DRSTP ANNUAL REPORTS|
2013 - 2017 (to be published)
Previous reports: 2012 - 2011 - 2010 - 2009 - 2008 - 2007 - 2006 - 2005
The DRSTP Annual Report provides an overview of the educational and research activities. The Annual Report also presents two research highlights written by staff members of the Research School. In addition, it offers information, such as a list of the participating staff, of the PhD students, a comprehensive list of publications, as well as other relevant statistics.
We would like to thank all of those who contributed to the Research School during the past years.
Prof. H. Stoof
Prof. E.P. Verlinde
Chair Governing Board
Two highlights from the DRSTP Annual Report 2013
Black holes, space time and quantum entanglement
Contributed by Professor Erik Verlinde, University of Amsterdam
Quantum entanglement plays a key role in research into the quantum structure of spacetime and black holes. Entanglement means that the quantum characteristics of two parts the quantum system are strongly related to each other. Scientists measure the degree of entanglement by determining the value of the entanglement entropy. If the vacuum state of the spacetime is divided into two parts then the entanglement entropy of the spacetime is found to have a universal value. This value is equal to a quarter of the surface area of the separating wall. The existence of this quantum entanglement is an important condition for the continuity and regularity of spacetime.
This new insight has led to a heated discussion about the nature of the event horizon of a black hole. When a pair of particles arises from the vacuum near such an event horizon, one of the particles can fall into the black hole while the other escapes in the form of radiation. Through this Hawking radiation the entanglement entropy of the black hole seems to increase. At the same time the black hole loses energy, as a result of which the area of its event horizon decreases and hence it reduces its quantum information. In a recent article American researchers argue that the tension between the increasing entanglement on the one hand and the decreasing area of the event horizon on the other (and therefore reduced information) leads to the paradoxical conclusion that the event horizon is not a regular part of spacetime.
Researchers from the FOM programme 'A String Theoretic Approach to Quantum Matter and Cosmology' have played an important role in these developments. In a series of articles (1, 2, 3, 4) the researchers have demonstrated that the entanglement between a black hole and the outside world can be used to reconstruct the interior of the black hole, as a result of which the regular character of the event horizon is retained.
Furthermore, in recent work the entanglement of a random area within the anti-de Sitter space has been calculated, and for the first time it was explicitly confirmed that this is the same as one quarter of the surface area. Both results are an important step forwards in the research into the quantum structure of spacetime.
Figure 3.1: What happens with Schrödinger's cat if this jumps into a black hole? The current scientific discussion about quantum entanglement at the event horizon of black holes can be viewed as a continuation of older familiar discussions, such as the EPR paradox and the quantum measurement problem ('Schrödinger's cat') in the context of quantum gravitation.
Interaction induced chiral Px + i Py superfluid in optical lattices
Contributed by Professor Cristiane Morais Smith, Utrecht University
The experimental realization of Bose-Einstein condensation (BEC) in 1995 with ultracold quantum gases -- a state of matter that had been theoretically predicted since 1925 -- has opened a new path in quantum optics. This achievement was possible due to the development of new laser cooling techniques, which allowed us to reach the micro- and later the nano-Kelvin regime. Moreover, the possibility to construct optical lattices by superimposing counter-propagating laser light in one, two, or three dimensions has brought further impulse to the field.
By loading the optical lattices with ultracold atoms, one obtains a tunable and accessible quantum system that can serve as a quantum simulator of more complex and unaccessible condensed-matter systems, thus realizing the visionary idea of Feynman. In particular, ultracold atoms in optical lattices are a paradigm for the realization of strongly correlated models relevant for understanding, for example, high-temperature superconductors. The lattice geometry and dimension can be designed at will, and the lattices are usually free of defects, although the latter can also be introduced in a controlled way. Moreover, the atoms loaded into the lattices can be fermions, bosons, or a mixture of both, and their interactions can be tuned from attractive to repulsive by using Feshbach resonances.
