Vladimir M. Stojanović, Dr.
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Education
 BSc : University of Belgrade
 PhD : Carnegie Mellon University, Pittsburgh
Research Interests
 Quantum simulation of manybody systems and phases
 Quantum operator control and solidstate quantum computation
 Stronglycoupled electronphonon systems and smallpolaron models
 Superfluidity and related coherence phenomena with ultracold atomic gases
 Electronic properties of organic semiconductors and graphenebased nanostructures
Publications
Show all abstracts.1.  Analog superconducting quantum simulator for Holstein polarons 
F. Mei, V. M. Stojanović, I. Siddiqi, and L. Tian. arXiv:1307.0906
We propose an analog quantum simulator for the Holstein molecularcrystal
model based on a dispersive superconducting circuit QED system composed of
transmon qubits and microwave resonators. By varying the circuit parameters,
one can readily access both the adiabatic and the antiadiabatic regimes of
this model, and realize the coupling strengths required for smallpolaron
formation. We present a pumping scheme for preparing smallpolaron states of
arbitrary quasimomentum within time scales much shorter than the qubit
decoherence time. The ground state of the system is characterized by anomalous
amplitude fluctuation and measurementbased momentum squeezing in the resonator
modes.
 
2.  Strategy for implementing stabilizerbased codes on solidstate qubits 
T. Tanamoto, V. M. Stojanović, C. Bruder, and D. Becker. Phys. Rev. A 87, 052305 (2013)
We present a method for implementing stabilizerbased codes with encoding
schemes of the operator quantum error correction paradigm, e.g., the "standard"
fivequbit and CSS codes, on solidstate qubits with Ising or XYtype
interactions. Using pulse sequences, we show how to induce the effective
dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of
stabilizer operators for a given code. Within this approach, the encoded states
(ground states of the stabilizer Hamiltonian) can be prepared without
measurements and preserved against both the time evolution governed by the
original qubit Hamiltonian, and energynonconserving errors caused by the
environment.
 
3.  Quantum simulation of smallpolaron formation with trapped ions 
V. M. Stojanović, T. Shi, C. Bruder, and J. I. Cirac. Phys. Rev. Lett. 109, 250501 (2012)
We propose an analog quantum simulation of smallpolaron physics using a onedimensional system of trapped ions acted upon by offresonant standing waves. This system, envisioned as an array of microtraps, in the singleexcitation case allows the realization of the antiadiabatic regime of the Holstein model. We show that the strong excitationphonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonondressed excitation.
 
4.  Superfluid drag of twospecies BoseEinstein condensates in optical lattices 
P. P. Hofer, C. Bruder, and V. M. Stojanović. Phys. Rev. A 86, 033627 (2012)
We study twospecies BoseEinstein condensates in quasi twodimensional
optical lattices of varying geometry and potential depth. Based on the
numerically exact Bloch and Wannier functions obtained using the planewave
expansion method, we quantify the drag (entrainment coupling) between the
condensate components. This drag originates from the (short range)
interspecies interaction and increases with the kinetic energy. As a result of
the interplay between interaction and kinetic energy effects, the
superfluiddrag coefficient shows a nonmonotonic dependence on the lattice
depth. To make contact with future experiments, we quantitatively investigate
the drag for mass ratios corresponding to relevant atomic species.
 
5.  Preserving universal resources for oneway quantum computing 
T. Tanamoto, D. Becker, V. M. Stojanović, and C. Bruder. Phys. Rev. A 86, 032327 (2012)
The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do
not have ground states that are the graph states needed in measurementbased
quantum computation. Various highlyentangled manybody states have been
suggested as a universal resource for this type of computation, however, it is
not easy to preserve these states in solidstate systems due to their short
coherence times. Here we propose a scheme for generating a Hamiltonian that has
a cluster state as ground state. Our approach employs a series of pulse
sequences inspired by established NMR techniques and holds promise for
applications in many areas of quantum information processing.
 
