Influence of Superconducting Leads Energy Gap on Electron Transport Through Double Quantum Dot by Markovian Quantum Master Equation Approach

Abstract

The superconducting reservoir effect on the current carrying transport of a double quantum dot in Markovian regime is investigated. For this purpose, a quantum master equation (QME) at finite temperature is derived for the many-body density matrix of an open quantum system. The dynamics and the steady-state properties of the double quantum dot system for arbitrary bias are studied. We will show that how the populations and coherencies of the system states are affected by superconducting leads. The energy parameter of system contains essentially four contributions due to dots system-electrodes coupling, intra dot coupling, two quantum dots inter coupling and superconducting gap. The coupling effect of each energy contribution is applied to currents and coherencies results. In addition, the effect of energy gap is studied by considering the amplitude and lifetime of coherencies to get more current through the system. IntroductionRecent years, it has received remarkable progress in experimental techniques to study the electron transport through nanoscopic systems where semiconductor quantum dots (QDs) are connected to superconducting electrodes [1][2][3][4][5].When the coupling in superconductor is sufficient, the Cooper pairs in low temperatures develop global coherency, which suppress the global macroscopic superconductivity. These studies are desirable for very sensitive and controllable coherent switching devices which make it possible to investigate quantum computing and different quantum effects of fundamental physics, such as single electron tunneling, quantum phase transition, and macroscopic condensation [6][7][8][9]. Keldysh nonequilibrium Green's functions (NEGF) [10,11], scattering theory(ST) [12,13] and quantum master equation (QME) [14][15][16][17]approaches can be used to study the nonequilibrium electron transport through a quantum system (QD or single molecule). ST is limited to elastic processes while the NEGF can treat in elastic and inelastic ones. Both approaches are applied to the tunneling coupling exactly, but usually the correlations inside the dot are fully neglected or the mean field and perturbation theory is used. QME is an alternative tool for studying the irreversible dynamics of quantum systems coupled to a macroscopic environment. This approach treats the correlations inside the dot very accurately (even exactly in the case of model systems) but the tunneling is usually considered in the Born-Markov approximation. Markovian quantum master equation [18,19] provides an intuitive understanding the non-equilibrium transport problem of the system dynamics [20]and has been used in various fields such as quantum optics [21,22], solid state physics [23],and chemical dynamics [24].For example, electrons tunneling through molecules, coupled QDs [25] and superconducting systems have been studied by this approach. Recently, QME approach has been applied to investigate electron tunneling through molecules or coupled QDs [26,27] such as, studying the rectification properties of a system of coupled...

Robust entanglement of an asymmetric quantum dot molecular system in a Josephson junction

“…Therefore, we can rewrite the current formula, Eq. (6) , as [58] , [69] : where shows the contribution of lead ν in matrix . In the steady-state of the system, by taking so long time ( ), the stationary transport is shown in Fig.…”

“…Also, QDs in normal biased-voltage junctions have extensively been used experimentally [48] , [49] , [50] and theoretically [51] , [52] , [53] . Recently, quantum transport through the QDs system in contact with Josephson junctions (JJs) which act as the single transistors to filter the transfer of electrons has attracted a great deal of attention [54] , [55] , [56] , [57] , [58] .…”

Polaronic Entanglement of Quantum dot Molecule in a voltage-controlled junction

“…( 8) can be rewritten in the matrix form as ρ = M ρ, where matrix M corresponds to the characteristics of the master equation. According to the matrix formalism of QME, we can express the electric current as [8,35,36]:…”

Robust entanglement of an asymmetric quantum dot molecular system in a Josephson junction

“…In general case, the interaction Hamiltonian can be considered as ĤI = α Âα Bα with the operators Âα and Bα which satisfy the commutation relation [A α , B α ] = 0 and act on the system and leads Hilbert spaces, respectively. Finally, the master equation for the central system of QDM in the presence of superconducting leads is derived as: According to the BCS theory, the superconducting density of states R ν (E) is defined [66][67][68]:…”

“…Also, QDs in normal biased-voltage junctions have extensively been used experimentally [58][59][60] and theoretically [61][62][63]. Recently, quantum transport through the QDs system in contact with Josephson junctions (JJs) which act as the single transistors to filter the transfer of electrons have attracted a great deal of attention [64][65][66][67][68].…”