# Quantum technologies

Dieter Meschede's research group
Group members
Dr. Andrea Alberti
 Position: Principal investigator
 Field of research: Few-atom quantum systemsDigital quantum simulators
 Address: Institut für Angewandte Physik Wegelerstr. 8 D-53115 Bonn Germany
 Office room: 318
 E-mail: This e-mail address is being protected from spam bots, you need JavaScript enabled to view it. Office: +49 228 73-3471 Fax: +49 228 73-3474

### Miscellaneous:

Listen to the interview with Forschung aktuell of Deutschlandfunk on the atom sorting machine (“Sortiergerät für Atome: Forscher präparieren Quantenregister im Rekordtempo” broadcast on March 9th, 2017). These results have been recently published in Phys. Rev. Lett. Phys. Rev. Lett. 118, 065302 (2017).

## Publications

• F. Bleckmann, Z. Cherpakova, S. Linden and A. Alberti
Spectral imaging of topological edge states in plasmonic waveguide arrays, Phys. Rev. B 96, 045417 (2017)arXivBibTeX
ABSTRACT »

We report on the observation of a topologically protected edge state at the interface between two topologically distinct domains of the Su-Schrieffer-Heeger model, which we implement in arrays of evanescently coupled dielectric-loaded surface plasmon polariton waveguides. Direct evidence of the topological character of the edge state is obtained through several independent experiments: Its spatial localization at the interface as well as the restriction to one sublattice is confirmed by real-space leakage radiation microscopy. The corresponding momentum-resolved spectrum obtained by Fourier imaging reveals the midgap position of the edge state as predicted by theory.

• C. F. Roos, A. Alberti, D. Meschede, P. Hauke and H. Häffner
Revealing quantum statistics with a pair of distant atoms, arXiv:1706.04231 [quant-ph], (2017)BibTeX
ABSTRACT »

Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions.

• T. Rakovszky, J. Asbóth and A. Alberti
Detecting topological invariants in chiral symmetric insulators via losses, Phys. Rev. B: Rapid Comm. 95, 201407(R) (2017)arXivBibTeX
ABSTRACT »

We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Rudner and Levitov, [Phys. Rev. Lett. 102, 065703 (2009)]. We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.

• J. Asbóth and A. Alberti
Spectral flow and global topology of the Hofstadter butterfly, Phys. Rev. Lett. 118, 216801 (2017)arXivBibTeX
ABSTRACT »

We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy gaps as the magnetic field is varied by one flux quantum, is determined by the spectral flow of energy eigenstates crossing gaps as the field is tuned. We find that for each gap this spectral flow is equal to the topological invariant of the gap, i.e., the net number of edge modes traversing the gap. For periodically driven systems, our results apply to the spectrum of quasienergies. In this case, the spectral flow of the sum of all the quasienergies gives directly the Rudner-Lindner-Berg-Levin invariant that characterizes the topological phases of a periodically driven system.

• C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola and A. Alberti
High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms, Opt. Lett. 42, 1043 (2017)arXivBibTeX
ABSTRACT »

We have designed, built, and characterized a high- resolution objective lens that is compatible with an ultra-high vacuum environment. The lens system ex- ploits 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 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.

• C. Robens, J. Zopes, W. Alt, S. Brakhane, D. Meschede and A. Alberti
Low-entropy states of neutral atoms in polarization-synthesized optical lattices, Phys. Rev. Lett. 118, 065302 (2017)arXivBibTeX
ABSTRACT »

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.

• A. Alberti and S. Wimberger
Quantum walk of a Bose-Einstein condensate in the Brillouin zone, Accepted in Phys. Rev. A, arXiv:1705.00512, (2017)arXivBibTeX
ABSTRACT »
We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is  displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow a robust implementation of quantum walks with  several tens of steps at least.  In addition, onsite atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone.
• C. Robens, S. Brakhane, W. Alt, D. Meschede, J. Zopes and A. Alberti
Fast, high-precision optical polarization synthesizer for ultracold-atom experiments, arXiv:1608.02410, (2016)arXivBibTeX
ABSTRACT »

We propose a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists in superposing 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. To assess the precision of the synthesized polarization states, we characterize static spatial variations of the polarization over the wavefront, as well as the noise spectral density of temporal fluctuations. We find that static polarization distortions limit the extinction ratio to 2x10-5, corresponding to a 0.01% reduction of the degree of polarization (DOP). We also obtain that temporal fluctuations give rise to a 0.2º uncertainty in the state of polarization (SOP). We recently demonstrated an application of the polarization synthesizer (Robens et al., arXiv:1608.02410) to create two fully independent, controllable optical lattices, which trap atoms depending on their internal spin state. Probing ultracold atoms in polarization-synthesized optical lattices, we obtain an independent, complementary characterization of the optical performance of the polarization synthesizer.

