Michał Karski

Quantum Walk in Position Space with Single Optically Trapped Atoms

Strolling Out on a Quantum Walk In a random walk, a walker moves one step to the left or one step to the right depending on the outcome of a coin toss. The distribution between possible locations is well known and forms the basis for algorithms in information processing, describing diffusion processes in physics or biology, and has even been used as a model for stock market prices. Karski et al. (p. 174) use a single caesium atom trapped in a one-dimensional optical lattice to implement the quantum counterpart—a quantum walk. The coherence of a quantum system results in a departure from the classical picture, producing a distribution that is quite different that depends on the internal state of the atom. The results may have implications for search algorithms and quantum information processing protocols. A single cesium atom trapped in an optical lattice is used to illustrate a quantum walk. The quantum walk is the quantum analog of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.

Nearest-neighbor detection of atoms in a 1D optical lattice by fluorescence imaging.

We overcome the diffraction limit in fluorescence imaging of neutral atoms in a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm, we reliably infer the separation of two atoms down to nearest neighbors. We observe light induced losses of atoms occupying the same lattice site, while for atoms in adjacent lattice sites, no losses due to light induced interactions occur. Our method points towards characterization of correlated quantum states in optical lattice systems with filling factors of up to one atom per lattice site.

Microwave Control of Atomic Motion in Optical Lattices

We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97% and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long-range quantum transport.

Digital atom interferometer with single particle control on a discretized space-time geometry

Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 × 10-4 in units of gravitational acceleration g.

Imprinting patterns of neutral atoms in an optical lattice using magnetic resonance techniques

We prepare arbitrary patterns of neutral atoms in a one- dimensional (1D) optical lattice with single-site precision using microwave radiation in a magnetic field gradient. We give a detailed account of the current limitations and propose methods to overcome them. Our results have direct relevance for addressing planes, strings or single atoms in higher-dimensional optical lattices for quantum information processing or quantum simulations with standard methods in current experiments. Furthermore, ourfindings pave the way for arbitrary single-qubit control with single-site resolution.

Electron spectra close to a metal-to-insulator transition

A high-resolution investigation of the electron spectra close to the metal-to-insulator transition in dynamic mean-field theory is presented. An all-numerical, consistent confirmation of a smooth transition at zero temperature is provided. In particular, the separation of energy scales is verified. Unexpectedly, sharp peaks at the inner Hubbard band edges occur in the metallic regime. They are signatures of the important interaction between single-particle excitations and collective modes.

Single-particle dynamics in the vicinity of the Mott-Hubbard metal-to-insulator transition

The single-particle dynamics close to a metal-to-insulator transition induced by strong repulsive interaction between the electrons is investigated. The system is described by a half-filled Hubbard model which is treated by dynamic mean-field theory evaluated by high-resolution dynamic density-matrix renormalization. We provide theoretical spectra with momentum resolution which facilitate the comparison to photoelectron spectroscopy.

Direct Observation and Analysis of Spin Dependent Transport of Single Atoms in a 1D Optical Lattice

We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by

Matter wave interference of single trapped atoms

\pi

Quantum transport of single neutral atoms

causes displacement of the