The exchange fluctuation theorem in quantum mechanics

We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same order of the coupling. We then discover a condition for the exchange fluctuation theorem to hold in the presence of a finite heat transfer, namely the commutable-coupling condition. We explicitly calculate the deviation from the exchange fluctuation theorem as well as the heat transfer for simple models. We confirm for the models that the deviation indeed has a finite value as far as the coupling between the two systems is finite except for the special point of the commutable-coupling condition. We also confirm analytically that the commutable-coupling condition indeed lets the exchange fluctuation theorem hold exactly under a finite heat transfer.Comment: 16 pages, 3 figures, to appear in Progress of Theoretical Physics, Vol. 121, No. 6 (2009

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Electronic Structure of Multiple Dots

We calculate, via spin density functional theory (SDFT) and exact diagonalization, the eigenstates for electrons in a variety of external potentials, including double and triple dots. The SDFT calculations employ realistic wafer profiles and gate geometries and also serve as the basis for the exact diagonalization calculations. The exchange interaction J between electrons is the difference between singlet and triplet ground state energies and reflects competition between tunneling and the exchange matrix element, both of which result from overlap in the barrier. For double dots, a characteristic transition from singlet ground state to triplet ground state (positive to negative J) is calculated. For the triple dot geometry with 2 electrons we also find the electronic structure with exact diagonalization. For larger electron number (18 and 20) we use only SDFT. In contrast to the double dot case, the triple dot case shows a quasi-periodic fluctuation of J with magnetic field which we attribute to periodic variations of the basis states in response to changing flux quanta threading the triple dot structure.Comment: 3 pages, 4 figure

Semiconductor quantum dots for electron spin qubits

We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates