My work

Currently, I study coherent dipolar energy transfer between resonant levels of ultra-cold Rydberg atoms (Scholak, Wellens, and Buchleitner 2014), specifically, of the non-radiative exchange of an excitation among a large number of randomly distributed atoms. I conduct large-scale numerical surveys on the statistics of clouds with a large number of atoms $N$ and compare them to results of established random matrix theories, Euclidean and stable random matrix theory, for instance. I also work on analytical treatments for the asymptotic limit, where $N \to \infty$.

During my PhD, I worked on excitonic energy transport in disordered networks (Scholak et al. 2011; Scholak 2011), in particular, pigment-protein complexes with strong dipole-dipole interactions. I employed evolution strategies to numerically optimize the energy transport in these systems. I got heavily involved in the ongoing debate on the mechanisms that drive efficient transport across photosynthetic complexes.

In the group of Paul Brumer, one of my main concerns has been the substantiation of quantum coherence effects in the control of atomic and molecular processes with lasers, i.e. quantum coherent control (Scholak and Brumer 2014). To this end, I integrated coherent control ideas with concepts of quantum interferometry, in particular, the complementarity of waves and particles, suggesting the possibility to observe non-trivial quantum effects in new scenarios of two-color phase control.


Publications

In preparation
  1. Scholak, Torsten, and Paul Brumer, 2015, “Nonclassical Interference versus Classical Nonlinear Response: When Is Coherent Control Truly Quantum?”
    View

    Addressed the long standing issue of the significance of quantum coherence and nonclassical effects in scenarios of coherent phase control ⋅ Showed that two-color weak-field phase control, the archetype of the all-optical control methods, is an analogue of a purely classical control phenomenon ⋅ Introduced a new, unifying framework called the coherent control interferometer ⋅ Studied quantitative wave-particle complementarity in the setting of coherent phase control ⋅ Designed two new quantum coherent control scenarios: quantum erasure and quantum delayed choice coherent control ⋅ Showed that the nonclassicality and the genuine randomness of these new scenarios can be certified by Bell inequality tests.

    @unpublished{scholak2015nonclassical,
      annote = {Addressed the long standing issue of the significance of quantum coherence and nonclassical effects in scenarios of coherent phase control ⋅ Showed that two-color weak-field phase control, the archetype of the all-optical control methods, is an analogue of a purely classical control phenomenon ⋅ Introduced a new, unifying framework called the coherent control interferometer ⋅ Studied quantitative wave-particle complementarity in the setting of coherent phase control ⋅ Designed two new quantum coherent control scenarios: quantum erasure and quantum delayed choice coherent control ⋅ Showed that the nonclassicality and the genuine randomness of these new scenarios can be certified by Bell inequality tests.},
      author = {Scholak, Torsten and Brumer, Paul},
      date-added = {2015-03-01 17:01:29 +0000},
      date-modified = {2015-03-01 17:02:42 +0000},
      month = jan,
      note = {in preparation},
      title = {Nonclassical interference versus classical nonlinear response: When is coherent control truly quantum?},
      year = {2015}
    }
    
  2. Scholak, Torsten, Thomas Wellens, and Andreas Buchleitner, 2015, “Excitation Energy Transfer in Ultracold Rydberg Gases.”
    View

    Found that the nature of excitation energy transfer (EET) in a Rydberg gas can be controlled via the dipole blockade effect ⋅ Analyzed the ensemble-averaged mean-square displacement ⋅ Studied the spatial distribution of the system’s eigenstates.

    @unpublished{scholak2015excitation,
      annote = {Found that the nature of excitation energy transfer (EET) in a Rydberg gas can be controlled via the dipole blockade effect ⋅ Analyzed the ensemble-averaged mean-square displacement ⋅ Studied the spatial distribution of the system's eigenstates.},
      author = {Scholak, Torsten and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 16:58:59 +0000},
      date-modified = {2015-03-02 06:36:32 +0000},
      month = jan,
      note = {in preparation},
      title = {Excitation energy transfer in ultracold Rydberg gases},
      year = {2015}
    }
    
Journal articles
  1. Scholak, Torsten, Thomas Wellens, and Andreas Buchleitner, 2014, “Spectral Backbone of Excitation Transport in Ultracold Rydberg Gases,” Phys. Rev. A 90 (American Physical Society), 063415. doi:10.1103/PhysRevA.90.063415.
    View Download PDF.

    Studied spectral structure underlying excitonic energy transfer in ultracold Rydberg gases ⋅ Found evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance ⋅ Discovered that the dipole blockade effect in Rydberg gases can be leveraged to manipulate the localization transition.

    The spectral structure underlying excitonic energy transfer in ultracold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels’ spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the relative weight of localized states is reduced. At the same time, the spectral statistics, in particular, the density of states and the nearest-neighbor level-spacing statistics, exhibits a transition from approximately a 1-stable Lévy to a Gaussian orthogonal ensemble. Deviations from random matrix statistics are shown to stem from correlations between interatomic interaction strengths that lead to an asymmetry of the spectral density and profoundly affect localization properties. We discuss approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

    @article{scholak2014spectral,
      annote = {Studied spectral structure underlying excitonic energy transfer in ultracold Rydberg gases ⋅ Found evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance ⋅ Discovered that the dipole blockade effect in Rydberg gases can be leveraged to manipulate the localization transition.},
      author = {Scholak, Torsten and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:02 +0000},
      date-modified = {2015-03-01 05:48:42 +0000},
      doi = {10.1103/PhysRevA.90.063415},
      journal = {Phys. Rev. A},
      month = dec,
      number = {6},
      pages = {063415},
      publisher = {American Physical Society},
      title = {Spectral backbone of excitation transport in ultracold Rydberg gases},
      volume = {90},
      year = {2014},
      bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevA.90.063415}
    }
    
  2. Scholak, Torsten, and Paul Brumer, 2014, “Certifying the Quantumness of a Generalized Coherent Control Scenario,” J. Chem. Phys. 141 (AIP Publishing), 204311. doi:10.1063/1.4902253.
    View Download PDF.

    Showed how to display the genuinely quantum nature of a generalized weak-field coherent control scenario (utilizing 1 vs. 2 photon excitation) via a Bell-CHSH test.

    We consider the role of quantum mechanics in a specific coherent control scenario, designing a “coherent control interferometer” as the essential tool that links coherent control to quantum fundamentals. Building upon this allows us to rigorously display the genuinely quantum nature of a generalized weak-field coherent control scenario (utilizing 1 vs. 2 photon excitation) via a Bell-CHSH test. Specifically, we propose an implementation of “quantum delayed-choice” in a bichromatic alkali atom photoionization experiment. The experimenter can choose between two complementary situations, which are characterized by a random photoelectron spin polarization with particle-like behavior on the one hand, and by spin controllability and wave-like nature on the other. Because these two choices are conditioned coherently on states of the driving fields, it becomes physically unknowable, prior to measurement, whether there is control over the spin or not.

    @article{scholak2014certifying,
      annote = {Showed how to display the genuinely quantum nature of a generalized weak-field coherent control scenario (utilizing 1 vs. 2 photon excitation) via a Bell-CHSH test.},
      author = {Scholak, Torsten and Brumer, Paul},
      date-added = {2015-03-01 05:20:59 +0000},
      date-modified = {2015-03-01 05:49:57 +0000},
      doi = {10.1063/1.4902253},
      journal = {J. Chem. Phys.},
      month = nov,
      number = {20},
      pages = {204311},
      publisher = {AIP Publishing},
      title = {Certifying the quantumness of a generalized coherent control scenario},
      volume = {141},
      year = {2014},
      bdsk-url-1 = {http://dx.doi.org/10.1063/1.4902253}
    }
    
  3. Zech, Tobias, Mattia Walschaers, Torsten Scholak, Roberto Mulet, Thomas Wellens, and Andreas Buchleitner, 2013, “Quantum Transport in Biological Functional Units: Noise, Disorder, Structure,” Fluct. Noise Lett. 12 (World Scientific Publishing Company), 1340007. doi:10.1142/S0219477513400075.
    View Download PDF.

    Showed that 3D structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations.

    Through simulations of quantum coherent transport on disordered molecular networks, we show that three dimensional structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations. Furthermore, configurations that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

    @article{zech2013quantum,
      annote = {Showed that 3D structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations.},
      author = {Zech, Tobias and Walschaers, Mattia and Scholak, Torsten and Mulet, Roberto and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:07 +0000},
      date-modified = {2015-03-01 05:47:35 +0000},
      doi = {10.1142/S0219477513400075},
      journal = {Fluct. Noise Lett.},
      month = jun,
      number = {02},
      pages = {1340007},
      publisher = {World Scientific Publishing Company},
      title = {Quantum Transport in Biological Functional Units: Noise, Disorder, Structure},
      volume = {12},
      year = {2013},
      bdsk-url-1 = {http://dx.doi.org/10.1142/S0219477513400075}
    }
    
  4. Scholak, Torsten, Tobias Zech, Thomas Wellens, and Andreas Buchleitner, 2011, “Disorder-Assisted Exciton Transport,” Acta Phys. Pol. A 120 (Institute of Physics, Polish Academy of Science), 89. Available at: http://przyrbwn.icm.edu.pl/APP/ABSTR/120/a120-6a-52.html.
    View Download PDF.

    Discussed the role of disorder for the optimization of exciton transport in the FMO (Fenna-Matthews-Olson) light harvesting complex ⋅ Demonstrated the existence of a small fraction of optimal, though highly asymmetric, non-periodic conformations, which yield near-to-optimal coherent excitation transport.

    We discuss the possibly constructive role of disorder for the optimization of exciton transport in the FMO (Fenna􏰂Matthews􏰂Olson) light harvesting complex. Our analysis, which models the FMO as a 3D random graph, demonstrates the existence of a small fraction of optimal, though highly asymmetric, non-periodic conformations, which yield near-to-optimal coherent excitation transport. We argue that, on transient time scales, such quantum interference enhanced transport does always better than stochastic activation.

    @article{scholak2011disorder,
      annote = {Discussed the role of disorder for the optimization of exciton transport in the FMO (Fenna-Matthews-Olson) light harvesting complex ⋅ Demonstrated the existence of a small fraction of optimal, though highly asymmetric, non-periodic conformations, which yield near-to-optimal coherent excitation transport.},
      author = {Scholak, Torsten and Zech, Tobias and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:08 +0000},
      date-modified = {2015-03-01 15:55:23 +0000},
      journal = {Acta Phys. Pol. A},
      month = dec,
      number = {6A},
      pages = {89},
      publisher = {Institute of Physics, Polish Academy of Science},
      title = {Disorder-Assisted Exciton Transport},
      url = {http://przyrbwn.icm.edu.pl/APP/ABSTR/120/a120-6a-52.html},
      volume = {120},
      year = {2011},
      bdsk-url-1 = {http://przyrbwn.icm.edu.pl/APP/ABSTR/120/a120-6a-52.html}
    }
    
  5. Scholak, Torsten, Thomas Wellens, and Andreas Buchleitner, 2011, “Optimal Networks for Excitonic Energy Transport,” J. Phys. B 44 (IOP Publishing), 184012. doi:10.1088/0953-4075/44/18/184012.
    View Download PDF.

    Investigated coherent and incoherent excitation transfer in a random network with dipole-dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms.

    We investigate coherent and incoherent excitation transfer in a random network with dipole–dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms. For this purpose, we introduce and compare two different measures (the maximum output probability and the average transfer time) for the efficiency of transport from the input to the output site. We especially focus on optimal configurations which maximize the transfer efficiency and the impact of dephasing noise on the transport dynamics. For most configurations of the random network, the transfer efficiency increases when adding noise, giving rise to essentially classical transport. These noise-assisted configurations are, however, systematically less efficient than the optimal configurations. The latter reach their highest efficiency for purely coherent dynamics, i.e. in the absence of noise.

    @article{scholak2011optimal,
      annote = {Investigated coherent and incoherent excitation transfer in a random network with dipole-dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms.},
      author = {Scholak, Torsten and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:09 +0000},
      date-modified = {2015-03-01 05:45:12 +0000},
      doi = {10.1088/0953-4075/44/18/184012},
      journal = {J. Phys. B},
      month = sep,
      number = {18},
      pages = {184012},
      publisher = {IOP Publishing},
      title = {Optimal networks for excitonic energy transport},
      volume = {44},
      year = {2011},
      bdsk-url-1 = {http://dx.doi.org/10.1088/0953-4075/44/18/184012}
    }
    
  6. ———, 2011, “The Optimization Topography of Exciton Transport,” Europhys. Lett. 96 (IOP Publishing), 10001. doi:10.1209/0295-5075/96/10001.
    View Download PDF.

    Showed that configurations of a random molecular network that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

    Stunningly large exciton transfer rates in the light harvesting complex of photosynthesis, together with recent experimental 2D spectroscopic data, have spurred a vivid debate on the possible quantum origin of such efficiency. Here we show that configurations of a random molecular network that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

    @article{scholak2011optimization,
      annote = {Showed that configurations of a random molecular network that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.},
      author = {Scholak, Torsten and Wellens, Thomas and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:10 +0000},
      date-modified = {2015-03-01 05:46:22 +0000},
      doi = {10.1209/0295-5075/96/10001},
      journal = {Europhys. Lett.},
      month = aug,
      number = {1},
      pages = {10001},
      publisher = {IOP Publishing},
      title = {The optimization topography of exciton transport},
      volume = {96},
      year = {2011},
      bdsk-url-1 = {http://dx.doi.org/10.1209/0295-5075/96/10001}
    }
    
  7. Scholak, Torsten, Fernando de Melo, Thomas Wellens, Florian Mintert, and Andreas Buchleitner, 2011, “Efficient and Coherent Excitation Transfer across Disordered Molecular Networks,” Phys. Rev. E 83 (American Physical Society), 021912. doi:10.1103/PhysRevE.83.021912.
    View Download PDF.

