# Quantum technologies

Dieter Meschede's research group
Group members
Professor Dr. Artur Widera
 Present position: Professor at Technische Universität Kaiserslautern
 Last positionin our group: Assistant
 Field of researchin our group: Few-atom quantum systemsCavity QEDBEC

## Publications(up to 2016)

### 2016

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

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

### 2013

• 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.

### 2012

• N. Spethmann, F. Kindermann, S. John, C. Weber, D. Meschede and A. Widera
Dynamics of single neutral impurity atoms immersed in an ultracold gas, Phys. Rev. Lett. 109, 235301 (2012)arXivBibTeX
ABSTRACT »
We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.
• S. Brakhane, W. Alt, T. Kampschulte, M. Martinez-Dorantes, R. Reimann, S. Yoon, A. Widera and D. Meschede
Bayesian Feedback Control of a Two-Atom Spin-State in an Atom-Cavity System, Phys. Rev. Lett. 109, 173601 (2012)arXivBibTeX
ABSTRACT »
We experimentally demonstrate real-time feedback control of the joint spin-state 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 two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte-Carlo 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.
• 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.
• N. Spethmann, F. Kindermann, S. John, C. Weber, D. Meschede and A. Widera
Inserting single Cs atoms into an ultracold Rb gas, Appl. Phys. B 106, 513 (2012)arXivBibTeX
ABSTRACT »
We report on the controlled insertion of individual Cs atoms into an ultracold Rb gas at ≈400 nK. This requires one to combine the techniques necessary for cooling, trapping and manipulating single laser cooled atoms around the Doppler temperature with an experiment to produce ultracold degenerate quantum gases. In our approach, both systems are prepared in separated traps and then combined. Our results pave the way for coherent interaction between a quantum gas and a single or few neutral atoms of another species.

### 2011

• M. Karski, L. Förster, J. Choi, W. Alt, A. Alberti, A. Widera and D. Meschede
Direct Observation and Analysis of Spin-Dependent Transport of Single Atoms in a 1D Optical Lattice, J. Korean Phys. Soc. 59, 2947 (2011)arXivBibTeX
ABSTRACT »
We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by $\pi$ causes displacement of the $\sigma^{+}$- and $\sigma^{-}$-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.
• A. Widera, W. Alt and D. Meschede
Coherently Walking, Rocking and Blinding Single Neutral Atoms, J. Phys.: Conf. Ser. 264, 012021 (2011)BibTeX
ABSTRACT »
Advances in the preparation and detection, but most importantly in the coherent manipulation of single neutral atoms have allowed the observation of intriguing phenomena of quantum physics in recent years. We discuss developments to prepare and detect single neutral atoms in a one-dimensional optical lattice potential with single site resolution. Moreover, using two different experimental techniques, a state-dependent optical lattice potential on the one hand and a high-finesse optical cavity on the other hand, we have obtained coherent control over single neutral atoms. The former has enabled us to observe the quantum walk of atoms in position space, and to coherently control the motion of trapped atoms via microwave radiation. The latter offers a means to non-destructively detect the atomic spin state, thereby revealing quantum jumps of single atoms, or the altered optical properties of single atoms when subject to electromagnetically-induced transparency.
• A. Mawardi, S. Hild, A. Widera and D. Meschede
ABCD-treatment of a propagating doughnut beam generated by a spiral phase plate, Optics Express 19, 21205-21210 (2011)BibTeX
ABSTRACT »
We apply the Collins-Huygens integral to analytically describe propagation of a doughnut beam generated by a spiral phase plate. Measured beam profiles in free space and through an ABCD-lens system illustrate excellent agreement with theory. Applications range from the creation of optical beams with angular momentum to microscopy to trapping neutral atoms. The method extends to other beam shaping components, too.

