Publications (85)284.78 Total impact
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ABSTRACT: We study a few Fermi atoms interacting through attractive contact forces in a onedimensional trap by means of numerical exact diagonalization. From the combined analysis of energies and wave functions of correlated ground and excited states we find evidence of BCSlike pairing even for very few atoms. For moderate interaction strength, we reproduce the evenodd oscillation of the separation energy observed in [G. Zuern, A. N. Wenz, S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, Phys. Rev. Lett. 111, 175302 (2013)]. For stronger interactions nonlinear, cooperative effects emerge, including non trivial spatial arrangement of atomic Cooper pairs in the trap.04/2014; 
Article: Three interacting atoms in a onedimensional trap: A benchmark system for computational approaches
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ABSTRACT: We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a onedimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark for exactdiagonalization technique (also known as full configuration interaction), which is found to slowly converge in the case of strong interatomic attraction.Journal of Physics B Atomic Molecular and Optical Physics 10/2013; 47(6). · 2.03 Impact Factor 
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ABSTRACT: A simple theory for the tunneling of two cold atoms out of a trap in the presence of an attractive contact force is developed. Two competing decay channels, respectively for singleatom and boundpair tunneling, contribute independently to the decay law of the mean atom number in the trap. The singleatom tunneling rate is obtained through the quasiparticle wave function formalism. For pair tunneling an effective equation for the centerofmass motion is derived, so the calculation of the corresponding tunneling rate is again reduced to a simpler onebody problem. The predicted dependence of tunneling rates on the interaction strength qualitatively agrees with a recent measurement of the twoatom decay time [G. Zuern, A. N. Wenz, S. Murmann, T. Lompe, and S. Jochim, arXiv:1307.5153].Physical Review A 08/2013; 88(4). · 3.04 Impact Factor 
Article: Observation and spectroscopy of a twoelectron Wigner molecule in an ultraclean carbon nanotube
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ABSTRACT: Two electrons on a string form a simple model system where Coulomb interactions are expected to play an interesting role. In the presence of strong interactions, these electrons are predicted to form a Wigner molecule, separating to the ends of the string. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet so far a direct measurement of such a spectrum in a controllable onedimensional setting is still missing. Here we use an ultraclean carbon nanotube to realize this system in a tunable potential. Using tunnelling spectroscopy we measure the addition spectra of two interacting carriers, electrons or holes, and identify seven lowenergy states characterized by their exchange symmetries. The formation of a Wigner molecule is evident from a tenfold quenching of the fundamental excitation energy as compared with the noninteracting value. Our ability to tune the twocarrier state in space and to study it for both electrons and holes provides an unambiguous demonstration of this strongly interacting quantum ground state. O ne of the simplest realizations of an interacting quantummechanical system is that of two electrons on a string. The behavior of this system is governed by the balance between kinetic and interaction energies. When kinetic energy dominates, the electrons occupy particleinabox levels along the string. In contrast, when interactions dominate, a Wignermolecule ground state is formed, in which the repulsion of the two electrons drives them to localize at the two sides of the string 1,2 . Owing to the fermionic nature of the two particles their total wavefunction is antisymmetric with respect to electron exchange, leading to an intimate connection between their realspace and spinspace behaviours. Consequently, the realspace charge separation in a Wigner molecule goes hand in hand with a spinspace signature, namely a pronounced quenching of its spin excitation energies 3 . A carbon nanotube is an excellent system to search for the existence of a Wignermolecule ground state. This system is known to have strong electron–electron interactions 4–8 , and can be clean enough to allow measurements down to the singlecarrier limit 9,10 , made more accessible by recent technological breakthroughs 11–14 . Some of these measurements showed unexplained deviations from the expected shellfilling model, which hinted that interesting physics occur at low electronic numbers 9,11,12 . Compared with iii–v semiconductor systems 15–18 in which Wignermolecule formation has been explored previously, in suspended nanotubes the screening of Coulomb interactions is strongly reduced and the onedimensional confinement potential for electrons or holes can be shaped with gate electrodes. This ability to control the confining potential is critical because it allows one to distinguish between extrinsic electrostatic effects that spatially separate the two electrons and intrinsic separation driven by their repulsion. Furthermore, in addition to the conventional twofold spin degeneracy in other semiconductors, electrons in nanotubes possess a twofold orbital degeneracy (isospin), forming a fourfold spin–isospin subspace. Recent experiments 12 have shown that the electrons'Nature Physics 07/2013; 9:576581. · 19.35 Impact Factor 
Article: Intervalley scattering induced by Coulomb interaction and disorder in carbonnanotube quantum dots