    Showed that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer that is robust against ambient dephasing and is associated with strong multisite entanglement ⋅ Offered an explanation for the efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

    We show that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer which is robust against ambient dephasing and associated with strong multisite entanglement. Such optimal, random molecular conformations may explain efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

    @article{scholak2011efficient,
      annote = {Showed that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer that is robust against ambient dephasing and is associated with strong multisite entanglement ⋅ Offered an explanation for the efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.},
      author = {Scholak, Torsten and de Melo, Fernando and Wellens, Thomas and Mintert, Florian and Buchleitner, Andreas},
      date-added = {2015-03-01 05:21:09 +0000},
      date-modified = {2015-03-01 05:44:18 +0000},
      doi = {10.1103/PhysRevE.83.021912},
      journal = {Phys. Rev. E},
      month = feb,
      number = {2},
      pages = {021912},
      publisher = {American Physical Society},
      title = {Efficient and coherent excitation transfer across disordered molecular networks},
      volume = {83},
      year = {2011},
      bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevE.83.021912}
    }
    
  8. Scholak, Torsten, Florian Mintert, and Cord Axel Müller, 2008, “Entanglement Witnesses from Single-Particle Interference,” EPL 83 (IOP Publishing), 60006. doi:10.1209/0295-5075/83/60006.
    View Download PDF.

    Described a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe.

    We describe a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe. After outlining the principle, we discuss specific realizations both with electrons in mesoscopic Aharonov-Bohm rings and with photons in standard Young’s double-slit or coherent-backscattering interferometers.

    @article{scholak2008entanglement,
      annote = {Described a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe.},
      author = {Scholak, Torsten and Mintert, Florian and Müller, Cord Axel},
      date-added = {2015-03-01 05:21:23 +0000},
      date-modified = {2015-03-01 16:57:13 +0000},
      doi = {10.1209/0295-5075/83/60006},
      journal = {EPL},
      month = sep,
      number = {6},
      pages = {60006},
      publisher = {IOP Publishing},
      title = {Entanglement witnesses from single-particle interference},
      volume = {83},
      year = {2008},
      bdsk-url-1 = {http://dx.doi.org/10.1209/0295-5075/83/60006}
    }
    
Book chapters
  1. Scholak, Torsten, Florian Mintert, Thomas Wellens, and Andreas Buchleitner, 2010, “Transport and Entanglement,” in Quantum Efficiency in Complex Systems, Part I: Biomolecular Systems, Part 1. Vol. 83. Semiconductors and Semimetals (Elsevier Science), pp. 1–38. doi:10.1016/B978-0-12-375042-6.00001-8.
    View

    Showed that excitation transport across molecular networks mimicking the FMO light-harvesting complex can be enhanced by quantum coherence on transient timescales.

    This chapter reviews the essential ingredients of quantum transport in disordered systems, and introduces measures of quantum coherence and entanglement in multisite systems. It explains excitation transport in Fenna–Matthews–Olsen (FMO)-like structures under strictly coherent conditions as well as in presence of a dephasing environment. The statistical treatment of excitation transport across a molecular network mimicking the FMO light-harvesting complex shows the potential of quantum coherence to enhance transport, on transient timescales. The transfer probability thus achieved can reach 100%—a value unachievable by classically diffusive, unbiased transport. Furthermore, because such quantum transfer is brought about by constructive multipath interference along intermediate sites of the molecular complex, coherent quantum transport is certainly faster than classically diffusive transport for comparable inter-site coupling strengths. Taking both transfer probability and transfer time together, coherence thus defines levels of quantum efficiency unreached by a classical transport process on the same network. The quantum coherence holds the potential to steer quantum transport efficiencies in engineered devices as abundant in semiconductor technology.

    @inbook{scholak2010transport,
      annote = {Showed that excitation transport across molecular networks mimicking the FMO light-harvesting complex can be enhanced by quantum coherence on transient timescales.},
      author = {Scholak, Torsten and Mintert, Florian and Wellens, Thomas and Buchleitner, Andreas},
      chapter = {1},
      date-added = {2015-03-01 05:21:11 +0000},
      date-modified = {2015-03-01 16:56:55 +0000},
      doi = {10.1016/B978-0-12-375042-6.00001-8},
      journal = {Quantum Efficiency in Complex Systems, Part I: Biomolecular Systems, Part 1},
      month = dec,
      pages = {1--38},
      publisher = {Elsevier Science},
      series = {Semiconductors and semimetals},
      title = {Transport and entanglement},
      volume = {83},
      year = {2010},
      bdsk-url-1 = {http://dx.doi.org/10.1016/B978-0-12-375042-6.00001-8}
    }
    
Theses
  1. Scholak, Torsten, 2011, “Transport and Coherence in Disordered Networks,” PhD thesis, (Universitätsbibliothek Freiburg). Available at: http://www.freidok.uni-freiburg.de/volltexte/8283/.
    View Download PDF.

