Leonid Förster

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.

Quantum engineering: An atom-sorting machine

Laser cooling and trapping techniques allow us to control and manipulate neutral atoms. Here we rearrange, with submicrometre precision, the positions and ordering of laser-trapped atoms within strings by manipulating individual atoms with optical tweezers. Strings of equidistant atoms created in this way could serve as a scalable memory for quantum information.

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.

Microwave control of atomic motional states in a spin-dependent optical lattice

Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms (F¨ orster et al 2009 Phys. Rev. Lett. 103 233001). Here, we discuss this method in greater detail, comparing it to the widely employed Raman sideband coupling method. We provide a simplified model for sideband cooling in a spin-dependent potential, and we discuss it in terms of the generalized Lamb–Dicke parameter. Using a master equation formalism, we present a quantitative analysis of the cooling performance for our experiment, which can be generalized to other experimental settings. We additionally use microwave sideband transitions to engineer motional Fock states and coherent states, and we devise a technique for measuring the population distribution of the prepared states. (Some figures may appear in colour only in the online journal)

Inserting two atoms into a single optical micropotential.

We recently demonstrated that strings of trapped atoms inside a standing wave optical dipole trap can be rearranged using optical tweezers [Y. Miroshnychenko, Nature 442, 151 (2006)]. This technique allows us to actively set the interatomic separations on the scale of the individual trapping potential wells. Here, we use such a distance-control operation to insert two atoms into the same potential well. The detected success rate of this manipulation is 16(-3)(+4)%, in agreement with the predictions of a theoretical model based on our experimental parameters.

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.

Number-triggered loading and collisional redistribution of neutral atoms in a standing wave dipole trap

We implement a technique for loading a preset number of up to 19 atoms from a magneto-optical trap into a standing wave optical dipole trap. The efficiency of our technique is characterized by measuring the atom number before and after the loading process. Our analysis reveals details of the trap dynamics that are usually masked when working with larger atomic ensembles. In particular, we identify a low-loss collisional blockade mechanism. It forces the atoms to redistribute in the periodic potential until they are all stored in individual trapping sites, thereby strongly reducing site occupation number fluctuations.

Precision preparation of strings of trapped neutral atoms

We have recently demonstrated the creation of regular strings of neutral caesium atoms in a standing wave optical dipole trap using optical tweezers (Miroshnychenko Y et al 2006 Nature (London) 442 151). The rearrangement is realized atom-by-atom, extracting an atom and re-inserting it at the desired position with submicrometer resolution. We describe our experimental setup in detail and present systematic measurements as well as simple analytical models for the resolution of the extraction process, for the precision of the insertion, and for heating processes. We compare two different methods of insertion, one of which permits the placement of two atoms into one optical micropotential. The theoretical models largely explain our experimental results and allow us to identify the main limiting factors for the precision and efficiency of the manipulations. Strategies for future improvements are discussed.

Adiabatic quantum state manipulation of single trapped atoms

We use microwave-induced adiabatic passages for selective spin flips within a string of optically trapped individual neutral Cs atoms. We position-dependently shift the atomic transition frequency with a magnetic field gradient. To flip the spin of a selected atom, we optically measure its position and sweep the microwave frequency across its respective resonance frequency. We analyze the addressing resolution and the experimental robustness of this scheme. Furthermore, we show that adiabatic spin flips can also be induced with a fixed microwave frequency by deterministically transporting the atoms across the position of resonance.