ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

QUANTUM COMPUTING

ATOMS AND CAVITY QED

A. Physical approach and perspective

Neutral-atom based systems are so far the only systems for QIPC in which both a significant control over few-particle system has been obtained and realizations of large-scale systems are already present in the laboratory. Neutral-atom systems provide excellent intrinsic scalability because the properties of an ensemble of atoms do not dramatically differ from an individual atom. Quantum information with neutral atoms therefore provides a unique opportunity to test and develop experimentally relevant QIPC schemes for large-scale systems.

All QIPC schemes based on neutral atoms employ a quantum register with trapped atoms carrying quantum information in internal atomic states. The schemes differ, however, in the way individual qubits are coupled during a gate operation. The schemes can roughly be divided into two categories:

• Firstly, a gate operation is performed by means of a controlled collision of two qubits. Such collisions require 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 (bottom-up approach), or by loading a Bose-Einstein condensate into an optical lattice (top-down approach). Both the bottom-up and the top-down approach offer the possibility of a massive parallelism, with many pairs of atoms colliding at once. The top-down approach is ideal to develop a quantum toolbox for simulating nontrivial many-body systems.
• Secondly, a gate operation is performed by exchanging a photon between two individual qubits. Such a scheme can be implemented 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 is realized either with Rydberg atoms in microwave cavities or 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.

In principle, the two schemes of implementing gates can be combined in one-and-the-same setup, for example by using atoms trapped in micro-magnetic potential wells produced by micron-sized current carrying wires or microscopic permanent magnets deposited on a chip. Such atom-chips are very promising building blocks for quantum logic gates because of their small size, intrinsic robustness, strong confinement, and potential scalability.

Besides performing discrete gate operations according to a predefined algorithm, neutral-atom systems are ideal for simulating quantum many-body systems. In general, quantum systems are very hard to simulate, given the fact that the dimension of the corresponding Hilbert space grows exponentially with the number of particles. This hinders our ability to understand the physical properties of general materials with a classical computer. However, using a quantum computer, it should be possible to simulate other quantum systems in a very efficient way.

Currently, both schemes of performing a gate operation with neutral atoms (collision or photon-exchange) are investigated experimentally in several dozen laboratories worldwide, about half of them located in Europe. The European groups working with a controllable number of atoms include I. Bloch (Mainz, D), T. Esslinger (Zurich, CH), P. Grangier (Orsay, F), S. Haroche (Paris, F), D. Meschede (Bonn, D), G. Rempe (Garching, D), H. Walther (Garching, D), and H. Weinfurter (Munich, D). Several other groups are presently setting up new experiments, including W. Ertmer (Hanover, D), E. Hinds (London, UK), J. Reichel (Paris, F), and J. Schmiedmayer (Heidelberg, D). The experimental program is strongly supported by implementation-oriented theory groups like H. Briegel (Innsbruck, A), K. Burnett (Oxford, UK), J. I. Cirac (Garching, D), A. Ekert (Cambridge, UK), P. L. Knight (London, UK), M. Lewenstein (Barcelona, E), K. Mølmer (Aarhus, Dk), M. B. Plenio (London, UK), W. Schleich (Ulm, D), P. Tombesi (Camerino, I), R. Werner (Braunschweig, D), M. Wilkens (Potsdam, D), and P. Zoller (Innsbruck, A). 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, partly because of the support provided by the European Union.

B. State of the art

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 to control and manipulate neutral atoms have been developed:

Optical tweezers and arrays of optical traps are ideal to perform collisional gates:

1. Bottom-up approach:
   • 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, and coherent write and read operations on individual qubits were performed.
   • Moreover, a small number of atoms were loaded into a two-dimensional array of dipole traps made with a microlens array, and the atoms were moved by moving the trap array.
2. Top-down approach:
   • 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.
   • A highly parallelized quantum gate was 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.

Cavity QED, possibly in combination with optical dipole traps, is the most promising technique for realizing an interface between different carriers of quantum information:

1. Probabilistic approach in free space:
   • A single trapped atom has been entangled with a single photon.
2. 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.
   • Gates have been demonstrated.
   • New tools for monitoring decoherence of mesoscopic quantum superpositions have been developed.
3. Deterministic approach with optical cavities:
   • The strong atom-photon coupling has been employed to realize a 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.
   • Moreover, single atoms were optically trapped inside a cavity.
   • A novel cooling technique avoiding spontaneous emission was successfully implemented.