### 2010

• M. Karski, L. Förster, J. Choi, A. Steffen, N. Belmechri, W. Alt, D. Meschede and A. Widera
Imprinting Patterns of Neutral Atoms in an Optical Lattice using Magnetic Resonance Techniques, New J. Phys. 12, 065027 (2010)arXivBibTeX
ABSTRACT »
We prepare arbitrary patterns of neutral atoms in a one-dimensional (1D) optical lattice with single-site precision using microwave radiation in a magnetic field gradient. We give a detailed account of the current limitations and propose methods to overcome them. Our results have direct relevance for addressing planes, strings or single atoms in higher-dimensional optical lattices for quantum information processing or quantum simulations with standard methods in current experiments. Furthermore, our findings pave the way for arbitrary single-qubit control with single-site resolution.
• S. Reick, K. Mølmer, W. Alt, M. Eckstein, T. Kampschulte, L. Kong, R. Reimann, A. Thobe, A. Widera and D. Meschede
Analyzing quantum jumps of one and two atoms strongly coupled to an optical cavity, J. Opt. Soc. Am. B 27, A152 (2010)arXivBibTeX
ABSTRACT »
We induce quantum jumps between the hyperfine ground states of one and two Cesium atoms, strongly coupled to the mode of a high-finesse optical resonator, and analyze the resulting random telegraph signals. We identify experimental parameters to deduce the atomic spin state nondestructively from the stream of photons transmitted through the cavity, achieving a compromise between a good signal-to-noise ratio and minimal measurement-induced perturbations. In order to extract optimum information about the spin dynamics from the photon count signal, a Bayesian update formalism is employed, which yields time-dependent probabilities for the atoms to be in either hyperfine state. We discuss the effect of super-Poissonian photon number distributions caused by atomic motion.
• T. Kampschulte, W. Alt, S. Brakhane, M. Eckstein, R. Reimann, A. Widera and D. Meschede
Optical control of the refractive index of a single atom, Phys. Rev. Lett. 105, 153603 (2010)arXivBibTeX
ABSTRACT »
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.
• C. Weber, S. John, N. Spethmann, D. Meschede and A. Widera
Single Cs Atoms as Collisional Probes in a large Rb Magneto-Optical Trap, Phys. Rev. A 82, 042722 (2010)arXivBibTeX
ABSTRACT »
We study cold interspecies collisions of cesium and rubidium in a strongly imbalanced system with single and few Cs atoms. Observation of the single-atom fluorescence dynamics yields insight into light-induced loss mechanisms, while both subsystems can remain in steady state. This significantly simplifies the analysis of the dynamics, as Cs-Cs collisions are effectively absent and the majority component remains unaffected, allowing us to extract a precise value of the Rb-Cs collision parameter. Extending our results to ground-state collisions would allow to use single neutral atoms as coherent probes for larger quantum systems.

### 2009

• M. Karski, L. Förster, J. Choi, W. Alt, A. Widera and D. Meschede
Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging, Phys. Rev. Lett. 102, 053001 (2009)arXivBibTeX
ABSTRACT »
We overcome the diffraction limit in fluorescence imaging of neutral atoms in a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm, we reliably infer the separation of two atoms down to nearest neighbors. We observe light induced losses of atoms occupying the same lattice site, while for atoms in adjacent lattice sites, no losses due to light induced interactions occur. Our method points towards characterization of correlated quantum states in optical lattice systems with filling factors of up to one atom per lattice site.
• L. Förster, M. Karski, J. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera, E. Montano, J. H. Lee, W. Rakreungdet and P. S. Jessen
Microwave Control of Atomic Motion in Optical Lattices, Phys. Rev. Lett. 103, 233001 (2009)arXivBibTeX
ABSTRACT »
We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97% and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long-range quantum transport.
• M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera
Quantum Walk in Position Space with Single Optically Trapped Atoms, Science 325, 174 (2009)arXivBibTeX
ABSTRACT »
The quantum walk is the quantum analog of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.
• M. Khudaverdyan, W. Alt, T. Kampschulte, S. Reick, A. Thobe, A. Widera and D. Meschede
Quantum jumps and spin dynamics of interacting atoms in a strongly coupled atom-cavity system , Phys. Rev. Lett. 103, 123006 (2009)arXivBibTeX
ABSTRACT »
We experimentally investigate the spin dynamics of one and two neutral atoms strongly coupled to a high finesse optical cavity. We observe quantum jumps between hyperfine ground states of a single atom. The interaction-induced normal-mode splitting of the atom-cavity system is measured via the atomic excitation. Moreover, we observe the mutual influence of two atoms simultaneously coupled to the cavity mode.