6.  Electronphonon coupling in crystalline organic semiconductors: Microscopic evidence for nonpolaronic charge carriers 
N. Vukmirović, C. Bruder, and V. M. Stojanović. Phys. Rev. Lett. 109, 126407 (2012)
We consider electron(hole)phonon coupling in crystalline organic
semiconductors, using naphthalene for our case study. Employing a
firstprinciples approach, we compute the changes in the selfconsistent
KohnSham potential corresponding to different phonon modes and go on to obtain
the carrierphonon coupling matrix elements (vertex functions). We then
evaluate perturbatively the quasiparticle spectral residues for electrons at
the bottom of the lowestunoccupied (LUMO) and holes at the top of the
highestoccupied (HOMO) band, respectively obtaining $Z_{\textrm{e}}\approx
0.74$ and $Z_{\textrm{h}}\approx 0.78$. Along with the widely accepted notion
that the carrierphonon coupling strengths in polyacenes decrease with
increasing molecular size, our results provide a strong microscopic evidence
for the previously conjectured nonpolaronic nature of bandlike carriers in
these systems.
 
7.  Quantumcontrol approach to realizing a Toffoli gate in circuit QED 
V. M. Stojanović, A. Fedorov, A. Wallraff, and C. Bruder. Phys. Rev. B 85, 054504 (2012)
We study the realization of a Toffoli gate with superconducting qubits in a circuitQED setup using quantumcontrol methods. Starting with optimized piecewiseconstant control fields acting on all qubits and typical strengths of XYtype coupling between the qubits, we demonstrate that the optimal gate fidelities are affected only slightly by a "lowpass" filtering of these fields with the typical cutoff frequencies of microwave driving. Restricting ourselves to the range of controlfield amplitudes for which the leakage to the noncomputational states of a physical qubit is heavily suppressed, we theoretically predict that in the absence of decoherence and leakage, within 75 ns a Toffoli gate can be realized with intrinsic fidelities higher than 90%, while fidelities above 99% can be reached in about 140 ns.
 
8.  Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit 
R. Heule, C. Bruder, D. Burgarth, and V. M. Stojanović. ( Selected Highlight Paper ; Featured in Europhysics News ) Eur. Phys. J. D 63, 41 (2011)
We investigate anisotropic $XXZ$ Heisenberg spin1/2 chains with control
fields acting on one of the end spins, with the aim of exploring local quantum
control in arrays of interacting qubits. In this work, which uses a recent
Liealgebraic result on the local controllability of spin chains with
"alwayson" interactions, we determine piecewiseconstant control pulses
corresponding to optimal fidelities for quantum gates such as spinflip (NOT),
controlledNOT (CNOT), and squarerootofSWAP ($\sqrt{\textrm{SWAP}}$). We
find the minimal times for realizing different gates depending on the
anisotropy parameter $\Delta$ of the model, showing that the shortest among
these gate times are achieved for particular values of $\Delta$ larger than
unity. To study the influence of possible imperfections in anticipated
experimental realizations of qubit arrays, we analyze the robustness of the
obtained results for the gate fidelities to random variations in the
controlfield amplitudes and finite rise time of the pulses. Finally, we
discuss the implications of our study for superconducting chargequbit arrays.
 
9.  Local quantum control of Heisenberg spin chains 
R. Heule, C. Bruder, D. Burgarth, and V. M. Stojanović. Phys. Rev. A 82, 052333 (2010)
Motivated by some recent results of quantum control theory, we discuss the
feasibility of local operator control in arrays of interacting qubits modeled
as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at
finding piecewiseconstant control pulses that lead to optimal fidelities for a
chosen set of quantum gates. We analyze the robustness of the obtained results
for the gate fidelities to random errors in the control fields, finding that
with faster switching between piecewiseconstant controls the system is less
susceptible to these errors. The observed behavior falls into a generic class
of physical phenomena that are related to a competition between resonance and
relaxationtype behavior, exemplified by motional narrowing in NMR experiments.
Finally, we discuss how the obtained optimal gate fidelities are altered when
the corresponding rapidlyvarying piecewiseconstant control fields are
smoothened through spectral filtering.
 
