Professor Dr. Dieter Meschede  

We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin1/2 particles carrying out a discretetime quantum walk in a twodimensional lattice. By Floquet engineering the quantumwalk protocol, an AharonovBohm geometric phase is imprinted onto closedloop paths in the lattice, thus realizing an abelian gauge field—the analog of a magnetic flux threading a twodimensional electron gas. We show that in the strong field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number—the socalled RLBL invariant—is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this article, we discuss an implementation of this scheme using neutral atoms in twodimensional spindependent optical lattices, which enables the generation of arbitrary magneticfield landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.
We report on vibrational groundstate cooling of a single neutral atom coupled to a highbandwidth FabryPérot cavity. The cooling process relies on degenerate Raman sideband transitions driven by dipole trap beams, which confine the atoms in three dimensions. We infer a onedimensional motional ground state population close to 90% by means of Raman spectroscopy. Moreover, lifetime measurements of a cavitycoupled atom exceeding 40 s imply threedimensional cooling of the atomic motion, which makes this resourceefficient technique particularly interesting for cavity experiments with limited optical acces.
We demonstrate the storage of 5 ns light pulses in a single rubidium atom coupled to a fiberbased optical resonator. Our storage protocol addresses a regime beyond the conventional adiabatic limit and approaches the theoretical bandwidth limit. We extract the optimal control laser pulse properties from a numerical simulation of our system and measure storage efficiencies of (8.2±0.6)%, in close agreement with the maximum expected efficiency. Such wellcontrolled and highbandwidth atomphoton interfaces are key components for future hybrid quantum networks.
We observe a sixfold Purcell broadening of the D_{2} line of an optically trapped ^{87}Rb atom strongly coupled to a fiber cavity. Under external illumination by a nearresonant laser, up to 90% of the atom's fluorescence is emitted into the resonant cavity mode. The subPoissonian statistics of the cavity output and the Purcell enhancement of the atomic decay rate are confirmed by the observation of a strongly narrowed antibunching dip in the photon autocorrelation function. The photon leakage through the highertransmission mirror of the singlesided resonator is the dominant contribution to the field decay (κ≈2π×50 MHz), thus offering a highbandwidth, fibercoupled channel for photonic interfaces such as quantum memories and singlephoton sources.
We employ active feedback to stabilize the frequency of single photons emitted by two separate quantum dots to an atomic standard. The transmission of a rubidiumbased Faraday filter serves as the error signal for frequency stabilization. We achieve a residual frequency deviation of <30 MHz, which is less than 1.5% of the quantum dot linewidth. Longterm stability is demonstrated by HongOuMandel interference between photons from the two quantum dots. Their internal dephasing limits the expected visibility to V = 40%. We observe V_{lock} = (41±5)% for frequencystabilized dots as opposed to V_{free} = (31±7)% for freerunning emission. Our technique reaches the maximally expected visibility for the given system and therefore facilitates quantum networks with indistinguishable photons from distributed sources.
We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists in superimposing two laser light fields with the same wavelength, but with opposite circular polarizations, where the phase and amplitude of each light field are individually controlled. We find that the polarizationsynthesized beam reaches a degree of polarization of 99.99%, which is mainly limited by static spatial variations of the polarization state over the beam profile. We also find that the depolarization caused by temporal fluctuations of the polarization state is about two orders of magnitude smaller. In a recent work, Robens et al. [Phys. Rev. Lett. 118, 065302 (2017)] demonstrated an application of the polarization synthesizer to create two independently controllable optical lattices, which trap atoms depending on their internal spin state. We here use ultracold atoms in polarizationsynthesized optical lattices to give an independent, in situ demonstration of the performance of the polarization synthesizer.
High radiation rates are usually associated with macroscopic lasers. Laser radiation is “coherent”—its amplitude and phase are welldefined—but its generation requires energy inputs to overcome loss. Excited atoms spontaneously emit in a random and incoherent fashion, and for N such atoms, the emission rate simply increases as N. However, if these atoms are in close proximity and coherently coupled by a radiation field, this microscopic ensemble acts as a single emitter whose emission rate increases as N2 and becomes “superradiant,” to use Dicke's terminology (1). On page 662 of this issue, Kim et al. (2) show the buildup of coherent light fields through collective emission from atomic radiators injected one by one into a resonator field. There is only one atom ever in the cavity, but the emission is still collective and superradiant. These results suggest another route toward thresholdless lasing.