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ABSTRACT: We develop a theory of intervalley Coulomb scattering in semiconducting carbonnanotube quantum dots, taking into account the effects of curvature and chirality. Starting from the effectivemass description of singleparticle states, we study the twoelectron system by fully including Coulomb interaction, spinorbit coupling, and shortrange disorder. We find that the energy level splittings associated with intervalley scattering are nearly independent of the chiral angle and, while smaller than those due to spinorbit interaction, large enough to be measurable.Physical Review B 06/2013; 88(12). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Scanning tunneling spectroscopy (STS) allows us to image single molecules decoupled from the supporting substrate. The obtained images are routinely interpreted as the square moduli of molecular orbitals, dressed by the meanfield electronelectron interaction. Here we demonstrate that the effect of electron correlation beyond the mean field qualitatively alters the uncorrelated STS images. Our evidence is based on the ab initio manybody calculation of STS images of planar molecules with metal centers. We find that manybody correlations alter significantly the image spectral weight close to the metal center of the molecules. This change is large enough to be accessed experimentally, surviving to moleculesubstrate interactions.Physical Review Letters 01/2013; 110(1):018305. · 7.94 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A theory for the tunneling of one atom out of a trap containing two interacting cold atoms is developed. The quasiparticle wave function, dressed by the interaction with the companion atom in the trap, replaces the noninteracting orbital at resonance in the tunneling matrix element. The computed decay time for two ^{6}Li atoms agrees with recent experimental results [G. Zürn, F. Serwane, T. Lompe, A. N. Wenz, M. G. Ries, J. E. Bohn, and S. Jochim, Phys. Rev. Lett. 108, 075303 (2012)], unveiling the "fermionization" of the wave function and a novel twobody effect.Physical Review Letters 03/2012; 108(11):115302. · 7.94 Impact Factor 
Article: Absence of Wigner molecules in onedimensional fewfermion systems with shortrange interactions
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ABSTRACT: We study by means of exactdiagonalization techniques the ground state of a fewfermion system with strong shortrange repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the groundstate density profile displays at strong coupling very well pronounced Friedel oscillations with a `4k_F periodicity', the pair correlation function does not show any signature of Wignermoleculetype correlations. For the sake of comparison, we present also numerical results for fewelectron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.Physical review. B, Condensed matter 02/2012; 86(7). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We observe a lowlying sharp spin mode of three interacting electrons in an array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic light scattering. The finding is enabled by a suppression of the inhomogeneous contribution to the excitation spectra obtained by reducing the number of optically probed quantum dots. Supported by configurationinteraction calculations we argue that the observed spin mode offers a direct probe of Stoner ferromagnetism in the simplest case of three interacting spin onehalf fermions.Physical review. B, Condensed matter 09/2011; 85(3). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate that the profile of the spaceresolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gatedefined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub) Kelvin range.Physical review. B, Condensed matter 09/2011; · 3.77 Impact Factor 
Article: Artificial atoms: Shape the wave.
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ABSTRACT: Tunnelling and capacitance spectroscopies are able to image the wavefunctions of electrons in atomlike solidstate systems as they are shaped by an external magnetic field.Nature Material 03/2011; 10(3):1735. · 35.75 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Scanning tunnelling spectroscopy (STS) visualizes electron states in both extended systems and nanoobjects, as quantum dots and molecules. Whereas bulk quantum states are insensitive to electron number fluctuations, an energy gap opens each time a new electron is injected by the STS tip into a sufficiently small system. This gap originates from the interaction of the next incoming electron with the others already present in the system. In this Coulomb blockade regime a fundamental question is whether the wave function of the "quasiparticle" added to the system imaged by the STS tip is sensitive to electronelectron interaction. Here we show that the STS images of single planar molecules with metal centres predicted by ab initio manybody calculations differ qualitatively from their uncorrelated counterparts. We find in the maps resolved at the Fermi energy that correlation significantly removes spectral weight from the metal atom, as well as the overall weight is remarkably reduced. This change may be measured and compared with STS images of molecules without the metal center, whose manybody and uncorrelated versions are alike.03/2011; 
Article: STM images of carbonnanotube quantum dots: Seeing a Wigner molecule of correlated electrons
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ABSTRACT: The paradigm of fewelectron complexes in quantum dots (QDs) relies on the idea that the lowest quantized levels are filled according to Pauli's exclusion principle. If Coulomb repulsion is sufficiently strong to overcome the kinetic energy cost of localization, a different scenario is predicted: a "Wigner" molecule (WM) forms, made of electrons frozen in space according to a geometrical pattern. Despite considerable experimental effort, evidence of the WM in semiconductor QDs has been elusive so far. Here we demonstrate theoretically that WMs occur in gatedefined QDs embedded in typical semiconducting carbon nanotubes (CNTs). The unambiguous signatures of the WM state must be searched in the scanning tunneling microscopy (STM) images of the electrons. Through exact diagonalisation (ED) calculations, we unveil the inherent features of the electron molecular states. We show that, like nuclei in a usual molecule, electrons have localized wave functions and hence negligible exchange interactions. ED results for single and double QDs provide a simple interpretation for transport experiments in ultraclean CNTs.03/2011;  [Show abstract] [Hide abstract]
