# Quantum technologies

Dieter Meschede's research group
Group members
Dr. Michal Karski
 Last positionin our group: Postdoc
 Field of researchin our group: Few-atom quantum systems

## Publications(up to 2016)

### 2016

• A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera and D. Meschede
Super-resolution microscopy of single atoms in optical lattices, New J. Phys. 18, 053010 (2016)arXivBibTeX
ABSTRACT »

We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.

### 2012

• A. Steffen, A. Alberti, W. Alt, N. Belmechri, S. Hild, M. Karski, A. Widera and D. Meschede
arXivBibTeX
ABSTRACT »
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.

### 2011

• M. Karski, L. Förster, J. Choi, W. Alt, A. Alberti, A. Widera and D. Meschede
Direct Observation and Analysis of Spin-Dependent Transport of Single Atoms in a 1D Optical Lattice, J. Korean Phys. Soc. 59, 2947 (2011)arXivBibTeX
ABSTRACT »
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 $\pi$ causes displacement of the $\sigma^{+}$- and $\sigma^{-}$-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.

### 2010

• M. Karski
State-selective transport of single neutral atoms, (2010), PhD thesisBibTeX
ABSTRACT »
The present work investigates the state-selective transport of single neutral cesium atoms in a one-dimensional optical lattice. It demonstrates experimental applications of this transport, including a single atom interferometer, a quantum walk and controlled two-atom collisions. The atoms are stored one by one in an optical lattice formed by a standing wave dipole trap. Their positions are determined with sub-micrometer precision, while atom pair separations are reliably inferred down to neighboring lattice sites using real-time numerical processing. Using microwave pulses in the presence of a magnetic field gradient, the internal qubit states, encoded in the hyperfine levels of the atoms, can be separately initialized and manipulated. This allows us to perform arbitrary single-qubit operations and prepare arbitrary patterns of atoms in the lattice with single-site precision. Chapter 1 presents the experimental setup for trapping a small number of cesium atoms in a one-dimensional optical lattice. Chapter 2 is devoted to fluorescence imaging of atoms, discussing the imaging setup, numeric methods and their performance in detail. Chapter 3 focuses on engineering of internal states of trapped atoms in the lattice using optical methods and microwave radiation. It provides a detailed investigation of coherence properties of our experimental system. Finally manipulation of individual atoms with almost single-site resolution and preparation of regular strings of atoms with predefined distances are presented. In Chapter 4, basic concepts, the experimental realization and the performance of the state-selective transport of neutral atoms over several lattice sites are presented and discussed in detail. Coherence properties of this transport are investigated in Chapter 5, using various two-arms single atom interferometer sequences in which atomic matter waves are split, delocalized, merged and recombined on the initial lattice site, while the interference contrast and the accumulated phase difference are measured. By delocalizing a single atom over several lattice sites, possible spatial inhomogeneities of fields along the lattice axis in the trapping region are probed. In Chapter 6, experimental realization of a discrete time quantum walk on a line with single optically trapped atoms is presented as an advanced application of multiple path quantum interference in the context of quantum information processing. Using this simple example of a quantum walk, fundamental properties of and differences between the quantum and classical regimes are investigated and discussed in detail. Finally, by combining preparation of atom strings, position-dependent manipulation of qubit states and state-selective transport, in Chapter 7, two atoms are deterministically brought together into contact, forming a starting point for investigating two-atom interactions on the most fundamental level. Future prospects and suggestions are finally presented in Chapter 8.
• M. Karski, L. Förster, J. Choi, A. Steffen, N. Belmechri, W. Alt, D. Meschede and A. Widera
Imprinting Patterns of Neutral Atoms in an Optical Lattice using Magnetic Resonance Techniques, New J. Phys. 12, 065027 (2010)arXivBibTeX
ABSTRACT »
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, our findings pave the way for arbitrary single-qubit control with single-site resolution.

### 2009

• M. Karski, L. Förster, J. Choi, W. Alt, A. Widera and D. Meschede
Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging, Phys. Rev. Lett. 102, 053001 (2009)arXivBibTeX
ABSTRACT »
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.
• L. Förster, M. Karski, J. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera, E. Montano, J. H. Lee, W. Rakreungdet and P. S. Jessen
Microwave Control of Atomic Motion in Optical Lattices, Phys. Rev. Lett. 103, 233001 (2009)arXivBibTeX
ABSTRACT »
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.
• M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera
Quantum Walk in Position Space with Single Optically Trapped Atoms, Science 325, 174 (2009)arXivBibTeX
ABSTRACT »
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.

### 2008

• M. Karski, C. Raas and G. S. Uhrig
Single-particle dynamics in the vicinity of the Mott-Hubbard metal-to-insulator transition, Phys. Rev. B 77, 075116 (2008)arXivBibTeX
ABSTRACT »
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.

### 2005

• M. Karski, C. Raas and G. S. Uhrig
Electron spectra close to a metal-to-insulator transition, Phys. Rev. B 72, 113110 (2005)arXivBibTeX
ABSTRACT »
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.

### 2004

• M. Karski
Dynamische Molekularfeldtheorie mittels dynamischer Dichtematrix-Renormierung, Diplomarbeit an der Universität zu Köln, (2004)BibTeX