• C. Robens, W. Alt, C. Emary, D. Meschede and A. Alberti
Atomic "bomb testing": the Elitzur-Vaidman experiment violates the Leggett-Garg inequality, Appl. Phys. B 123, 12 (2016)arXivBibTeX
ABSTRACT »

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.

• T. Groh, S. Brakhane, W. Alt, D. Meschede, J. Asbóth and A. Alberti
Robustness of topologically protected edge states in quantum walk experiments with neutral atoms, Phys. Rev. A (editor's suggestion) 94, 013620 (2016)arXivBibTeX
ABSTRACT »

Discrete-time 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 two-dimensional discrete-time 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 spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional 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.

• 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.

• S. Brakhane and A. Alberti
Technical Note: Stress-Induced Birefringence in Vacuum Systems, White paper, (2016)BibTeX
ABSTRACT »

Even scientific grade optical glasses show birefringence when small external forces are applied to the sample. Stress-induced birefringence can be particularly detrimental to the state of polarization of light when a laser beam is transmitted through the glass. This is especially the case for glass windows of a vacuum chamber. Since compensation of spatially inhomogeneous birefringence is extremely challenging, it should be prevented by proper design of the vacuum chamber. Birefringence below 0.2 nm/cm can be achieved by thoroughly choosing glass material with low stress optical coefficient and mounting geometry. Applications strongly depend on light polarization are quantum technologies such as precision metrology, quantum computation and quantum simulations based on ions or atoms.

• S. Brakhane, W. Alt, D. Meschede, C. Robens, G. Moon and A. Alberti
Ultra-low birefringence dodecagonal vacuum glass cell, Rev. Sci. Instrum. 86, 126108 (2015)arXivBibTeX
ABSTRACT »

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 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.

• C. Robens, W. Alt, D. Meschede, C. Emary and A. Alberti
Ideal Negative Measurements in Quantum Walks Disprove Theories Based on Classical Trajectories, Phys. Rev. X 5, 011003 (2015)arXivBibTeX
ABSTRACT »

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 Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interaction-free 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 Leggett-Garg 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.

• S. Brakhane, W. Alt, D. Meschede, C. Robens and A. Alberti
Polarisationserhaltende Vakuum-Zelle zur Anwendung oder Messung elektromagnetischer Wellen im Vakuum, Patent pending, (2015)BibTeX
ABSTRACT »

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.

• C. Robens, S. Brakhane, D. Meschede and A. Alberti
Quantum Walks With Neutral Atoms: Quantum Interference Effects of One and Two Particles, Proceedings of the XXII International Conference ICOLS, (2015)arXivBibTeX
ABSTRACT »

We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of single-particle quantum interference based on the violation of the Leggett-Garg inequality and, more recently, to probe two-particle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discrete-time quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.

• A. Alberti, W. Alt, R. Werner and D. Meschede
Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments, New J. Phys. 16, 123052 (2014)arXivBibTeX
ABSTRACT »

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk 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 long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary 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.

• A. Steffen, W. Alt, M. Genske, D. Meschede, C. Robens and A. Alberti
In-situ measurement of vacuum window birefringence by atomic spectroscopy, Rev. Sci. Instrum. 84, 126103 (2013)arXivBibTeX
ABSTRACT »

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.

• M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede and A. Alberti
Electric quantum walks with individual atoms, Phys. Rev. Lett. 110, 190601 (2013)arXivBibTeX
ABSTRACT »
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 vs. dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.
• C. Cedzich, T. Rybár, A. H. Werner, A. Alberti, M. Genske and R. F. Werner
Propagation of Quantum Walks in Electric Fields, Phys. Rev. Lett. 111, 160601 (2013)arXivBibTeX
ABSTRACT »
We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.
• N. Belmechri, L. Förster, W. Alt, A. Widera, D. Meschede and A. Alberti
Microwave control of atomic motional states in a spin-dependent optical lattice, J. Phys. B: At. Mol. Opt. Phys. 46, 104006 (2013)arXivBibTeX
ABSTRACT »
Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms (Förster 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.
• A. Ahlbrecht, A. Alberti, D. Meschede, V. B. Scholz, A. H. Werner and R. F. Werner
Molecular binding in interacting quantum walks, New J. Phys. 14, 073050 (2012)arXivBibTeX
ABSTRACT »

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 wave-function 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 quasi-particle effects in quantum many body systems.