    A current and actively discussed issue are the mechanisms that drive efficient transport across photosynthetic light-harvesting complexes. Recent experiments detected long-lived quantum coherence in these systems, in the process rendering some long-accepted textbook knowledge obsolete: Although the very fabric of life—atoms and molecules—is of a quantum nature, these effects were thought to be irrelevant for most biological processes, simply because they operate at room temperature and involve vastly many degrees of freedom. Could nature, in order to enhance the efficiency of principal tasks, take advantage of quantum mechanical coherent dynamics? In this thesis, we will investigate the transport properties of an ensemble of spatially disordered, finitely sized molecular networks with dipolar interactions in order to model energy transport in photosynthetic complexes in consideration of the variability of organic samples and the experimental uncertainties. For this task, we employ and compare several measures of transport efficiency. In contrast to the widely used hypothesis stating that quantum coherence effects generally lead to localization and thus hinder transport, we will identify certain rare optimal conformations featuring fast and perfectly efficient transport of energy—solely by means of constructive quantum interference. Furthermore, we will unveil that efficient transport is always associated with the build-up of strong multisite entanglement. Adding dephasing noise—which gradually destroys interference and thereby gives rise to essentially classical transport—increases the transport efficiency of most configurations, but, as we show, the highest efficiencies are attained only by the optimal configurations in case of purely coherent dynamics, i.e., in the absence of noise. Finally, we attempt to extrapolate the transport statistics to infinitely sized systems.

    @phdthesis{scholak2011transport,
      author = {Scholak, Torsten},
      date-added = {2015-03-01 05:21:10 +0000},
      date-modified = {2015-03-02 06:01:15 +0000},
      month = sep,
      school = {Universitätsbibliothek Freiburg},
      title = {Transport and coherence in disordered networks},
      url = {http://www.freidok.uni-freiburg.de/volltexte/8283/},
      year = {2011},
      bdsk-url-1 = {http://www.freidok.uni-freiburg.de/volltexte/8283/}
    }
    
  2. ———, 2008, “Photon-Interferenz Bei Streuung an Verschränkten Atomen,” Master's thesis, (Universität Bayreuth).
    View Download PDF.

    In dieser Arbeit wird ein Vorschlag zur Implementierung von Verschränkungszeugen mittels Ein-Teilchen-Interferenz vorgestellt. Nach Behandlung des allgemeinen Konzeptes werden mögliche Realisationen einerseits mit Elektronen in mesoskopischen Aharonov-Bohm-Ringen als auch mit Photonen und Atomen in der Youngschen Doppelspalt- sowie einer Doppelstreuanordnung diskutiert.

    @mastersthesis{scholak2008photon,
      author = {Scholak, Torsten},
      date-added = {2015-03-01 05:25:59 +0000},
      date-modified = {2015-03-01 16:17:05 +0000},
      language = {german},
      month = jan,
      school = {Universität Bayreuth},
      title = {Photon-Interferenz bei Streuung an verschränkten Atomen},
      year = {2008}
    }
    

Talks and posters

2013 Gordon conference poster

  1. Scholak, Torsten, 2014, “Excitation Energy Transfer in Ultracold Rydberg Gases” (invited seminar talk at the IQC in Waterloo, Canada).
    View Download PDF.

    Rydberg atoms are highly excited neutral atoms with exceptional properties. Not long ago, interest in Rydberg atoms was limited to their spectroscopic properties. However, in recent years, Rydberg science has become increasingly interdisciplinary. It is now a rapidly progressing research area at the crossroads of atomic, optical, condensed matter physics, and quantum information science with a host of possible applications. Groundbreaking experiments demonstrate the promise of Rydberg systems not only for quantum information processing, but also for exploring the long-range nature of the strong Rydberg-Rydberg interaction that gives rise to many-particle correlations and excitation energy transfer (EET). After an introduction to Rydberg physics, I will focus on our theoretical research work on the quantum-coherent EET through "frozen" Rydberg gas clouds, in which the atoms have been slowed down almost to a full stop. For these systems, I reveal how the nature of EET can be controlled via the dipole blockade. This effect is known to lead to a proximity-dependent suppression of Rydberg excitations and the emergence of ordered excitation structures from a disordered gas. For weak blockade, we predict the transient localization of EET on small clusters of two or more atoms. For stronger blockade, however, EET will be significantly faster, since the excitations are efficiently migrated by delocalized states. I will illustrate this with our results on the spectral and eigenvector structure of the Rydberg gas ensemble. My talk is concluded by an outline of upcoming milestones and their challenges.

    @misc{scholak2014excitation,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:27:52 +0000},
      date-modified = {2015-03-02 16:34:42 +0000},
      howpublished = {invited seminar talk at the IQC in Waterloo, Canada},
      month = dec,
      status = {talk},
      title = {Excitation energy transfer in ultracold Rydberg gases},
      year = {2014}
    }
    
  2. ———, 2014, “Spectral Signatures of Excitation Transport in Ultracold Rydberg Gases” (poster presented at the workshop on Ultracold Rydberg Physics in Granada, Spain).
    View Download PDF.

