optical dipole traps, is a very promising technique for realizing an interface between different carriers of quantum information, implemented either with free-space atoms emitting photons in a random direction (probabilistic approach), or with atoms in high-finesse cavities where the strong atom-photon coupling guarantees full control over photon emission and absorption (deterministic approach). The latter approach can be realized both with Rydberg atoms in microwave cavities as well as with ground-state atoms in optical cavities. If each atom resides in its own cavity, the scheme guarantees addressability and scalability in a unique way. As quantum information is exchanged via flying photons, the individual qubits of the quantum register can easily be separated by a large distance. The photon-based scheme is therefore ideal to build a distributed quantum network. The main achievements in this sector include: Probabilistic approach in free space: A single trapped atom has been entangled with a single photon. Two-photon interference effects of the Hong-Ou-Mandel type between single photons emitted by separate atoms have been observed. Deterministic approach using microwave cavities: Circular Rydberg atoms and superconducting cavities are proven tools for fundamental tests of quantum mechanics and quantum logic: Complex entanglement manipulations on individually addressed qubits with long coherence times have been realized, including quantum gates. New tools for monitoring the decoherence of mesoscopic quantum superpositions have been developed. Deterministic approach with optical cavities: The strong atom-photon coupling has been employed to realize a quasi-deterministic source of flying single photons, a first step towards a true quantum-classical interface. With single photons, two-photon interference effects of the Hong-Ou-Mandel type have been observed. These experiments demonstrate that photons emitted from an atom-cavity system show coherence properties well suited for quantum networking. Single atoms were optically trapped inside a cavity for such a long time that experiments can be performed with just one single atom, and cooling techniques avoiding spontaneous emission were successfully implemented. Single individually addressable atoms were deterministically transported in and out of a cavity by means of an optical conveyor belt. Most of the achievements reported in this section have been realized first within European labs, and the European leadership in that field is quite clear.