Projects

Our research focuses on the design and functionality of mesoscopic solid state devices, their transport and noise properties, and their potential use in quantum information theory. We have suggested specific mesoscopic structures allowing for the study of basic quantum phenomena such as entanglement and wave function collapse. We have shown how to test for the non-​classical correlations through the use of a Bell inequality test based on current-​current cross correlators. We have suggested a design for a solid-​state entangler using a normal-​metal--superconductor junction injecting entangled pairs of quasi-​particles into a normal-​metal lead. Here, the quantum correlated two-​particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin-​ and orbital degrees of freedom. In an alternative setup with a normal-​metal device in a fork geometry the entanglement is produced via postselection in the measurement process (non-​interacting limit). Both, the dc and pulsed production of entangled pairs has been analyzed. In our recent work we have unveiled the relation between the fidelity (stability under perturbation) of a quantum system and the generating function of full counting statistics and have analyzed the possibility of their measurement using a quantum bit as a measurement device, including an optimized algorithm that describes how to measure the generating function using qubits. This result has lead us to devise a new algorithm for quantum counting that resembles Kitaev's phase estimation algorithm. In an experimental work using a qubit sensor, we compared the efficiency of the Kitaev and the quantum Fourier transform algorithms in quantum measurement. Finally, we have pursued some new ideas in quantum thermodynamics, proposing a quantum Maxwell demon that allows to run a quantum engine without producing waste heat, consuming purity instead.

Literature:
[1] G.B. Lesovik, F. Hassler, and G. Blatter, Using Qubits for Measuring Fidelity in Mesoscopic Systems, Phys. Rev. Lett. 96, 106801 (2006).
[2] M.V. Suslov, G.B. Lesovik, and G. Blatter, Quantum abacus for counting and factorizing numbers, Phys. Rev. A 83, 052317 (2011).
[3] A.V. Lebedev, G.B. Lesovik, and G. Blatter, Optimal non-invasive measurement of Full Counting Statistics by a single qubit, Phys. Rev. B 93, 115140 (2016).
[4] A.V. Lebedev, D. Oehri, G.B. Lesovik, and G. Blatter, Trading coherence and entropy by a quantum Maxwell demon, Phys. Rev. A 94, 052133 (2016).
[5] S. Danilin, A.V. Lebedev, A. Vepsälaäinen, G.B. Lesovik, G. Blatter, and G.S. Paraoanu, Quantum-enhanced magnetometry by phase estimation algorithms with a single artificial atom, npj Quantum Information 4, 29 (2018).

In a quantum computer the information is stored in arrays of quantum two-​level systems; these qubits generalize the notion of the well known bit in a classical computer. Execution of a quantum algorithm involves quantum gates, unitary operations rotating individual qubits and entangling them pairwise. Superconducting solid-​state qubits are promising candidates for the hardware implementation of scalable quantum information processors; quantum fluctuations are introduced through small-​capacitance Josephson junctions and the frustrating drive is introduced through a gate potential (charge-​qubit) or a magnetic flux (phase-​ or flux qubit). We have proposed various designs for the solid-​state implementation of qubits based on superconducting structures: We have shown how to build a quiet qubit using superconductors with d-​wave symmetry and have suggested a first design for topological computing based on a quantum Josephson junction array. In our most recent proposal we suggest to exploit the symmetry properties of a tetrahedral structure (four equal islands with pairwise symmetric coupling) in order to emulate a spin-​1/2 system in zero field with quadratic noise stability and generically large quantum fluctuations, an ideal starting point for a qubit. We have investigated a generic decoherence channel in superconducting qubits which is due to phonon radiation in the Josephson junctions arising from the piezoelectric coupling between the dynamic superconducting phase and the junction insulator. Combining our interests in qubits and quantum information, we have tested the performance of both qubit and qutrit devices as magnetic-field sensors using new measurement algorithms.

Literature:
[1] L.B. Ioffe, V.B. Geshkenbein, M.V. Feigel’man, A. L. Fauchere, and G. Blatter, Environmentally Decoupled SDS-Wave Josephson Junctions for Quantum Computing, Nature 398, 679 (1999).
[2] L.B. Ioffe, M.V. Feigel'man, A. Ioselevich, D. Ivanov, M. Troyer, and G. Blatter,Topologically protected quantum bits from Josephson junction arrays, Nature 415, 503 (2002).
[3] M.V. Feigel'man, L.B. Ioffe, V.B. Geshkenbein, P. Dayal, and G. Blatter, Superconducting Tetrahedral Qubits, Phys. Rev. Lett. 92, 098301 (2004).