    The spectral signatures of excitonic energy transfer in ultra-cold Rydberg gas clouds are studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong long-range dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are short-range. In the spectral level spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the degree of localization in the system is reduced. At the same time, the spectral statistics – in particular, the density of states and the nearest neighbor level spacing statistics – change their approximate agreement from the 1-stable Lévy to the Gaussian orthogonal random matrix ensemble. Deviations to random matrix statistics are identified to stem from corre- lations between atomic interactions that lead to an asymmetry of the spectral density and are also shown to have a profound influence on localization. We solve approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

    @misc{scholak2014spectralsignatures,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:35:22 +0000},
      date-modified = {2015-03-02 16:37:46 +0000},
      howpublished = {poster presented at the workshop on Ultracold Rydberg Physics in Granada, Spain},
      month = sep,
      status = {poster},
      title = {Spectral signatures of excitation transport in ultracold Rydberg gases},
      year = {2014}
    }
    
  3. ———, 2014, “Excitation Transport in Ultracold Rydberg Gases” (talk given at the YEA meeting and idea factory in Granada, Spain).
    View Download PDF.

    The spectral signatures of excitonic energy transfer in ultra-cold Rydberg gas clouds are studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong long-range dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are short-range. In the spectral level spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the degree of localization in the system is reduced. At the same time, the spectral statistics – in particular, the density of states and the nearest neighbor level spacing statistics – change their approximate agreement from the 1-stable Lévy to the Gaussian orthogonal random matrix ensemble. Deviations to random matrix statistics are identified to stem from corre- lations between atomic interactions that lead to an asymmetry of the spectral density and are also shown to have a profound influence on localization. We solve approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

    @misc{scholak2014excitationtransport,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:37:51 +0000},
      date-modified = {2015-03-02 16:39:20 +0000},
      howpublished = {talk given at the YEA meeting and idea factory in Granada, Spain},
      month = sep,
      status = {talk},
      title = {Excitation transport in ultracold Rydberg gases},
      year = {2014}
    }
    
  4. ———, 2013, “Delayed Choice Quantum Coherent Control” (poster presented at the 2013 Gordon Research Conference on Quantum Control of Light & Matter in Mount Holyoke College, USA).
    View Download PDF.
    @misc{scholak2013delayed,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:39:33 +0000},
      date-modified = {2015-03-02 16:40:22 +0000},
      howpublished = {poster presented at the 2013 Gordon Research Conference on Quantum Control of Light \& Matter in Mount Holyoke College, USA},
      month = jul,
      status = {poster},
      title = {Delayed choice quantum coherent control},
      year = {2013}
    }
    
  5. ———, 2011, “Energy Transport in Disordered Networks — From Transport Efficiency of Photosynthetic Light-Harvesting to Coherent Interactions in Frozen Rydberg Gases” (talk given at the workshop on Quantum Coherence In Energy Conversion in Freiburg, Germany).
    View Download PDF.
    @misc{scholak2011energy,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:43:55 +0000},
      date-modified = {2015-03-02 16:44:58 +0000},
      howpublished = {talk given at the workshop on Quantum Coherence In Energy Conversion in Freiburg, Germany},
      month = oct,
      status = {talk},
      title = {Energy transport in disordered networks --- From transport efficiency of photosynthetic light-harvesting to coherent interactions in frozen Rydberg gases},
      year = {2011}
    }
    
  6. ———, 2011, “On the Efficiency of Excitonic Energy Transport” (talk given at the 2011 Conference on Quantum Information & Quantum Control, Toronto, Canada).
    View Download PDF.

    What is the role of quantum coherence for the mechanisms underlying efficient energy transport though photosynthetic light-harvesting complexes? To explore this question, we conduct a large-scale statistical survey of excitation transport in ensembles of spatially disordered, finitely sized molecular networks with dipolar interactions in the presence of tunable dephasing noise, and we compare the efficiency of noise-assisted transport with that achievable by means of constructive quantum interference. In contrast to the common presumption that coherent effects generally lead to localization and thus to suppression of transport, we prove the existence of certain rare optimal molecular configurations that mediate highly efficient coherent excitation transport. Although dephasing noise – which gradually destroys interference and thereby gives rise to essentially classical transport – enhances the efficiency of most configurations in our statistical ensemble, the detected optimal configurations yield systematically higher transport efficiencies and attain the maximum efficiency in the absence of noise. These insights – combined with recent experimental demonstrations of long-lived coherence in certain light-harvesting structures – provide a strong hint that nature takes advantage of quantum mechanical coherent dynamics in order to enhance the efficiency of principal tasks.