10.  Polaronic signatures and spectral properties of graphene antidot lattices 
V. M. Stojanović, N. Vukmirović, and C. Bruder. Phys. Rev. B 82, 165410 (2010)
We explore the consequences of electronphonon (eph) coupling in graphene antidot lattices (graphene nanomeshes), i.e., triangular superlattices of circular holes (antidots) in a graphene sheet. They display a direct band gap whose magnitude can be controlled via the antidot size and density. The relevant coupling mechanism in these semiconducting counterparts of graphene is the modulation of the nearestneighbor electronic hopping integrals due to lattice distortions (Peierlstype eph coupling). We compute the full momentum dependence of the eph vertex functions for a number of representative antidot lattices. Based on the latter, we discuss the origins of the previously found large conductionband quasiparticle spectral weight due to eph coupling. In addition, we study the nonzeromomentum quasiparticle properties with the aid of the selfconsistent Born approximation, yielding results that can be compared with future angleresolved photoemission spectroscopy measurements. Our principal finding is a significant eph mass enhancement, an indication of polaronic behavior. This can be ascribed to the peculiar momentum dependence of the eph interaction in these narrowband systems, which favors small phonon momentum scattering. We also discuss implications of our study for recently fabricated largeperiod graphene antidot lattices.
 
11.  Electronphonon coupling in graphene antidot lattices: An indication of polaronic behavior 
N. Vukmirović, V. M. Stojanović, and M. Vanević. ( Selected Editors' Suggestion ) Phys. Rev. B 81, 041408(R) (2010)
We study graphene antidot lattices  superlattices of perforations (antidots) in a graphene sheet  using a model that accounts for the phononmodulation of the πelectron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semiempirical interatomic potentials. Based on the adopted model and the obtained phonon modes, we quantify the nature of chargecarriers in the system by computing the quasiparticle spectral weight due to the electronphonon interaction for an excess electron in the conduction band. We show that the phononinduced renormalization is much stronger than in graphene, with the effective electron masses exhibiting an interesting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of electronic transport in graphene antidot lattices.
 
12.  Character of electronic states in graphene antidot lattices: Flat bands and spatial localization 
M. Vanević, V. M. Stojanović, and M. Kindermann. Phys. Rev. B 80, 045410 (2009)
Graphene antidot lattices have recently been proposed as a new breed of graphenebased superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasiflat bands at low energies. We predict the realspace electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied lowenergy localized states compete with states induced by the superlatticescale defects in this system, which have been proposed as hosts for electronspin qubits. Furthermore, we suggest that local moments formed in these midgap zeroenergy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.
 
13.  Quantumentanglement aspects of polaron systems 
V. M. Stojanović and M. Vanević. ( Selected Editors' Suggestion ) Phys. Rev. B 78, 214301 (2008)
We describe quantum entanglement inherent to the polaron ground states of coupled electronphonon (or, more generally, particlephonon) systems based on a model comprising both local (Holsteintype) and nonlocal (Peierlstype) couplings. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particlephonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particlephonon entanglement. In particular, we find a compelling evidence for the existence of a nonanalyticity in the entanglement entropies with respect to the Peierlscoupling strength. The occurrence of such nonanalyticity  not accompanied by an actual quantum phase transition  reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantumdissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the selftrapped region where the smallpolaron states are nearly maximally mixed.
 
14.  Incommensurate superfluidity of bosons in a doublewell optical lattice 
V. M. Stojanović, C. Wu, W. V. Liu, and S. Das Sarma. Phys. Rev. Lett. 101, 125301 (2008)
We study bosons in the first excited Bloch band of a doublewell optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases, the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearestneighbor tunneling time scales, in contrast with that of a simple singlewell lattice. In addition, for sufficiently small lattice depths, the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the timereversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.
 