Cooling atoms to the nano-​Kelvin regime allows for the realization and study of new thermodynamic phase transitions and their associated phases, with an interesting synergy emerging between the fields of quantum atom optics and condensed matter physics. Among the topics of interest are the study of the superfluid to Mott-​insulator phase transition appearing in cold bosonic systems subject to an optical lattice, the realization of a BCS-​type condensate in a fermionic system, the investigation of effects due to disorder and reduced dimensionality, proposals for novel quantum phases and associated transitions, and, most recently, the engineering of systems with topological properties. In our work, we have studied Bloch oscillations in confined atomic gases, the instability towards the Mott insulator appearing in one-​dimensional confined Bose gases, the appearance of a supersolid phase in two-​dimensional mixed Fermion-​Boson systems and its instability towards phase separation. We have investigated the dynamic properties of the Bose-​Hubbard model in the vicinity of the Mott-​insulator to superfluid phase transition and have predicted both phase (Goldstone) and amplitude (Higgs) type excitations that have been later observed in experiments. Finally, we have studied competing orders (triangular, square, solitonic stripes) in systems with long-range interactions, specifically two-dimensional dipolar gases trapped in an optical lattice of variable strength.

Literature:
[1] H.P. Büchler, G. Blatter, and W. Zwerger, Commensurate-incommensurate transition of cold atoms in an optical lattice, Phys. Rev. Lett. 90, 130401 (2003).
[2] H.P. Büchler and G. Blatter, Supersolid versus phase separation in atomic Bose-Fermi mixtures, Phys. Rev. Lett. 91, 130404 (2003).
[3] S.D. Huber, E. Altman, H.P. Büchler, and G. Blatter, Dynamical properties of ultra-cold bosons in an optical lattice, Phys. Rev. B 75, 085106 (2007).
[4] S.D. Huber, B. Theiler, E. Altman, and G. Blatter, The Amplitude Mode in the Quantum Phase Model, Phys. Rev. Lett. 100, 050404 (2008).

Photonic modes trapped in non-linear cavities have established themselves as a new platform in quantum engineering. These systems are inherently non-equilibrium and require to included pumping and dissipation in their description. Paradigmatic models are the Jaynes-Cumming-Hubbard model (with a two-level system serving as the non-linear element) or the Bose-Hubbard model (with a Kerr non-linearity). We have studied the equilibrium phase diagram and dynamical properties of the polaritonic Jaynes-Cummings-Hubbard model to find the equivalent behaviour as in the corresponding atomic system (lobes, Goldstone and Higgs modes). Going to the driven-dissipative setting, we have predicted a van der Waals type gas-liquid transition in the photonic Bose-Hubbard model. Introducing frustration through interference (in a Lieb lattice), the resulting flat bands boost the interaction and generate an incompressible photonic gas with short-range density order—the latter can be pushed to exhibit quasi-long range order upon properly tuned pumping.  

Literature:
[1] S. Schmidt and G. Blatter, Strong coupling theory for the Jaynes-Cummings-Hubbard model, Phys. Rev. Lett. 103, 086403 (2009).
[2] S. Schmidt and G. Blatter,Excitations of Strongly Correlated Lattice Polaritons, Phys. Rev. Lett. 104, 216402 (2010).
[3] F. Nissen, S. Schmidt, M. Biondi, G. Blatter, H.E. Türeci, and J. Keelin,Nonequilibrium Dynamics of Coupled Qubit-Cavity Arrays, Phys. Rev. Lett. 108, 233603 (2012).
[4] M. Biondi, E.P.L. van Nieuwenburg, G. Blatter, S.D. Huber, and S. Schmidt, Incompressible polaritons in a flat band, Phys. Rev. Lett. 115, 143601 (2015).
[5] M. Biondi, G. Blatter, H.E. Türeci, and S. Schmidt, Nonequilibrium gas-liquid transition in the driven-dissipative photonic lattice, Phys. Rev. A 96, 043809 (2017).

In recent years, graphene and other two-dimensional (2D) so-called van der Waals materials have developed into versatile material engineering platforms. Deposition and stacking techniques at small angles produce moiré patterns that can be used in band engineering and in the manipulation of the topological properties that are inherent in the Dirac cones of the original 2D material. Such a new type of material engineering allows for system tuning with the prospect for novel phenomena, the most spectacular so-far being the discovery of superconductivity at the magic angle in twisted bilayer graphene. When subjecting graphene to a periodic substrate potential, e.g., hexa-Boron Nitrite (hBN), the structure of backfolded bands depends on the symmetry properties of the substrate potential, with inversion--anti-symmetric scattering components potentially inducing topological minibands: in our work [1], we have mapped out the various possibilities in constructing topological bands with interesting Berry curvature maps. In another work [2] on twisted bilayer graphene, we combine twist-angle tuning and electric interlayer bias to generate tunable magnetism: our small twist-angle produces flat bands away from charge neutrality that are very susceptible to interlayer bias. While the flat band in combination with Coulomb interaction produces the desired magnetism, electric tuning generates valley flux that disperses these bands and thereby quenches the magnetic order.  

