Observing crossover between quantum speed limits.

Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds, which relate the maximum speed of evolution to the system's energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multilevel system by following the motion of a single atom in an optical trap using fast matter wave interferometry. We find two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the quantum evolution deviates from the geodesic path in the Hilbert space of the multilevel system. Our results are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.

Tunable fiber Fabry-Perot cavities with high passive stability.

We present three high finesse tunable monolithic fiber Fabry-Perot cavities (FFPCs) with high passive mechanical stability. The fiber mirrors are fixed inside slotted glass ferrules, which guarantee an inherent alignment of the resonators. An attached piezoelectric element enables fast tuning of the FFPC resonance frequency over the entire free-spectral range for two of the designs. Stable locking of the cavity resonance is achieved for sub-Hertz feedback bandwidths, demonstrating the high passive stability. At the other limit, locking bandwidths up to tens of kilohertz, close to the first mechanical resonance, can be obtained. The root-mean-square frequency fluctuations are suppressed down to ∼2% of the cavity linewidth. Over a wide frequency range, the frequency noise is dominated by the thermal noise limit of the system's mechanical resonances. The demonstrated small footprint devices can be used advantageously in a broad range of applications like cavity-based sensing techniques, optical filters or quantum light-matter interfaces.

High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms.

We have designed, built, and characterized a high-resolution objective lens that is compatible with an ultrahigh vacuum environment. The lens system exploits the principle of the Weierstrass sphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 µm. Our two-lens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning near-field optical microscopy, to measure the point spread function (PSF) of a high NA optical system. From the PSF, we infer the wavefront aberration for the entire field of view of about 75 µm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technologies such as quantum control of atoms in optical microtraps with an unprecedented spatial resolution and photon collection efficiency.

Low-Entropy States of Neutral Atoms in Polarization-Synthesized Optical Lattices.

We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atom-sorting algorithm with logarithmic complexity, which is enabled by polarization-synthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottom-up approach to creating ultralow-entropy states of a many-body system.

Simple mechanisms of early life - simulation model on the origin of semi-cells.

The development of first cellular structures played an important role in the early evolution of life. Early evolution of life probably took place on a molecular level in a reactive environment. The iron-sulfur theory postulates the formation of cell-like structures on catalytic surfaces. Experiments show that H2S together with FeS and other metallic centers drive auto-catalytic surface reactions, in which organic molecules such as pyruvic and amino acids occur. It is questionable which mechanisms are needed to form cell-like structures under these conditions. To address this question, we implemented a model system featuring the fundamentals of molecular dynamics: heat, attraction, repulsion and formation of covalent bonds. Our basic model exhibits a series of essential processes: self-organization of lipid micelles and bilayers, formation of fluid filled cavities, flux of molecules along membranes, transport of energized groups towards sinks and whole colonies of cell-like structures on a larger scale. The results demonstrate that only a few features are sufficient for discovering hitherto non described phenomena of self-assembly and dynamics of cell-like structures as candidates for early evolving proto-cells. Significance statement The quest for a possible origin of life continues to be one of the most fascinating problems in biology. In one theoretical scenario, early life originated from a solution of reactive chemicals in the ancient deep sea, similar to conditions as to be found in thermal vents. Experiments have shown that a variety of organic molecules, the building blocks of life, form under these conditions. Based on such experiments, the iron-sulfur theory postulates the growth of cell-like structures at certain catalytic surfaces. For an explanation and proof of such a process we have developed a computer model simulating molecular assembly of lipid bilayers and formation of semi-cell cavities. The results demonstrate the possibility of cell-like self-organization under appropriate physico-chemical conditions.

Atomic "bomb testing": the Elitzur-Vaidman experiment violates the Leggett-Garg inequality.

Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object-in a dramatic scenario, a bomb-without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett-Garg inequality-a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett-Garg inequality.

Cavity-modified collective Rayleigh scattering of two atoms.

We report on the observation of cooperative radiation of exactly two neutral atoms strongly coupled to the single mode field of an optical cavity, which is close to the lossless-cavity limit. Monitoring the cavity output power, we observe constructive and destructive interference of collective Rayleigh scattering for certain relative distances between the two atoms. Because of cavity backaction onto the atoms, the cavity output power for the constructive two-atom case (N=2) is almost equal to the single-emitter case (N=1), which is in contrast to free-space where one would expect an N^{2} scaling of the power. These effects are quantitatively explained by a classical model as well as by a quantum mechanical model based on Dicke states. We extract information on the relative phases of the light fields at the atom positions and employ advanced cooling to reduce the jump rate between the constructive and destructive atom configurations. Thereby we improve the control over the system to a level where the implementation of two-atom entanglement schemes involving optical cavities becomes realistic.