Recently we have demonstrated scalable, nondestructive, and highfidelity detection of the internal state of ^{87}Rb neutral atoms in optical dipole traps using statedependent fluorescence imaging [M. MartinezDorantes, W. Alt, J. Gallego, S. Ghosh, L. Ratschbacher, Y. Völzke, and D. Meschede, Phys. Rev. Lett. 119, 180503 (2017)]. In this paper we provide experimental procedures and interpretations to overcome the detrimental effects of heatinginduced trap losses and state leakage. We present models for the dynamics of optically trapped atoms during statedependent fluorescence imaging and verify our results by comparing Monte Carlo simulations with experimental data. Our systematic study of dipole force fluctuations heating in optical traps during nearresonant illumination shows that offresonant light is preferable for state detection in tightly confining optical potentials.
Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics dier in the exchange phase, either 0 or π, which the wavefunction acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wavefunction. We discuss possible implementations with a pair of trapped atoms or ions.
We demonstrate the parallel and nondestructive readout of the hyperfine state for optically trapped ^{87}Rb atoms. The scheme is based on stateselective fluorescence imaging and achieves detection fidelities > 98% within 10 ms, while keeping 99% of the atoms trapped. For the readout of dense arrays of neutral atoms in optical lattices, where the fluorescence images of neighboring atoms overlap, we apply a novel image analysis technique using Bayesian inference to determine the internal state of multiple atoms. Our method is scalable to large neutral atom registers relevant for future quantum information processing tasks requiring fast and nondestructive readout and can also be used for the simultaneous readout of quantum information stored in internal qubit states and in the atoms’ positions.
We create lowentropy states of neutral atoms by utilizing a conceptually new opticallattice technique that relies on a highprecision, highbandwidth synthesis of light polarization. Polarizationsynthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two longlived 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 atomsorting algorithm with logarithmic complexity, which is enabled by polarizationsynthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottomup approach to creating ultralowentropy states of a manybody system.
We have designed, built, and characterized a high resolution objective lens that is compatible with an ultrahigh vacuum environment. The lens system ex ploits the principle of the Weierstrasssphere 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 twolens 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 nearfield optical microscopy, to measure the point spread function of a high NA optical system. From the point spread function, 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 technolo gies such as quantum control of atoms in optical mi crotraps with an unprecedented spatial resolution and photon collection efficiency.
Quanteninformationstechnologien gehören zu den boomenden Forschungsgebieten. Längst geht es nicht mehr allein um Grundlagenforschung, sondern um handfeste technische Anwendungen. Im Fokus ist die abhörsichere Kommunikation. Ein Interview mit Dieter Meschede, Leiter der Arbeitsgruppe Quantentechnologie an der Universität Bonn und künftiger Präsident der Deutschen Physikalischen Gesellschaft.
Discretetime quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one and twodimensional discretetime quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spindependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spindependent discrete shift operations in a twodimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.
Fiber FabryPerot cavities, formed by micromachined mirrors on the endfacets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber FabryPerot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezomechanically actuated cavity with feedback based on the PoundDreverHall locking technique is compared to a novel rigid cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal selflocking and external temperature tuning. Furthermore, we present a general analysis of the mode matching problem in fiber FabryPerot cavities, which explains the asymmetry in their reflective line shapes and has important implications for the optimal alignment of the fiber resonators. Finally, we discuss the issue of fibergenerated background photons. We expect that our results contribute towards the integration of highfinesse fiber FabryPerot cavities into compact and robust quantumenabled devices in the future.
We report on image processing techniques and experimental procedures to determine the latticesite 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 superresolution 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 superresolution 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 subpixel 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.
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 interactionfree measurement scheme can be put in direct relation with falsification tests of the macrorealistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spindependent optical lattice to show explicitly a violation of the LeggettGarg inequality—a quantitative criterion fulfilled by macrorealistic physical theories. To perform interactionfree 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 pushout technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the LeggettGarg inequality.
We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ violation of the LeggettGarg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, welldefined trajectories. We use socalled ideal negative measurements—an essential requisite for any genuine LeggettGarg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interactionfree measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the LeggettGarg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.