    @misc{scholak2011ontheefficiencyfields,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 18:01:29 +0000},
      date-modified = {2015-03-02 18:03:30 +0000},
      howpublished = {talk given at the 2011 Conference on Quantum Information \& Quantum Control, Toronto, Canada},
      month = aug,
      status = {talk},
      title = {On the efficiency of excitonic energy transport},
      year = {2011}
    }
    
  7. ———, 2011, “On the Efficiency of Excitonic Energy Transport” (poster presented at the 2011 Gordon Research Conference on Quantum Control of Light & Matter — Mount Holyoke College).
    View Download PDF.
    @misc{scholak2011ontheefficiency,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:46:31 +0000},
      date-modified = {2015-03-02 16:47:36 +0000},
      howpublished = {poster presented at the 2011 Gordon Research Conference on Quantum Control of Light \& Matter --- Mount Holyoke College},
      month = jul,
      status = {poster},
      title = {On the efficiency of excitonic energy transport},
      year = {2011}
    }
    
  8. ———, 2011, “Optimal Molecular Networks for Excitonic Energy Transport” (talk given at the 2011 DPG Spring Meeting in Dresden, Germany).
    View Download PDF.

    Our study of coherent excitation transfer in finitely sized disordered molecular networks reveals certain optimal conformations that feature fast and perfectly efficient transport of energy – solely by means of constructive quantum interference. The properties and mechanics of these remarkable conformations are the subject of this talk. Our insights may help to better understand the efficient energy transfer in photosynthetic light-harvesting complexes.

    @misc{scholak2011optimaldresden,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:47:44 +0000},
      date-modified = {2015-03-02 16:50:53 +0000},
      howpublished = {talk given at the 2011 DPG Spring Meeting in Dresden, Germany},
      month = mar,
      status = {talk},
      title = {Optimal molecular networks for excitonic energy transport},
      year = {2011}
    }
    
  9. ———, 2011, “Optimal Molecular Networks for Excitonic Energy Transport” (talk given at the workshop on Dynamical control of quantum correlations in Heidelberg, Germany).
    View Download PDF.
    @misc{scholak2011optimalheidelberg,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:49:28 +0000},
      date-modified = {2015-03-02 16:50:45 +0000},
      howpublished = {talk given at the workshop on Dynamical control of quantum correlations in Heidelberg, Germany},
      month = jan,
      status = {talk},
      title = {Optimal molecular networks for excitonic energy transport},
      year = {2011}
    }
    
  10. ———, 2010, “Entanglement-Enhanced Energy Transport” (talk given at the conference on “New Perspectives In Quantum Statistics And Correlations” at the Akademie der Wissenschaften in Heidelberg, Germany).
    View Download PDF.
    @misc{scholak2010entanglementheidelberg,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:52:35 +0000},
      date-modified = {2015-03-02 16:54:11 +0000},
      howpublished = {talk given at the conference on ``New Perspectives In Quantum Statistics And Correlations'' at the Akademie der Wissenschaften in Heidelberg, Germany},
      month = mar,
      status = {talk},
      title = {Entanglement-enhanced energy transport},
      year = {2010}
    }
    
  11. ———, 2010, “Entanglement-Enhanced Energy Transport” (talk given at the 2010 DPG Spring Meeting in Hannover, Germany).
    View Download PDF.

    In many areas of physics we witness dramatic differences between classical and quantum transport. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the environment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional efficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such efficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal coherent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex.

    @misc{scholak2010entanglementhannover,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:51:03 +0000},
      date-modified = {2015-03-02 16:54:18 +0000},
      howpublished = {talk given at the 2010 DPG Spring Meeting in Hannover, Germany},
      month = mar,
      status = {talk},
      title = {Entanglement-enhanced energy transport},
      year = {2010}
    }
    
  12. ———, 2010, “Entanglement-Enhanced Efficient Energy Transport” (talk given at the 31th EAS (Energiereiche Atomare Stöße) meeting in Riezlern, Austria).
    View Download PDF.

    In many areas of physics we witness dramatic differences between classical and quantum transport. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the environment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional efficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such efficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal coherent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex.

    @misc{scholak2010entanglementriezlern,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:59:23 +0000},
      date-modified = {2015-03-02 17:09:29 +0000},
      howpublished = {talk given at the 31th EAS (Energiereiche Atomare Stöße) meeting in Riezlern, Austria},
      month = feb,
      status = {talk},
      title = {Entanglement-enhanced efficient energy transport},
      year = {2010}
    }
    
  13. ———, 2009, “Exciton Transport in Ordered and Disordered Samples of Cold Rydberg Atoms” (talk given at the 2009 DPG Spring Meeting in Hamburg, Germany).
    View Download PDF.

    We study coherent dipolar energy transfer between resonant levels of Rydberg atoms. We determine the transport properties by examining the spectral structure and the associated eigenfunctions. To highlight the impact of disorder on the Rydberg exciton transport, we introduce a disorder parameter allowing us to switch continuously from an ordered to a completely disordered sample of atoms. Special attention is dedicated to the transition from diffusive to non-diffusive transport, as well as to the metamorphosis of the nearest-neighbor level spacing distribution from Wigner to Poisson.