Literature:
[1] T. M. R. Wolf, O. Zilberberg, I. Levkivskyi, G. Blatter, Substrate-induced topological minibands in graphene, Phys. Rev. B 98, 125408 (2018).
[2] T. M. R. Wolf, J. L. Lado, G. Blatter, O. Zilberberg, Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene, Phys. Rev. Lett. 123, 096802 (2019).
 

Disordered systems exhibit interesting thermodynamic and nonequilibrium properties relevant to the functionality of magnetic and superconducting systems. We have studied dirty elastic manifolds in the context of vortex matter physics and the properties of various types of glasses, such as spin, structural, and gauge glasses. Questions of interest are the basic understanding of the glass phase (droplet picture versus replica symmetry breaking, structural properties of the vortex glass phase), the thermodynamic properties of the glass transition (e.g., scaling laws and universality, entropy crisis in structural glasses), and the influence of thermal and quantum fluctuations on the response properties of a glass (creep dynamics). We make use of various analytical (replica approach, instantons, functional renormalization group) and numerical techniques (parallel tempering Monte Carlo and cluster algorithms). Recent interest is in the analytical description of the glass transition in a model liquid, various properties of the random directed polymer problem including an exact solution via the combination of replica and Bethe Ansatz techniques, and, most recently, the distribution function of velocities in the Burgers equation.

Literature:
[1] D.A. Gorokhov, D.S. Fisher, and G. Blatter, Quantum Collective Creep: a Quasiclassical Langevin Equation Approach, Phys. Rev. B 66, 214203 (2002).
[2] V.S. Dotsenko, L.B. Ioffe, V.B. Geshkenbein, S.E. Korshunov and G. Blatter, Joint free energy distribution in the random directed polymer problem, Phys. Rev. Lett. 100, 050601 (2008).
[3] V.S. Dotsenko, V.B. Geshkenbein, D.A. Gorokhov, and G. Blatter, Free-energy distribution functions for the randomly forced directed polymer, Phys. Rev. B 82, 174201 (2010).
[4] S.E. Korshunov, V.B. Geshkenbein, and G. Blatter, Finite-temperature perturbation theory for the random directed polymer problem, JETP 117, 570 (2013).

 

With the discovery of high temperature superconductivity in cuprate materials, both microscopic and phenomenological descriptions of these superconductors had to be rebuilt. While the quest for a new microscopic theory is still ongoing, the development of a new Vortex Matter phenomenology has been hugely successful. With our work, we have contributed to the development of this new Vortex Matter phenomenology that applies to anisotropic or layered, disordered, and strongly fluctuating type II superconductors. Particular research topics studied in the past are the theory of classical and quantum creep of vortices, classical and quantum melting, the decoupling transition in layered systems, the anisotropic scaling theory, quantum depinning, weak collective pinning and functional renormalization group theory, the effects of correlated disorder, vortex dynamics, Hall effect, vortex charge, the structure of vortices in d-​wave superconductors, and the electronic structure and dissipation in moderately clean superconductors. Further work, has focused on the zero-​field superconductor to normal transition in bi- and multilayer systems and the density functional theory of bulk and surface melting of the pancake-​vortex lattice in layered superconductors. In recent years, we have set out to develop the strong pinning theory as a new paradigm for vortex pinning. Our studies include the description and phase diagram for the weak-to-strong pinning crossover, the determination of critical currents, the (excess) current-voltage characteristic typical of the strong pinning scenario, thermal creep, and the inclusion of correlations between individual defects at the weak-to-strong pinning transition.

 

Literature:
[1] G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Vortices in high temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994).
[2] G. Blatter and V.B. Geshkenbein, Vortex Matter, The Physics of Superconductors, Vol. 1, Conventional and High-​Tc superconductors, eds. K.H. Bennemann and J.B. Ketterson (Springer, Berlin, 2008), pp 495.
[3] G. Blatter, V.B. Geshkenbein, and J.A.G. Koopmann, Weak- to Strong Pinning Crossover, Phys. Rev. Lett. 92, 067009 (2004).
[4] A. Thomann, V. Geshkenbein, and G. Blatter, Dynamical Aspects of Strong Pinning of Magnetic Vortices in Type-II Superconductors, Phys. Rev. Lett. 108, 217001 (2012).
[5] R. Willa, V.B. Geshkenbein, R. Prozorov, and G. Blatter, Campbell response in type-II superconductors under strong pinning conditions, Phys. Rev. Lett. 115, 207001 (2015).
[6] M. Buchacek, R. Willa, V.B. Geshkenbein, and G. Blatter, Persistence of pinning and creep beyond critical drive within the strong pinning paradigm, Phys. Rev. B 98, 094510 (2018).

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