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 losslesscavity 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 twoatom case (N=2) is almost equal to the singleemitter case (N=1), which is in contrast to freespace 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 twoatom entanglement schemes involving optical cavities becomes realistic.
We report on an ultralow birefringence dodecagonal glass cell for ultrahigh vacuum applications. The epoxybonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stressinduced 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 ºC, 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.
Die Erfindung betrifft ein Verfahren, eine Vorrichtung und die Verwendung einer Vorrichtung zur Anwendung oder Messung polarisierter elektromagnetischer Strahlung im Vakuum, wobei die Doppelbrechung Δn < 10^{6} beträgt.
We report on the state of the art of quantum walk experiments with neutral atoms in statedependent optical lattices. We demonstrate a novel statedependent transport technique enabling the control of two spinselective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of singleparticle quantum interference based on the violation of the LeggettGarg inequality and, more recently, to probe twoparticle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discretetime quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.
We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a highfinesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)–like interference in an atomic lambdatype configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.
We analyze the quantum jumps of an atom interacting with a cavity field, where strong coupling makes the cavity transmission depend on the timedependent atomic state. In our analysis we employ a Bayesian approach that conditions the population of the atomic states at time t on the cavity transmission observed both before and after t, and we show that the state assignment by this approach is more decisive than the usual conditional quantum states based on only earlier measurement data. We also provide an iterative protocol which, together with the atomic state populations, simultaneously estimates the atomic jump rates and the transmission signal distributions from the measurement data. Finally, we take into account technical fluctuations in the observed signal, e.g., due to spatial motion of the atom within the cavity, by representing atomic states by several hidden states, thereby significantly improving the state's recovery.
We discuss decoherence in discretetime quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantumwalk experiments realized with neutral atoms walking in an optical lattice.
From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic—instead of diffusive—expansion in position space is not a good indicator of the range of coherent delocalization.
We provide further physical insight by distinguishing the effects of short and longtime spin dephasing mechanisms. We introduce the concept of coherence length in the discretetime quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasistationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences.
For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.
We experimentally realize an enhanced Raman control scheme for neutral atoms that features an intrinsic suppression of the twophoton carrier transition, but retains the sidebands which couple to the external degrees of freedom of the trapped atoms. This is achieved by trapping the atom at the node of a blue detuned standing wave dipole trap, that acts as one field for the twophoton Raman coupling. The improved ratio between cooling and heating processes in this configuration enables a five times lower fundamental temperature limit for resolved sideband cooling. We apply this method to perform Raman cooling to the twodimensional vibrational ground state and to coherently manipulate the atomic motion. The presented scheme requires minimal additional resources and can be applied to experiments with challenging optical access, as we demonstrate by our implementation for atoms strongly coupled to an optical cavity.
We present an insitu method to measure the birefringence of a single vacuum window by means of microwave spectroscopy on an ensemble of cold atoms. Stressinduced birefringence can cause an ellipticity in the polarization of an initially linearlypolarized 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.
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 spindependent 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 spacetime analogue of the wellknown spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separationtolocalization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nanoresolution quantum probes in precision measurements, being able to measure potential gradients with precision 5×10^{4} in units of gravitational acceleration g.
We experimentally demonstrate realtime feedback control of the joint spinstate of two neutral Caesium 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 twoatom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with MonteCarlo simulations. On average, the feedback loops achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.
We show that the presence of an interaction in the quantum walk of two atoms leads to the formation of a stable compound, a molecular state. The wavefunction of the molecule decays exponentially in the relative position of the two atoms, hence it constitutes a true bound state. Furthermore, for a certain class of interactions we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right. We propose a setup for the experimental realization as well as sketch the possibility to observe quasiparticle effects in quantum many body systems.
We have directly observed spindependent 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 π causes displacement of the σ^{+} and σ^{–}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.
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 twophoton resonance, increasing the storage time of our atoms twentyfold to about 16 seconds. Our result points towards alloptical switching with single photons.
We optically detect the positions of single neutral cesium atoms stored in a standing wave dipole trap with a subwavelength resolution of 143 nm rms. The distance between two simultaneously trapped atoms is measured with an even higher precision of 36 nm rms. We resolve the discreteness of the interatomic distances due to the 532 nm spatial period of the standing wave potential and infer the exact number of trapping potential wells separating the atoms. Finally, combining an initial position detection with a controlled transport, we place single atoms at a predetermined position along the trap axis to within 300 nm rms.