• 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.
• M. G. Tarallo, A. Alberti, N. Poli, M. L. Chiofalo, F. Wang and G. M. Tino
arXivBibTeX
ABSTRACT »
In this paper we describe and compare different methods used for accurate determination of forces acting on matter-wave packets in optical lattices. The quantum interference nature responsible for the production of both Bloch oscillations and coherent delocalization is investigated in detail. We study conditions for optimal detection of Bloch oscillation for a thermal ensemble of cold atoms with a large velocity spread. We report on the experimental observation of resonant tunneling in an amplitude-modulated (AM) optical lattice up to the sixth harmonic with Fourier-limited linewidth. We then explore the fundamental and technical phenomena which limit both the sensitivity and the final accuracy of the atomic force sensor at 10^{-7} precision level [1], with an analysis of the coherence time of the system and addressing few simple setup changes to go beyond the current accuracy.
• 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.
• N. Poli, F. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli and G. M. Tino
Precision Measurement of Gravity with Cold Atoms in an Optical Lattice and Comparison with a Classical Gravimeter, Phys. Rev. Lett. 106, 038501 (2011)BibTeX
ABSTRACT »
We report on a precision measurement of gravitational acceleration using ultracold strontium atoms confined in an amplitude-modulated vertical optical lattice. An uncertainty Δg/g≈10-7 is reached by measuring at the 5th harmonic of the Bloch frequency. The value obtained with this microscopic quantum system is consistent with the one measured with a classical gravimeter. Using lattice modulation to prepare the atomic sample, we also achieve high visibility of Bloch oscillations for ∼20  s. These results can be of relevance for testing gravitational redshift and Newtonian law at micrometer scale.
• A. Alberti, G. Ferrari, V. V. Ivanov, M. L. Chiofalo and G. M. Tino
Atomic wave packets in amplitude-modulated vertical optical lattices, New J. Phys. 12, 065037 (2010)BibTeX
ABSTRACT »

We report on the realization of dynamical control of transport for ultra-cold 88Sr atoms loaded in an accelerated amplitude-modulated one-dimensional (1D) optical lattice. We show that the behavior of the dynamical system can be viewed as if traveling wave packets were moving in a static lattice whose energy dispersion can be tailored at will in width, amplitude and phase. One basic control operation is a reversible switch between Wannier–Stark localization and driven transport based on coherent tunneling. Performing modulation sequences of this operation within a Loschmidt-echo scheme, we are able to reverse the atomic group velocities at once. We then apply the technique to demonstrate a novel mirror for matter waves working independently of the momentum state. We finally discuss advantages of amplitude over previously reported phase modulation techniques for applications in force measurements at micrometric scales.

• A. Alberti, V. V. Ivanov, G. M. Tino and G. Ferrari
Engineering the quantum transport of atomic wavefunctions over macroscopic distances, Nature Phys. 5, 547 (2009)BibTeX
ABSTRACT »

The manipulation of matter waves had an important role in the history of quantum mechanics. The first experimental validation of matter-wave behaviour was the observation of diffraction of matter by crystals, followed by interference experiments with electrons, neutrons, atoms and molecules using gratings and Young's double slit. More recently, matter-wave manipulation has become a building block for quantum devices such as quantum sensors and it has an essential role in a number of proposals for implementing quantum computers. Here, we demonstrate the coherent control of the spatial extent of an atomic wavefunction by reversibly stretching and shrinking the wavefunction over a distance of more than one millimetre. The quantum-coherent process is fully deterministic, reversible and in quantitative agreement with an analytical model. The simplicity of its experimental implementation could ease applications in the field of quantum transport and quantum processing.

• F. Sorrentino, A. Alberti, G. Ferrari, V. V. Ivanov, N. Poli, M. Schioppo and G. M. Tino
Quantum sensor for atom-surface interactions below 10μm, Phys. Rev. A 79, 013409 (2009)BibTeX
ABSTRACT »

We report the realization of a quantum device for force sensing at the micrometric scale. We trap an ultracold Sr88 atomic cloud with a one-dimensional (1D) optical lattice; then we place the atomic sample close to a test surface using the same optical lattice as an elevator. We demonstrate precise positioning of the sample at the micrometer scale. By observing the Bloch oscillations of atoms into the 1D optical standing wave, we are able to measure the total force on the atoms along the lattice axis, with a spatial resolution of few micrometers. We also demonstrate a technique for transverse displacement of the atoms, allowing us to perform measurements near either transparent or reflective test surfaces. In order to reduce the minimum distance from the surface, we compress the longitudinal size of the atomic sample by means of an optical tweezer. This system is suited for studies of atom-surface interaction at short distance, such as measurement of the Casimir force and the search for possible non-Newtonian gravity effects.

• V. V. Ivanov, A. Alberti, M. Schioppo, G. Ferrari, M. Artoni, M. L. Chiofalo and G. M. Tino
Coherent Delocalization of Atomic Wave Packets in Driven Lattice Potentials, Phys. Rev. Lett. 100, 043602 (2008)BibTeX
ABSTRACT »

Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here observed by monitoring the in situ wave-packet extent. By varying the modulation frequency, we find resonances at integer multiples of the Bloch frequency. The resonances show a Fourier-limited width for interrogation times up to 2 s. This can also be used to determine the gravity acceleration with ppm resolution.