Dimitrije Stepanenko
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

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Example textPublications
Show all abstracts.1.  Spin electric effects in molecular antiferromagnets 
Mircea Trif, Filippo Troiani, Dimitirje Stepanenko, and Daniel Loss. Phys. Rev. B 82, 045429 (2010); arXiv:1001.3584.
Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective lowenergy spin Hamiltonians suitable for encoding qubits and implementing spinbased quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By grouptheoretical symmetry analysis we find that the spinelectric coupling in triangular molecules is governed by the modification of the exchange interaction, and is possible even in the absence of spinorbit coupling. In pentagonal molecules the spinelectric coupling can exist only in the presence of spinorbit interaction. This kind of coupling is allowed for both $s=1/2$ and $s=3/2$ spins at the magnetic centers. Within the Hubbard model, we find a relation between the spinelectric coupling and the properties of the chemical bonds in a molecule, suggesting that the best candidates for strong spinelectric coupling are molecules with nearly degenerate bond orbitals. We also investigate the possible experimental signatures of spinelectric coupling in nuclear magnetic resonance and electron spin resonance spectroscopy, as well as in the thermodynamic measurements of magnetization, electric polarization, and specific heat of the molecules.
 
2.  Interference of heavy holes in an AharonovBohm ring 
Dimitrije Stepanenko, Minchul Lee, Guido Burkard, and Daniel Loss. Phys. Rev. B 79, 235301 (2009); arXiv:0811.4566.
We study the coherent transport of heavy holes through a onedimensional ring
in the presence of spinorbit coupling. Spinorbit interaction of holes, cubic
in the inplane components of momentum, gives rise to an angular momentum
dependent spin texture of the eigenstates and influences transport. We analyze
the dependence of the resulting differential conductance of the ring on hole
polarization of the leads and the signature of the textures in the
AharonovBohm oscillations when the ring is in a perpendicular magnetic field.
We find that the polarizationresolved conductance reveals whether the dominant
spinorbit coupling is of Dresselhaus or Rashba type, and that the cubic
spinorbit coupling can be distinguished from the conventional linear coupling
by observing the fourpeak structure in the AharonovBohm oscillations.
 
3.  Quantum computing with molecular magnets 
Dimitrije Stepanenko, Mircea Trif, and Daniel Loss. Inorganica Chimica Acta 361, 3740 (2008)  
4.  SpinElectric Coupling in Molecular Magnets 
Mircea Trif, Filippo Troiani, Dimitrije Stepanenko, and Daniel Loss. Phys. Rev. Lett. 101, 217201 (2008); arXiv:0805.1158.
We study the triangular antiferromagnet Cu$_3$ in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spinelectric coupling caused by an interplay between spin exchange, spinorbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spinelectric effects.
 
5.  Quantum gates between capacitively coupled double quantum dot twospin qubits 
Dimitrije Stepanenko and Guido Burkard. Phys. Rev. B 75, 085324 (2007); condmat/0610377.
We study the twoqubit controllednot gate operating on qubits encoded in the spin state of a pair of electrons in a double quantum dot. We assume that the electrons can tunnel between the two quantum dots encoding a single qubit, while tunneling between the quantum dots that belong to different qubits is forbidden. Therefore, the two qubits interact exclusively through the direct Coulomb repulsion of the electrons. We find that entangling twoqubit gates can be performed by the electrical biasing of quantum dots and/or tuning of the tunneling matrix elements between the quantum dots within the qubits. The entangling interaction can be controlled by tuning the bias through the resonance between the singlyoccupied and doublyoccupied singlet ground states of a double quantum dot.
 
6.  Optical preparation of nuclear spins coupled to a localized electron spin 
Dimitrije Stepanenko and Guido Burkard. Proceedings of the 2006 MS+S Conference, World Scientific 2008  
7.  Enhancement of electron spin coherence by optical preparation of nuclear spins 
Dimitrije Stepanenko, Guido Burkard, Geza Giedke, and Atac Imamoglu. Phys. Rev. Lett. 96, 136401 (2006); condmat/0512362.
We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. When a pair of applied laser fields satisfy twophoton resonance between the two ground electronic spin states, detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. If the spin were driven into a coherent population trapping state where no light scattering takes place, then the nuclear state would be projected into an eigenstate of the Overhauser field operator and electron decoherence due to nuclear spins would be suppressed: we show that this limit can be approached by adapting the laser frequencies when a photon is detected. We use a Lindblad equation to describe the time evolution of the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 ns to 500 ns after a preparation time of 10 microseconds.
 
8.  Universal Quantum Computation through Control of SpinOrbit Coupling 
D. Stepanenko and N. E. Bonesteel. Phys. Rev. Lett. 93, 140501 (2004); quantph/0403023.
We propose a method for quantum computation which uses control of spinorbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spinorbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single qubit rotations or controlledNot gates scales as the inverse of a dimensionless measure of the degree of control of spinorbit coupling.
 
9.  SpinOrbit Coupling and TimeReversal Symmetry in Quantum Gates 
D. Stepanenko, N.E. Bonesteel, D.P. DiVincenzo, G. Burkard, and Daniel Loss. Phys. Rev. B 68, 115306 (2003); condmat/0303474.
We study the effect of spinorbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spinorbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the fourdimensional Hilbert space of two qubits. If the precession axis is fixed, timesymmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from timesymmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spinorbit coupling and time asymmetry of the pulse.
 
10.  Anisotropic Spin Exchange in Pulsed Quantum Gates 
N.E. Bonesteel, D. Stepanenko, and D.P. DiVincenzo. Phys. Rev. Lett. 87, 207901 (2001); quantph/0106161.
We show how to eliminate the firstorder effects of the spinorbit interaction in the performance of a twoqubit quantum gate. Our procedure involves tailoring the time dependence of the coupling between neighboring spins. We derive an effective Hamiltonian which permits a systematic analysis of this tailoring. Timesymmetric pulsing of the coupling automatically eliminates several undesirable terms in this Hamiltonian. Well chosen pulse shapes can produce an effectively isotropic exchange gate, which can be used in universal quantum computation with appropriate coding.
