R. J. C. Spreeuw

A classical analogy of entanglement

A classical analogy of quantum mechanical entanglement is presented, using classical light beams. The analogy can be pushed a long way, only to reach its limits when we try to represent multiparticle, or nonlocal, entanglement. This demonstrates that the latter is of exclusive quantum nature. On the other hand, the entanglement of different degrees of freedom of the same particle might be considered classical. The classical analog cannot replace Einstein-Podolsky-Rosen type experiments, nor can it be used to build a quantum computer. Nevertheless, it does provide a reliable guide to the intuition and a tool for visualizing abstract concepts in low-dimensional Hilbert spaces.

Implementation of Quantum Search Algorithm using Classical Fourier Optics

We report on an experiment on Grovers quantum search algorithm showing that classical waves can search a N-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in approximately square root[N] iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the size of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.

LASER-LIKE SCHEME FOR ATOMIC-MATTER WAVES

We present a scheme for a laser-like source of atoms, starting from atomic de Broglie wave resonators, for which we seek to overcome losses by gain. The resonators are blue-detuned optical dipole-force traps, which can be loaded continuously or repetitively with laser-cooled atoms. This is achieved by trapping the atoms in a different internal state than that used for laser cooling. The transfer of cold atoms into the trapped states involves emission of a photon and can be stimulated by the presence of identical bosonic atoms in the final atomic state. Numerical simulations show threshold behaviour, mode competition and Poissonian atom statistics above threshold.

Two-dimensional array of microtraps with atomic shift register on a chip

Arrays of trapped atoms are the ideal starting points for developing registers comprising large numbers of physical qubits for storing and processing quantum information. One very promising approach involves neutral atom traps produced on microfabricated devices known as atom chips, as almost arbitrary trap configurations can be realized in a robust and compact package. Until now, however, atom chip experiments have focused on small systems incorporating single or only a few individual traps. Here, we report experiments on a two-dimensional array of trapped ultracold atom clouds prepared using a simple magnetic-film atom chip. We are able to load atoms into hundreds of tightly confining and optically resolved array sites. We then cool the individual atom clouds in parallel to the critical temperature required for quantum degeneracy. Atoms are shuttled across the chip surface utilizing the atom chip as an atomic shift register and local manipulation of atoms is implemented using a focused laser to rapidly empty individual traps.

Classical wave-optics analogy of quantum information processing

An analogous model system for quantum information processing is discussed, based on classical wave optics. The model system is applied to three examples that involve three qubits: (i) three-particle Greenberger-Horne-Zeilinger entanglement, (ii) quantum teleportation, and (iii) a simple quantum error correction network. It is found that the model system can successfully simulate most features of entanglement, but fails to simulate quantum nonlocality. Investigations of how far the classical simulation can be pushed show that quantum nonlocality is the essential ingredient of a quantum computer, even more so than entanglement. The well-known problem of exponential resources required for a classical simulation of a quantum computer, is also linked to the nonlocal nature of entanglement, rather than to the nonfactorizability of the state vector.

Spatially resolved excitation of Rydberg atoms and surface effects on an atom chip

We demonstrate spatially resolved, coherent excitation of Rydberg atoms on an atom chip. Electromagnetically induced transparency (EIT) is used to investigate the properties of the Rydberg atoms near the gold-coated chip surface. We measure distance-dependent shifts ({approx}10 MHz) of the Rydberg energy levels caused by a spatially inhomogeneous electric field. The measured field strength and distance dependence is in agreement with a simple model for the electric field produced by a localized patch of Rb adsorbates deposited on the chip surface during experiments. The EIT resonances remain narrow (<4 MHz) and the observed widths are independent of atom-surface distance down to {approx} 20 {mu}m, indicating relatively long lifetime of the Rydberg states. Our results open the way to studies of dipolar physics, collective excitations, quantum metrology, and quantum information processing involving interacting Rydberg excited atoms on atom chips.

Lattice of microtraps for ultracold atoms based on patterned magnetic films

We have realized a two-dimensional permanent magnetic lattice of Ioffe-Pritchard microtraps for ultracold atoms. The lattice is formed by a single 300-nm magnetized layer of FePt, patterned using optical lithography. Our magnetic lattice consists of more than 15 000 tightly confining microtraps with a density of 1250 traps/mm{sup 2}. Simple analytical approximations for the magnetic fields produced by the lattice are used to derive relevant trap parameters. We load ultracold atoms into at least 30 lattice sites at a distance of approximately 10 {mu}m from the film surface. The present result is an important first step toward quantum information processing with neutral atoms in magnetic lattice potentials.

Detection of small atom numbers through image processing

We demonstrate improved detection of small trapped atomic ensembles through advanced postprocessing and optimal analysis of absorption images. A fringe-removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation in well-localized ensembles and is applied to real experimental data to measure the population differences and intrinsic atom shot noise between spatially separated ensembles each comprising between 10 and 2000 atoms. The combined techniques improve our signal-to-noise ratio by a factor of 3, to a minimum resolvable population difference of 17 atoms, close to our ultimate detection limit.

Magnetic-film atom chip with 10 μm period lattices of microtraps for quantum information science with Rydberg atoms

We describe the fabrication and construction of a setup for creating lattices of magnetic microtraps for ultracold atoms on an atom chip. The lattice is defined by lithographic patterning of a permanent magnetic film. Patterned magnetic-film atom chips enable a large variety of trapping geometries over a wide range of length scales. We demonstrate an atom chip with a lattice constant of 10 μm, suitable for experiments in quantum information science employing the interaction between atoms in highly excited Rydberg energy levels. The active trapping region contains lattice regions with square and hexagonal symmetry, with the two regions joined at an interface. A structure of macroscopic wires, cutout of a silver foil, was mounted under the atom chip in order to load ultracold (87)Rb atoms into the microtraps. We demonstrate loading of atoms into the square and hexagonal lattice sections simultaneously and show resolved imaging of individual lattice sites. Magnetic-film lattices on atom chips provide a versatile platform for experiments with ultracold atoms, in particular for quantum information science and quantum simulation.

Optimized magnetic lattices for ultracold atomic ensembles

We introduce a general method for designing tailored lattices of magnetic microtraps for ultracold atoms on the basis of patterned permanently magnetized films. A fast numerical algorithm is used to automatically generate patterns that provide optimal atom confinement while respecting desired lattice symmetries and trap parameters. The algorithm can produce finite and infinite lattices of any plane symmetry; we focus specifically on square and triangular lattices, which are of interest for future experiments. Typical trap parameters, as well as the impact of realistic imperfections such as finite lithographic resolution and magnetic inhomogeneity, are discussed. The designer lattices presented open new avenues for quantum simulation and quantum information processing with ultracold atoms on atom chips.