Note: Ultra-low birefringence dodecagonal vacuum glass cell.

We report on an ultra-low birefringence dodecagonal glass cell for ultra-high vacuum applications. The epoxy-bonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stress-induced birefringence. We characterize the birefringence Δn of each window with the cell under vacuum conditions, obtaining values around 10(-8). After baking the cell at 150 °C, we reach a pressure below 10(-10) mbar. In addition, each window is antireflection coated on both sides, which is highly desirable for quantum optics experiments and precision measurements.

Impact of a high magnetic field on the orientation of gravitactic unicellular organisms--a critical consideration about the application of magnetic fields to mimic functional weightlessness.

The gravity-dependent behavior of Paramecium biaurelia and Euglena gracilis have previously been studied on ground and in real microgravity. To validate whether high magnetic field exposure indeed provides a ground-based facility to mimic functional weightlessness, as has been suggested earlier, both cell types were observed during exposure in a strong homogeneous magnetic field (up to 30 T) and a strong magnetic field gradient. While swimming, Paramecium cells were aligned along the magnetic field lines; orientation of Euglena was perpendicular, demonstrating that the magnetic field determines the orientation and thus prevents the organisms from the random swimming known to occur in real microgravity. Exposing Astasia longa, a flagellate that is closely related to Euglena but lacks chloroplasts and the photoreceptor, as well as the chloroplast-free mutant E. gracilis 1F, to a high magnetic field revealed no reorientation to the perpendicular direction as in the case of wild-type E. gracilis, indicating the existence of an anisotropic structure (chloroplasts) that determines the direction of passive orientation. Immobilized Euglena and Paramecium cells could not be levitated even in the highest available magnetic field gradient as sedimentation persisted with little impact of the field on the sedimentation velocities. We conclude that magnetic fields are not suited as a microgravity simulation for gravitactic unicellular organisms due to the strong effect of the magnetic field itself, which masks the effects known from experiments in real microgravity.

Electric quantum walks with individual atoms.

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances versus dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.

Note: In situ measurement of vacuum window birefringence by atomic spectroscopy.

We present an in situ method to measure the birefringence of a single vacuum window by means of microwave spectroscopy on an ensemble of cold atoms. Stress-induced birefringence can cause an ellipticity in the polarization of an initially linearly polarized laser beam. The amount of ellipticity can be reconstructed by measuring the differential vector light shift of an atomic hyperfine transition. Measuring the ellipticity as a function of the linear polarization angle allows us to infer the amount of birefringence Δn at the level of 10(-8) and identify the orientation of the optical axes. The key benefit of this method is the ability to separately characterize each vacuum window, allowing the birefringence to be precisely compensated in existing vacuum apparatuses.

Bayesian feedback control of a two-atom spin-state in an atom-cavity system.

We experimentally demonstrate real-time feedback control of the joint spin-state of two neutral cesium atoms inside a high finesse optical cavity. The quantum states are discriminated by their different cavity transmission levels. A Bayesian update formalism is used to estimate state occupation probabilities as well as transition rates. We stabilize the balanced two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte Carlo simulations. On average, the feedback loop achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.

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 x 10(-4) in units of gravitational acceleration g.

From cells to organisms: current topics in mathematical and theoretical biology.

At the beginning of this special issue of Acta Biotheoretica carrying the above title, we present a brief overview on currently important topics that have been brought up during the last "European Conference on Mathematical and Theoretical Biology" in Edinburgh. After emphasizing the need for a "synthetic biology" also from the side of theory, model building and analysis, we survey most plenary talks of this Conference and a selected series of eigth review articles, which are mainly related to corresponding minisymposia, reflecting the current state of the art and the lively discussion within this interdisciplinary field.

Measurement of submicrometre diameters of tapered optical fibres using harmonic generation.

Applications of subwavelength-diameter optical fibres in nonlinear optics require precise knowledge of the submicrometre fibre waist diameter. We demonstrate a new technique for optical measurement of the diameter based on second- and third-harmonic generation with an accuracy of better than 2%. To generate the harmonic light, inter-modal phase matching must be achieved. We find that the phase-matching condition allows us to unambiguously deduce the fibre diameter from the wavelength of the harmonic light. High-resolution scanning electron microscope imaging is used to verify the results.

Generalized voronoi tessellation as a model of two-dimensional cell tissue dynamics.

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein-Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.

Optical control of the refractive index of a single atom.

We experimentally demonstrate the elementary case of electromagnetically induced transparency with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons.

Quantum walk in position space with single optically trapped atoms.

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.