### 2008

• F. Gerbier, S. Trotzky, S. Fölling, U. Schnorrberger, J. D. Thompson, A. Widera, I. Bloch, L. Pollet, M. Troyer, B. Capogrosso-Sansone, N. V. Prokof'ev and B. V. Svistunov
Expansion of a Quantum Gas Released from an Optical Lattice, Phys. Rev. Lett. 101, 155303 (2008)arXivBibTeX
ABSTRACT »
We analyze the interference pattern produced by ultracold atoms released from an optical lattice, commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite times of flight the resulting density distribution can, however, be significantly altered, similar to a near-field diffraction regime in optics. We illustrate our findings with a simple model and realistic quantum Monte Carlo simulations for bosonic atoms and compare the latter to experiments.
• A. Widera, S. Trotzky, P. Cheinet, S. Fölling, F. Gerbier, I. Bloch, V. Gritsev, M. D. Lukin and E. Demler
Quantum spin dynamics of squeezed Luttinger liquids in two-component atomic gases, Phys. Rev. Lett. 100, 140401 (2008)arXivBibTeX
ABSTRACT »
We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.
• M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera and D. Meschede
Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator, New J. Phys. 10, 073023 (2008)arXivBibTeX
ABSTRACT »
We experimentally investigate the interaction between one and two atoms and the field of a high-finesse optical resonator. Laser-cooled caesium atoms are transported into the cavity using an optical dipole trap. We monitor the interaction dynamics of a single atom strongly coupled to the resonator mode for several hundred milliseconds by observing the cavity transmission. Moreover, we investigate the position-dependent coupling of one and two atoms by shuttling them through the cavity mode. We demonstrate an alternative method, which suppresses heating effects, to analyze the atom-field interaction by retrieving the atom from the cavity and by measuring its final state.

### 2007

• S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller and I. Bloch
Direct Observation of Second Order Atom Tunnelling, Nature 448, 1029-1032 (2007)arXivBibTeX
ABSTRACT »
Tunnelling of material particles through a classically impenetrable barrier constitutes one of the hallmark effects of quantum physics. When interactions between the particles compete with their mobility through a tunnel junction, intriguing dynamical behaviour can arise because the particles do not tunnel independently. In single-electron or Bloch transistors, for example, the tunnelling of an electron or Cooper pair can be enabled or suppressed by the presence of a second charge carrier due to Coulomb blockade. Here we report direct, time-resolved observations of the correlated tunnelling of two interacting ultracold atoms through a barrier in a double-well potential. For the regime in which the interactions between the atoms are weak and tunnel coupling dominates, individual atoms can tunnel independently, similar to the case of a normal Josephson junction. However, when strong repulsive interactions are present, two atoms located on one side of the barrier cannot separate, but are observed to tunnel together as a pair in a second-order co-tunnelling process. By recording both the atom position and phase coherence over time, we fully characterize the tunnelling process for a single atom as well as the correlated dynamics of a pair of atoms for weak and strong interactions. In addition, we identify a conditional tunnelling regime in which a single atom can only tunnel in the presence of a second particle, acting as a single atom switch. Such second-order tunnelling events, which are the dominating dynamical effect in the strongly interacting regime, have not been previously observed with ultracold atoms. Similar second-order processes form the basis of superexchange interactions between atoms on neighbouring lattice sites of a periodic potential, a central component of proposals for realizing quantum magnetism.
• T. Müller, S. Fölling, A. Widera and I. Bloch
State preparation and dynamics of ultracold atoms in higher lattice orbitals, Phys. Rev. Lett. 99, 200405 (2007)arXivBibTeX
ABSTRACT »
We report on the realization of a multiorbital system with ultracold atoms in the excited bands of a 3D optical lattice by selectively controlling the band population along a given lattice direction. The lifetime of the atoms in the excited band is found to be considerably longer (10–100 times) than the characteristic time scale for intersite tunneling, thus opening the path for orbital selective many-body physics with ultracold atoms. Upon exciting the atoms from an initial lowest band Mott-insulating state to higher lying bands, we observe the dynamical emergence of coherence in 1D (and 2D), compatible with Bose-Einstein condensation to a nonzero momentum state.
• F. Gerbier, S. Fölling, A. Widera and I. Bloch
arXivBibTeX
ABSTRACT »
In response to a recent manuscript [cond-mat/0609685] on the analysis of interference patterns produced by ultracold atoms released from an optical lattice, we point out that in the presence of a Bose-Einstein condensate the interference pattern can be strongly modified by interaction effects and the presence of a harmonic trap superimposed on the lattice potential. Our results show that the visibility of the interference pattern is significant only if a sizeable condensate fraction is present in the trap.
• T. Gericke, F. Gerbier, A. Widera, S. Fölling, O. Mandel and I. Bloch
Adiabatic loading of a Bose-Einstein condensate in a 3D optical lattice, J. Mod. Opt. 54, 735 (2007)arXivBibTeX
ABSTRACT »
We experimentally investigate the adiabatic loading of a Bose-Einstein condensate into an optical lattice potential. The generation of excitations during the ramp is detected by a corresponding decrease in the visibility of the interference pattern observed after free expansion of the cloud. We focus on the superfluid regime, where we show that the limiting time scale is related to the redistribution of atoms across the lattice by single-particle tunnelling.

