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Physical Review B

Electron-photon interaction associated with uncertainty-based tunneling in a parallel double quantum dot

Kao-Chin Lin, Der-San Chuu

Published Mar 20, 2008• 1 citation
Publisher

Abstract

The electron-photon interaction associated with the uncertainty based tunneling (EPAUT) in the parallel double quantum dot system is studied. In the considered system, the electron interacts with the single mode detuning quantum photon field, i.e., ${\ensuremath{\omega}}_{\mathit{ph}}+\ensuremath{\Delta}={\ensuremath{\epsilon}}_{2}\ensuremath{-}{\ensuremath{\epsilon}}_{1}$, and transits between the quantum dots (QDs). The corresponding characteristic temperature is calculated and compared with the Kondo temperature to recognize the role of the related quantities. There are two energy uncertainties in the considered system. One is the energy difference between the energy of electron-photon interacting quasiparticle and the Fermi energy of the lead. The other is the detuning factor $\ensuremath{\Delta}$. Besides, $\ensuremath{\mid}\ensuremath{\Delta}∕\ensuremath{\pi}\ensuremath{\mid}$ is the bandwidth of the intermediate state of EPAUT. The peak of the density of state corresponding to the EPAUT rises when the temperature is in the order of or below the characteristic temperature. The EPAUT peak can be modified via tuning the Fermi energy of the lead connected to the adjoined QD. Hence, the conductance between the connected leads is varied via tuning the Fermi energy of the lead connected to the adjoined QD.

DOI
10.1103/physrevb.77.115339

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The electron-photon interaction associated with the uncertainty based tunneling (EPAUT) in the parallel double quantum dot system is studied. In the considered system, the electron interacts with the single mode detuning quantum photon field, i.e., \ensuremathωph+\ensuremathΔ=\ensuremathϵ2\ensuremath−\ensuremathϵ1{\ensuremath{\omega}}_{\mathit{ph}}+\ensuremath{\Delta}={\ensuremath{\epsilon}}_{2}\ensuremath{-}{\ensuremath{\epsilon}}_{1}\ensuremathωph​+\ensuremathΔ=\ensuremathϵ2​\ensuremath−\ensuremathϵ1​, and transits between the quantum dots (QDs). The corresponding characteristic temperature is calculated and compared with the Kondo temperature to recognize the role of the related quantities. There are two energy uncertainties in the considered system. One is the energy difference between the energy of electron-photon interacting quasiparticle and the Fermi energy of the lead. The other is the detuning factor \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ. Besides, \ensuremath∣\ensuremathΔ∕\ensuremathπ\ensuremath∣\ensuremath{\mid}\ensuremath{\Delta}∕\ensuremath{\pi}\ensuremath{\mid}\ensuremath∣\ensuremathΔ∕\ensuremathπ\ensuremath∣ is the bandwidth of the intermediate state of EPAUT. The peak of the density of state corresponding to the EPAUT rises when the temperature is in the order of or below the characteristic temperature. The EPAUT peak can be modified via tuning the Fermi energy of the lead connected to the adjoined QD. Hence, the conductance between the connected leads is varied via tuning the Fermi energy of the lead connected to the adjoined QD.
We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot tunnel coupling with high accuracy. The value and uncertainty of the tunnel coupling extracted from the microwave read-out technique are compared to a standard quantum point contact charge detection analysis. The two techniques are found to be consistent with a superior precision for the microwave experiment when tunneling rates approach the resonator eigenfrequency. Decoherence properties of the double dot are further investigated as a function of the number of electrons inside the dots. They are found to be similar in the single-electron and many-electron regimes suggesting that the density of the confinement energy spectrum plays a minor role in the decoherence rate of the system under investigation.
A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electron–electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying the numerical renormalization group (NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2e(2)/h) due to the underscreened Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to antiferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2 e 2 / h ) due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.
In this study, a model of a double-quantum-dot system driven by two-mode microwave photons is presented. The quantum master equation is derived from the system’s Hamiltonians, and the expression for the steady-state current is obtained. Electronic tunneling properties are then analyzed. The results revealed that different two-mode quantum microwave photons have varying effects on the tunneling current within the double-quantum-dot system, with a steplike current trend emerging. The tunneling current showed pronounced negative differential conductance for both coherent and squeezed microwave photons. Furthermore, the tunneling current was significantly influenced by changing the squeezing coefficient and phase. The asymmetric evolution of the tunneling current under varying bias voltages also depends on the asymmetry in system parameters. These findings are crucial for manipulating the transport properties of double-quantum-dot systems in nanostructured devices.