15.  Unconventional interaction between vortices in a polarized Fermi gas 
V. M. Stojanović, W. V. Liu, and Y. B. Kim. Ann. Phys. ( N.Y. ) 323, 989 (2008)
Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular BoseEinstein condensation. We study vortices in this novel state using a symmetrybased effective field theory, which captures the lowenergy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spinimbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermionpairing interaction is weak or strong. We find a remarkable, unconventional form of the interaction between vortices. The presence of gapless fermions gives rise to a spatially oscillating potential, akin to the RKKY indirectexchange interaction in nonmagnetic metals. We compare the parameters of the effective theory to the experimentally measurable quantities and further discuss the conditions for the verification of the predicted new feature. Our study opens up an interesting question as to the nature of the vortex lattice resulting from the competition between the usual repulsive logarithmic (2D Coulomb) and predominantly attractive fermioninduced interactions.
 
16.  Nonlocal electronphonon coupling: Consequences for the nature of polaron states 
V. M. Stojanović, P. A. Bobbert, and M. A. J. Michels. Phys. Rev. B 69, 144302 (2004)
We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electronphonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasifree character of the excitation. Our findings have implications for organic crystals of πconjugated molecules, where this electronphonon coupling mechanism plays an important role.
 
17.  Theory of polaron bandwidth narrowing in organic molecular crystals 
K. Hannewald, V. M. Stojanović, P. A. Bobbert, J. M. T. Schellekens, G. Kresse, and J. Hafner. Phys. Rev. B 69, 075211 (2004)
We present a theoretical description of polaron bandwidth narrowing in organic molecular crystals. Based on a solution of a HolsteinPeierls model for tightly bound electrons interacting with phonons, an explicit expression for the temperature dependence of the electronic bandwidths is found. This formula generalizes the result of Holstein polaron theory by treating local and nonlocal electronphonon coupling on equal footing. The usefulness of the method is demonstrated by model studies for oligoacene crystals from which microscopic insight into the relevance of the different coupling mechanisms is obtained.
 
18.  A note on temperaturedependent band narrowing in oligoacene crystals 
K. Hannewald, V. M. Stojanović, and P. A. Bobbert. J. Phys.: Condens. Matter 16, 2023 (2004)
We present a theoretical description of polaron band narrowing in oligoacene
crystals due to electronlattice interaction. The analysis is based on a model
which takes both local and nonlocal contributions to the electronphonon
coupling into account. Different approximation schemes are discussed and
compared. The theory is supplemented by quantitative abinitio calculations
of the temperature dependence of polaron bandwidths in oligoacene crystals
which show the important role of inplane nonlocal electronphonon coupling.

Recent talks
Quantum simulation of smallpolaron formation with trapped ions
Control of Complex Quantum Systems workshop, The Kavli Institute for Theoretical Physics, UC Santa Barbara, USA, March 26, 2013Polarons: from models to materials to quantum simulation
Atelier de physique theorique, University of Geneva, Switzerland, December 11, 2012
Theoretical Physics Colloquium, University of Konstanz, Germany, November 26, 2012
TCM seminar, Cavendish Laboratory, University of Cambridge, UK, November 15, 2012
Nano and Quantum Physics Seminar, University of Basel, Switzerland, October 1, 2012From quantum control to oneway quantum computing in interacting qubit arrays
2nd international SOLID workshop, Grenoble, France, February 21, 2012
ECOQAS11 workshop, Dresden, Germany, October 12, 2011
QIPC conference, Zurich, Switzerland, September 6, 2011Electronic properties of graphene antidot lattices
Mesoscopic Physics Seminar, Uni Wuerzburg, Germany, June 1, 2010
Condensed Matter Seminar, CEA Saclay, France, May 5, 2010
Teaching
Fall semester 2012: Theoretical SolidState Physics course
Miscellaneous
 Our work on organic semiconductors covered by the European Grid Infrastructure (May 14, 2013)
 2010 Best Tutor Award of FG14: section of physics and mathematics at the University of Basel (December 16, 2010)
 Poster on graphene antidot lattices ( Graphene Week 2012 Conference , Delft, The Netherlands, June 48, 2012)
 Poster on quantum control of interacting qubits at the First Meeting of the NCCRQIST (Arosa, January 1214, 2011)
 Rahel Heule's Master's Thesis on local quantum control (University of Basel, 2010)
 Rahel Heule wins the 2011 EmilieLouiseFrey Prize