### 2006

• F. Gerbier, S. Fölling, A. Widera, O. Mandel and I. Bloch
Probing Number squeezing of Ultracold Atoms across the Superfluid-Mott Insulator Transition, Phys. Rev. Lett. 96, 090401 (2006)arXivBibTeX
ABSTRACT »
The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.
• P. Treutlein, T. Steinmetz, Y. Colombe, B. Lev, P. Hommelhoff, J. Reichel, M. Greiner, O. Mandel, A. Widera, T. Rom, I. Bloch and T. W. Hänsch
Quantum information processing in optical lattices and magnetic microtraps, Fortschr. Phys. 54, 702-718 (2006)arXivBibTeX
ABSTRACT »
We review our experiments on quantum information processing with neutral atoms in optical lattices and magnetic microtraps. Atoms in an optical lattice in the Mott insulator regime serve as a large qubit register. A spin-dependent lattice is used to split and delocalize the atomic wave functions in a controlled and coherent way over a defined number of lattice sites. This is used to experimentally demonstrate a massively parallel quantum gate array, which allows the creation of a highly entangled many-body cluster state through coherent collisions between atoms on neighbouring lattice sites. In magnetic microtraps on an atom chip, we demonstrate coherent manipulation of atomic qubit states and measure coherence lifetimes exceeding one second at micron-distance from the chip surface. We show that microwave near-fields on the chip can be used to create state-dependent potentials for the implementation of a quantum controlled phase gate with these robust qubit states. For single atom detection and preparation, we have developed high finesse fiber Fabry-Perot cavities and integrated them on the atom chip. We present an experiment in which we detected a very small number of cold atoms magnetically trapped in the cavity using the atom chip.
• S. Fölling, A. Widera, T. Mueller, F. Gerbier and I. Bloch
Formation of spatial shell structures in the superfluid to Mott insulator transition, Phys Rev. Lett. 97, 060403 (2006)arXivBibTeX
ABSTRACT »
We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin-changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.
• A. Widera, F. Gerbier, S. Foelling, T. Gericke, O. Mandel and I. Bloch
Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87Rb atoms, New J. Phys. 8, 152 (2006)arXivBibTeX
ABSTRACT »
We report on precision measurements of spin-dependent interaction-strengths in the 87Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction Hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87Rb in the f = 1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87Rb in the f = 2 manifold, the data point towards an antiferromagnetic ground state; however our error bars do not exclude a possible cyclic phase.
• F. Gerbier, A. Widera, S. Fölling, O. Mandel and I. Bloch
Resonant control of spin dynamics in ultracold quantum gases by microwave dressing, Phys. Rev. A 73, 041602(R) (2006)arXivBibTeX
ABSTRACT »
We study experimentally interaction-driven spin oscillations in optical lattices in the presence of an off-resonant microwave field. We show that the energy shift induced by this microwave field can be used to control the spin oscillations by tuning the system either into resonance to achieve near-unity contrast or far away from resonance to suppress the oscillations. Finally, we propose a scheme based on this technique to create a flat sample with either singly or doubly occupied sites, starting from an inhomogeneous Mott insulator, where singly and doubly occupied sites coexist.