ABSTRACT: Scanning tunneling microscopy (STM) has been a fundamental tool to characterize manybody effects in condensed matter systems, from extended solids to quantum dots. STM of molecules decoupled from the supporting conductive substrate has the potential to extend STM characterization of manybody effects to the molecular world as well. In this paper, we describe a manybody tunneling theory for molecules decoupled from the STM substrate, and we report on the use of standard quantum chemical methods to calculate the quantities necessary to provide the "correlated" STM molecular image. The developed approach has been applied to 18 different molecules to explore the effects of their chemical nature and of their substituents, as well as to verify the possible contribution by transition metal centers. Whereas the bulk of calculations has been performed with the configuration interaction method with single and double excitations (CISD), because of the computational cost some tests have been also performed with the more accurate coupled cluster with single and double excitations (CCSD) method to quantify the importance of the computational level on manybody STM images. We have found that correlation induces a remarkable squeezing of the images, and that correlated images are not derived from HartreeFock HOMO or LUMO alone, but include contributions from other orbitals as well. Although correlation effects are too small to be resolved by present STM experiments for the studied molecules, our results provide hints for seeking out other species with larger, and possibly experimentally detectable, correlation effects.The Journal of Chemical Physics 01/2011; 134(2):024104. · 3.16 Impact Factor 
Article: Exchange and correlation effects in the transmission phase through a fewelectron quantum dot
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ABSTRACT: The transmission phase through a quantum dot with few electrons shows a complex, nonuniversal behavior. Here we combine configurationinteraction calculations treating rigorously Coulomb interaction and the Friedel sum rule to provide a rationale for the experimental findings. The phase evolution for more than two electrons is found to strongly depend on dot's shape and electron density, whereas from one to two the phase never lapses. In the Coulomb (Kondo) regime the phase shifts are significant fractions of pi (pi/2) for the second and subsequent charge addition if the dot is strongly correlated. These results are explained by the proper inclusion in the theory of Coulomb interaction, spin, and orbital degrees of freedom. Comment: RevTeX 4.0, 6 pages, 3 b/w figures. Physical Review B (2010), in pressPhysical review. B, Condensed matter 07/2010; · 3.77 Impact Factor 
Article: Correlated electrons in optically tunable quantum dots: building an electron dimer molecule.
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ABSTRACT: We observe the lowlying excitations of a molecular dimer formed by two electrons in a GaAs semiconductor quantum dot in which the number of confined electrons is tuned by optical illumination. By employing inelastic light scattering we identify the intershell excitations in the oneelectron regime and the distinct spin and charge modes in the interacting fewbody configuration. In the case of two electrons, a comparison with configurationinteraction calculations allows us to link the observed excitations with the breathing mode of the molecular dimer and to determine the singlettriplet energy splitting.Physical Review Letters 06/2010; 104(24):246802. · 7.94 Impact Factor 
Article: Visualizing electronic correlations in molecules: STM images from manybody abinitio calculations
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ABSTRACT: Single molecular orbitals are nowadays imaged in real space by both scanning tunnelling (STM) and photoemission spectroscopies. The key quantity provided by these techniques is the density of states an intrinsically manybody observable. For extended systems, its energy and momentum dependence signals intriguing phenomena like nonFermi liquid behavior, electron pairing, Kondo effect, Fermi edge singularity. For isolated molecules, the spaceresolved spectral density of states reduces to the wave function square modulus of the ``quasiparticle'' added to the system. The latter is sensitive to both correlation effects and changes of the electron number. Here we predict, on the basis of abinitio manybody calculations, that the orbital images of certain planar conjugated molecules are significantly modified by electron correlation. We find differences in the nodal plane orientations of HOMO and LUMO correlated orbitals with respect to the HartreeFock results, as well as spectral weight rearrangements all over the molecule. These features may be detected experimentally, providing an accessible signature of correlation effects in simple molecules.03/2010; 
Article: Probing collective modes of correlated states of few electrons in semiconductor quantum dots
Solid State Communications 09/2009; 149(35):1436. · 1.53 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy indeed some of them have already been observed by Deshpande and Bockrath [Nature Phys. 4, 314 (2008)]. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas lowenergy excitations are collective vibrations of electrons around their equilibrium positions. Comment: 12 pages (6 color figures, 3 b/w figures, 3 tables). This paper has been extensively revised, including more theoretical material, the discussion of experiments by Deshpande and Bockrath (Nature Phys. 2008) and Kuemmeth et al. (Nature 2008), the location of their quantumdot devices in the proposed theoretical phase diagram. To appear in Physical Review BPhysical review. B, Condensed matter 08/2009; · 3.77 Impact Factor
Publication Stats
690  Citations  
284.78  Total Impact Points  
Top Journals
Institutions

2011–2012

National Research Council
Roma, Latium, Italy


2006–2010

Scuola Normale Superiore di Pisa
 Laboratory NEST: National Enterprise for NanoScience and NanoTechnology
Pisa, Tuscany, Italy 
Nippon Telegraph and Telephone
Edo, Tōkyō, Japan


2009

Michigan State University
East Lansing, Michigan, United States


1998–2009

Università degli Studi di Modena e Reggio Emilia
 Department of Engineering "Enzo Ferrari"
Modène, EmiliaRomagna, Italy


2007

University of Hamburg
 Institute of Applied Physics
Hamburg, Hamburg, Germany


2005

Cineca
Casalecchio di Reno, EmiliaRomagna, Italy