We have characterized the spectroscopic properties of one of the first samples of blueemitting diode lasers based on GaN. With such a laser diode operated inside a standard extended cavity arrangement we find a modehop free tuning range of more than 20 GHz and a linewidth of 10 MHz. Dopplerfree spectroscopy on an indium atomic beam reveals the isotope shift between the two major indium isotopes as well as efficient optical pumping.
Using the stimulated force exerted by counterpropagating π pulses from a modelocked Ti:sapphire laser we have focused a beam of lasercooled cesium atoms along one dimension to about 57% of its original width in the detection zone. We determined the force profile outside and inside the overlap region of the pulses and found agreement with an earlier theoretical prediction. The scheme does not require an effective twolevel system and is therefore suitable for a large variety of elements.
Grofitechnisch angewandte optische Lithographieverfahrenstofien bei Auflosungen unter 100 nm auf eine prinzipielle Grenze. Die Lithographie mit neutralen Atomstrahlen bietet dazu insbesondere beim parallelen Schreiben periodischer Strukturen eine interessante, noch junge Alternative. Indem man die Wechselwirkung der Atome mit Lichtmasken ausnutzt, gelingt es, grofiflachig periodische Linienmuster und verschiedene zweidimensional periodische Strukturen mit einer Auflosung unter 100 nm zu erzeugen. Dabei werden Atome entweder direkt auf einem Substrat deponiert oder zur Modifikation organischer Resists genutzt. Der folgende Beitrag gibt einen herblick iiber den Stand der Lithographie mit Atomstrahlen.
Threshold photodetachment of negative hydrogen ions stored in a Penning trap has been studied. The electron afﬁnity of hydrogen is determined to 6082.8(7) cm^{−1} in good agreement with previous experiments. The Wigner law has been found to be valid in a region of 400 cm^{−1} above the threshold.
We have fabricated and investigated efficient magnetic lenses, waveguides, and mirrors from rare earth permanent materials. They are affordable and maintenance free. In contrast to corresponding light force components they do not need any supplies, they have large apertures, high reflectivity, and there is no spontaneous emission. The cylindrical shape of magnetic components is furthermore well suited to steer atomic beams.
With strong rareearth permanent magnets we have built highly refractive atomoptical components for lasercooled atoms. We have studied the influence of axially symmetric multipole components on a cesium atomic beam. In analogy to traditional optics the action of a quadrupole ring parallels a conical prism, or axicon. Hexapole lenses were applied for focusing with a more than 1000fold increase in atomic flux density at the focal spot and for imaging with the atomic beam. Two hexapole lenses were combined to form a telescope, which was operated off axis in order to separate fast thermal and slowed atoms. The experiments can approximately be described in terms of geometrical optics.
We have found that linearly polarized light can be used efficiently for optical trapping of cesium atoms in a magneticquadrupole field. The number and density of atoms of the trapped samples are comparable to a standard magnetooptical trap with σ^{+}  σ^{–} polarized light, but the influence of the magneticquadrupole strength is strikingly different. When the polarization of counterpropagating light beams is orthogonal, trapping is observed also for zero magnetic field.
We present the construction of arbitrary multipole field configurations from strong permanent magnets for trapping charged or neutral particles. A general analytic method for the design of threedimensional magnetic multipoles is discussed for an idealized continuously varying magnetisation taking advantage of the superposition principle. Simple recipes for constructing magnetic dipole and quadrupole fields are given with two types of elements, axially and radially magnetised rings. Cylindrical magnet components not only give free access to the experimental region of interest, but also allow for some tunability to reduce undesirable higher multipole orders. Measurements confirm theoretical predictions achieving useful magnetic fields of 1 T and steep gradients of 3 T/cm with high purity over several ccm.
We discuss an analytic method for the design of threedimensional magnetic multipoles from permanent magnet materials. The concept is explicited with an idealized, continuously varying magnetization. The effect of segmentation for realistic implementations is discussed. As an example we present an open, experimentally accessible cylindric structure for a dipole and a quadrupole field with high purity. The fields are useful over several cm^{3}.