Atom chips: The ability to magnetically trap and cool atoms close to a surface of a micro-fabricated substrate has led to an explosive development of atom chips in the past few years. The main achievements include:

1. Cooling of atoms to quantum degeneracy (Bose-Einstein condensation).
2. Transport of an ensemble of atoms using a magnetic conveyor belt.
3. Manipulation of atoms with electric and optical fields.
4. Very long coherence times by using appropriate qubit states.
5. Multilayer atom chips with sub-µm resolution and smooth magnetic potentials.

All of the achievements reported in this section have been realized within European labs, and in many cases they are purely European achievements, in the sense that they are not to be found in labs outside Europe.

C. Present challenges

Most neutral-atom systems have not yet demonstrated two-qubit operations, and some of them not even a single-qubit operation, mainly because the technology to perform single-atom experiments is relatively new (less than 10 years).

Optical tweezers and arrays of optical traps are most advanced in manipulating neutral-atom qubits.

1. In the bottom-up approach, the main challenges are first to implement a two-qubit quantum gate, e.g., using a controlled collision of two atoms, and then to increase the size of the quantum register to more than 2 atoms.
2. In the top-down approach, full addressability of each individual qubit of the closely spaced register is one of the main challenges.
3. In both approaches, the speed of a gate must eventually be increased by implementing a collision which exhibits a large cross section, for example by involving Rydberg atoms or molecular (e.g., Feshbach) interactions.

Cavity QED: The main difficulty in implementing QIPC protocols in present demonstration experiments is the enormous technological complexity required to obtain full control over both atoms and photons at the single-particle level.

1. The probabilistic approach suffers from the low efficiency of photon generation and detection, and the large solid angle of photon emission for a free-space atom.
2. The deterministic approach employing microwave cavities has intracavity-photon generation and absorption efficiencies close to 100%, and the implementation of simple algorithms is in view.
   • One of the main challenges is the demonstration of scalability. The preparation of a non-local entangled and possibly mesoscopic quantum state shared between two remote cavities is a major task.
   • Another challenge is the realization of quantum feedback or error correction schemes to preserve the quantum coherence of the field stored in a cavity with a finite quality factor.
3. The deterministic approach utilizing optical cavities has led to photon-emission efficiencies of up to about 30 %. Challenges are
   • To entangle in a deterministic manner a single atom with a single photon,
   • and to teleport the quantum states between distant photon-emitting and photon-receiving atoms.
   • In order to integrate individual quantum-network nodes into a scalable quantum-computing network, a set of individually addressable atoms located in different cavities must be implemented.
   • Moreover, single-photon quantum repeaters which are necessary to communicate quantum information over large distances need to be developed.
   • Ultimately, the gate speed should be increased by installing a few-wavelength long cavity. The combination of such a micro-cavity with presently available trapping and cooling techniques is a challenge.

In both the microwave and the optical domains, a method of deterministically transporting single atoms in and out of a cavity, for example by means of an optical conveyor belt, is needed to address the individual atoms of a stationary quantum register.

Atom chips: Despite their recent achievements, experiments with atom chips are still facing a large number of challenges for implementing QIPC.

1. An efficient scheme to address, manipulate and detect a single qubit in the microtrap of an atom chip must be developed.
2. A quantum memory, that is the reading and writing of quantum information into single atoms or atomic ensembles must be realized.
3. Next, a two-qubit quantum gate, for example by employing a controlled collision, must be implemented.
4. The full demonstration of the potential provided by atom chips requires the realization of large-scale integration, e.g., with several 10 qubits.
5. Potential roughness very close (µm) to micro-fabricated structures is of concern for qubit storage and transport. Even though for current-carrying structures the problem can be solved and compensated for by the design and fabrication methods as developed recently, micro-structures with fewer defects might be needed for permanent magnets.
6. Merging atom-chip technology and cavity QED is promising. High-finesse miniature optical or microwave cavities can be coupled to ground state or Rydberg atoms trapped on a chip. Coherence preserving trap architectures are an important first step towards a fully scalable architecture combining the best of both worlds.

All of the strategic challenges in this section represent current or planned activity at European labs.

D. Key references

A tutorial review on QIPC with atoms, ions and photons can be found in, e.g.:

[1] C. Monroe, Quantum Information Processing with Atoms and Photons, Nature 416, 238-246 (2002).

[2] J.I. Cirac and P. Zoller, New Frontiers in Quantum Information with Atoms and Ions, Physics Today 38-44 (March 2004).