### 2005

• A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel and I. Bloch
Coherent collisional spin dynamics in optical lattices, Phys. Rev. Lett. 95, 190405 (2005)arXivBibTeX
ABSTRACT »
We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.
• F. Gerbier, A. Widera, S. Fölling, O. Mandel, T. Gericke and I. Bloch
Interference pattern and visibility of a Mott insulator, Phys. Rev. A 72, 053606 (2005)arXivBibTeX
ABSTRACT »
We analyze theoretically the experiment reported in [F. Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005)]. There, the interference pattern produced by an expanding atomic cloud in the Mott insulator regime was observed, indicative of short-range coherence in the system. The latter was traced back to the presence of a small amount of particle-hole pairs in the insulating phase for finite lattice depths. We analyze the influence of these pairs on the interference pattern using a random phase approximation, and derive the corresponding visibility. We also account for the inhomogeneity inherent to atom traps in a local density approximation. The calculations reproduce the experimental observations, except for very large lattice depths. The deviation from the measurement in this range is attributed to the increasing importance of nonadiabatic effects.
• S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke and I. Bloch
Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature 434, 481-484 (2005)arXivBibTeX
ABSTRACT »
In a pioneering experiment1, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations—together with their fermionic counterparts—find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.
• F. Gerbier, A. Widera, S. Fölling, O. Mandel, T. Gericke and I. Bloch
Phase coherence of an atomic Mott insulator, Phys. Rev. Lett. 95, 050404 (2005)arXivBibTeX
ABSTRACT »
We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.

### 2004

• A. Widera, O. Mandel, M. Greiner, S. Kreim, T. W. Hänsch and I. Bloch
Entanglement Interferometry for Precision Measurement of Atomic Scattering Properties , Phys. Rev. Lett. 92, 160406 (2004)arXivBibTeX
ABSTRACT »
We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.
• B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch and I. Bloch
Tonks–Girardeau gas of ultracold atoms in an optical lattice , Nature 429, 277-281 (2004)BibTeX
ABSTRACT »
Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks–Girardeau gas, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution. Here we report the preparation of a Tonks–Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks–Girardeau regime by increasing the atoms' effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.
• T. Rom, T. Best, O. Mandel, A. Widera, M. Greiner, T. W. Hänsch and I. Bloch
State Selective Production of Molecules in Optical Lattices , Phys. Rev. Lett. 93, 073002 (2004)BibTeX
ABSTRACT »
We demonstrate quantum control over both internal and external quantum degrees of freedom in a high number of identical “chemical reactions,” carried out in an array of microtraps in a 3D optical lattice. Starting from a Mott insulating phase of an ultracold atomic quantum gas, we use two-photon Raman transitions to create molecules on lattice sites occupied by two atoms. In the atom-molecule conversion process, we can control both the internal rovibronic and external center of mass quantum state of the molecules. The lattice isolates the microscopic chemical reactions from each other, thereby allowing photoassociation spectra without collisional broadening even at high densities of up to 2×10^15   cm^-3.
• A. Widera, O. Mandel, M. Greiner, S. Kreim, T. W. Hänsch and I. Bloch
Entanglement Interferometry for Precision Measurement of Atomic Scattering Properties, Phys. Rev. Lett. 92, 160406 (2004)arXivBibTeX
ABSTRACT »
We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.

### 2003

• A. Widera
Controlled Cold Collisions: Towards Many-Particle Entanglement in Optical Lattices, Diplomarbeit an der Universität Würzburg/München, (2003)BibTeX
• O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch and I. Bloch
Coherent transport of neutral atoms in spin-dependent optical lattice potentials , Phys. Rev. Lett. 91, 010407 (2003)arXivBibTeX
ABSTRACT »
We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.
• O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch and I. Bloch
Controlled collisions for multi-particle entanglement of optically trapped atoms , Nature 425, 937-940 (2003)arXivBibTeX
ABSTRACT »
Entanglement lies at the heart of quantum mechanics, and in recent years has been identified as an essential resource for quantum information processing and computation. The experimentally challenging production of highly entangled multi-particle states is therefore important for investigating both fundamental physics and practical applications. Here we report the creation of highly entangled states of neutral atoms trapped in the periodic potential of an optical lattice. Controlled collisions between individual neighbouring atoms are used to realize an array of quantum gates, with massively parallel operation. We observe a coherent entangling–disentangling evolution in the many-body system, depending on the phase shift acquired during the collision between neighbouring atoms. Such dynamics are indicative of highly entangled many-body states; moreover, these are formed in a single operational step, independent of the size of the system.

### 2001

• A. Widera
Design and Construction of a Modular Spin-Flip Zeeman Slower, (2001), Diplom thesisBibTeX