Several interesting properties of ultracold atoms have been understood by now, such as Bloch oscillations, the quantum phase transition from a bosonic Mott-insulator into a superfluid phase, the crossover from a BEC to a BCS phase, as well as the establishment of a fermionic Mott insulator, to cite just a few (see Refs. - for a review). However, most of the effort was concentrated on studying ground-state equilibrium properties.
Ground-state Bose-Einstein condensates are s-wave like, and hence positive definite. If the cold-atom system should act as a quantum simulator for unconventional p- or d-wave superconductors, more complex order parameters are required, and one must achieve BEC in higher orbitals.
The first trials to generate higher-band Bose-Einstein condensates have failed because the lifetime of the excited states was too short to allow for condensation. Recently, this problem has been overcome in the group of A. Hemmerich in Hamburg, by using a bipartite optical lattice [4, 5]. In this case, the 2D optical lattice consists of a checkerboard of shallow and deep wells, and the overall first excited state is actually the ground state for the shallow wells. This trick increases the lifetime of this state considerably and allows for the observation of p-band Bose-Einstein condensates. The first observation of the phenomenon has hinted at the possibility of the creation of a Px + i Py phase, which spontaneously breaks time-reversal symmetry and exhibits staggered currents . However, other possible phases, such as an incoherent mixture of Px and Py condensates, a coherent mixture, or phase separation, could not be ruled out because they would lead to the same experimental output.
The next step was then to include interactions to lift the degeneracy among these different ground states, and to introduce some anisotropies in the 2D lattice, to reach a finer control of the experimental system that could permit to unequivocally determine whether the realized phase was indeed the long-sought time-reversal symmetry breaking one. In condensed matter, the search for a Px + i Py phase in unconventional superconductors has failed until now, with the exception of SrRu2, for which the problem is still open . These more refined experiments in bipartite optical lattices were performed in Hamburg, in the group of Andreas Hemmerich, and the theoretical calculations were performed in Utrecht, by Cristiane Morais Smith. The results obtained in the framework of a 3-band Hubbard model agree very well with the observations and confirm that indeed, a Px + i Py phase driven by interactions is favorable, because in this phase the on-site Hubbard repulsion is minimized . Staggered currents emerge in the system, and time-reversal symmetry is spontaneously broken.
Figure 3.2: In the center, a phase diagram obtained theoretically in the framework of the 3-band Hubbard model indicates the phases I and III, where striped phases occur (Px - Py and Px + Py, respectively). In the central region II, a time-reversal symmetry breaking phase sets in. The experimental data shows time-of-flight images, which detect the order in k-space
The experimental realization of bosonic order parameters with nodes, analogous to p- or d-wave superconductors, opens exciting perspectives for future research. The implementation of deeper potential wells should allow one to access a regime where Mott insulators with distinct orbital ordering is expected. In addition, if fermions are used instead of bosons, one could create new forms of topological matter. Cold atoms in higher bands are just in their infancy, but have already opened a fascinating arena where there should be many more surprises to come.
 I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
 M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De) and U. Sen, Adv. in Phys. 56, 243 (2007).
 I. Bloch, J. Dalibard, and S. Nascimbene, Nat. Phys. 8, 267 (2012).
 G. Wirth, M. Ölschläger, A. Hemmerich, Nat. Phys. 7, 147 (2011).
 M. Ölschläger, G. Wirth, T. Kock, and A. Hemmerich, Phys. Rev. Lett. 108, 075302 (2012).
 Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, and F. Lichtenberg, Nature 372, 532 (1994); Y. Maeno, S. Kittaka, T. Nomura, S. Yonezawa, K. Ishida, J. Phys. Soc. Jpn. 81, 011009 (2012).
 M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith, and A. Hemmerich, New Journal of Physics 15, 083041 (2013). This paper was selected as a highlight of the Condensed Matter Journal Club in September 2013.
Last update: 13-01-2018, 10.49