    @misc{scholak2009excitonhamburg,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 18:17:33 +0000},
      date-modified = {2015-03-02 18:18:28 +0000},
      howpublished = {talk given at the 2009 DPG Spring Meeting in Hamburg, Germany},
      month = mar,
      status = {talk},
      title = {Exciton transport in ordered and disordered samples of cold Rydberg atoms},
      year = {2009}
    }
    
  14. ———, 2009, “Exciton Transport in Ordered and Disordered Samples of Cold Rydberg Atoms” (talk given at the 30th EAS (Energiereiche Atomare Stöße) meeting in Riezlern, Austria).
    View Download PDF.

    We study coherent dipolar energy transfer between resonant levels of Rydberg atoms. We determine the transport properties by examining the spectral structure and the associated eigenfunctions. To highlight the impact of disorder on the Rydberg exciton transport, we introduce a disorder parameter allowing us to switch continuously from an ordered to a completely disordered sample of atoms. Special attention is dedicated to the transition from diffusive to non-diffusive transport, as well as to the metamorphosis of the nearest-neighbor level spacing distribution from Wigner to Poisson.

    @misc{scholak2009exciton,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 16:54:28 +0000},
      date-modified = {2015-03-02 17:04:09 +0000},
      howpublished = {talk given at the 30th EAS (Energiereiche Atomare Stöße) meeting in Riezlern, Austria},
      month = feb,
      status = {talk},
      title = {Exciton transport in ordered and disordered samples of cold Rydberg atoms},
      year = {2009}
    }
    
  15. ———, 2008, “Creating and Ascertaining Entanglement of Atoms by Photon Scattering” (poster presented at the 2008 DPG Spring Meeting in Darmstadt, Germany).
    View Download PDF.

    We study the light-scattering dynamics of two tightly trapped atoms with internal spin degrees of freedom. The aim is to manipulate populations and coherences by a selective tuning of photon field parameters like polarization. We are particularly interested in the preparation of entanglement and its subsequent witnessing by interaction with the driving laser field.

    @misc{scholak2008creating,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 17:15:04 +0000},
      date-modified = {2015-03-02 17:16:02 +0000},
      howpublished = {poster presented at the 2008 DPG Spring Meeting in Darmstadt, Germany},
      month = mar,
      status = {poster},
      title = {Creating and ascertaining entanglement of atoms by photon scattering},
      year = {2008}
    }
    
  16. ———, 2008, “Single-Particle Interference Can Witness Bipartite Entanglement” (talk given at the 2008 DPG Spring Meeting in Darmstadt).
    View Download PDF.

    We propose to realize entanglement witnesses in terms of the interference pattern of a single quantum probe. After giving a conceptional recipe, we discuss possible realizations both with electrons in mesoscopic Aharonov-Bohm rings and with photons in standard Young’s double-slit or coherent-backscattering interferometers.

    @misc{scholak2008singleparticle,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 17:16:47 +0000},
      date-modified = {2015-03-02 17:17:40 +0000},
      howpublished = {talk given at the 2008 DPG Spring Meeting in Darmstadt},
      month = mar,
      status = {talk},
      title = {Single-particle interference can witness bipartite entanglement},
      year = {2008}
    }
    
  17. ———, 2007, “Single-Probe Interference Can Witness Entanglement” (talk given at the 2007 YEP (Young European Physicists) Meetingin Frauenchiemsee, Germany).
    View Download PDF.

    We study the scattering of a single photon by two atoms whose spin-1/2 ground states are an entangled qubit pair. A lower bound on its concurrence can be obtained by measuring the visibility of the coherent-backscattering interference fringes in a suitable polarization configuration.

    @misc{scholak2007singleprobe,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 17:21:29 +0000},
      date-modified = {2015-03-02 17:26:04 +0000},
      howpublished = {talk given at the 2007 YEP (Young European Physicists) Meetingin Frauenchiemsee, Germany},
      month = sep,
      status = {talk},
      title = {Single-probe interference can witness entanglement},
      year = {2007}
    }
    
  18. ———, 2007, “Single-Probe Interference Can Witness Entanglement” (poster presented at the Bose-Einstein Condensates and Coherent Backscattering Workshop in Thurnau, Germany).
    View

    We study the scattering of a single photon by two atoms whose spin-1/2 ground states are an entangled qubit pair. A lower bound on its concurrence can be obtained by measuring the visibility of the coherent-backscattering interference fringes in a suitable polarization configuration.

    @misc{scholak2007singleprobethurnau,
      author = {Scholak, Torsten},
      date-added = {2015-03-02 17:29:48 +0000},
      date-modified = {2015-03-02 17:35:42 +0000},
      howpublished = {poster presented at the Bose-Einstein Condensates and Coherent Backscattering Workshop in Thurnau, Germany},
      month = sep,
      status = {talk},
      title = {Single-probe interference can witness entanglement},
      year = {2007}
    }