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Japanese Journal of Applied Physics

Steady-State Solution for Dark States Using a Three-Level System in Coupled Quantum Dots

Tetsufumi Tanamoto, Keiji Ono, Franco Nori

Published Feb 1, 2012• 5 citations
Publisher

Abstract

Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete energy levels of the system. Here, we theoretically solve the steady-state solutions of the density matrix equations for a thee-level double QD system and investigate the condition of the appearance of a dark state. We also numerically show the appearance of the dark state by time-dependent current characteristics.

DOI
10.7567/jjap.51.02bj07

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Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete energy levels of the system. Here, we theoretically solve the steady-state solutions of the density matrix equations for a thee-level double QD system and investigate the condition of the appearance of a dark state. We also numerically show the appearance of the dark state by time-dependent current characteristics.
Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete energy levels of the system. Here, we theoretically solve the steady-state solutions of the density matrix equations for a thee-level double QD system and investigate the condition of the appearance of a dark state. We also numerically show the appearance of the dark state by time-dependent current characteristics.
Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices.Dark states appear as a result of coherence between the electromagnetic fields and the discrete energy levels of the system.Here, we theoretically solve the steady-state solutions of the density matrix equations for a thee-level double QD system and investigate the condition of the appearance of a dark state.We also numerically show the appearance of the dark state by time-dependent current characteristics.
We theoretically investigate the coherent transfer of one electron between the ground states of a double coupled quantum dot structure. The coherent transfer of the electron is externally controlled by applied electromagnetic fields with on- or close-resonance driving frequencies and various shapes and duration. We derive the analytical expressions for the parameters of the external fields by approximating the quantum dot system as a three-level Λ-type system. The analytical solutions are compared with numerical results and good agreement is found. The control methods developed here are applicable in symmetric and asymmetric quantum dot nanostructures.
Atomic phase coherence (quantum interference) in a multilevel atomic gas exhibits a number of interesting phenomena. Such an atomic quantum coherence effect can be generalized to a quantum-dot molecular dielectric. Two quantum dots form a quantum-dot molecule, which can be described by a three-level Λ-configuration model {∣0⟩,∣1⟩,∣2⟩}\{ |0\rangle ,|1\rangle ,|2\rangle \} {∣0⟩,∣1⟩,∣2⟩}, i.e., the ground state of the molecule is the lower level |0〉 and the highly degenerate electronic states in the two quantum dots are the two upper levels ∣1⟩,∣2⟩|1\rangle ,|2\rangle ∣1⟩,∣2⟩. The electromagnetic characteristics due to the |0〉–|1〉 transition can be controllably manipulated by a tunable gate voltage (control field) that drives the |2〉–|1〉 transition. When the gate voltage is switched on, the quantum-dot molecular state can evolve from one steady state (i.e., |0〉–|1〉 two-level dressed state) to another steady state (i.e., three-level coherent-population-trapping state). In this process, the electromagnetic characteristics of a quantum-dot molecular dielectric, which is modified by the gate voltage, will also evolve. In this study, the transient evolutional behavior of the susceptibility of a quantum-dot molecular thin film and its reflection spectrum are treated by using the density matrix formulation of the multilevel systems. The present field-tunable and frequency-sensitive electromagnetic characteristics of a quantum-dot molecular thin film, which are sensitive to the applied gate voltage, can be utilized to design optical switching devices.
We present a theoretical study of the collective optical effects which can occur in groups of three and four quantum dots. We define conditions for stable subradiant (dark) states, rapidly decaying super-radiant states, and spontaneous trapping of excitation. Each quantum dot is treated like a two-level system. The quantum dots are, however, realistic, meaning that they may have different transition energies and dipole moments. The dots interact via a short-range coupling which allows excitation transfer across the dots, but conserves the total population of the system. We calculate the time evolution of single-exciton and biexciton states using the Lindblad equation. In the steady state the individual populations of each dot may have permanent oscillations with frequencies given by the energy separation between the subradiant eigenstates.
We present a model for quantum computation using nnn steady 3-level atoms kept inside a quantum cavity, or using nnn quantum-dots (QDs) kept inside a quantum cavity. In this model one external laser is pointed towards all the atoms/QDs, and nnn pairs of electrodes are addressing the atoms/QDs, so that each atom is addressed by one pair. The energy levels of each atom/QD are controlled by an external Stark field given to the atom/QD by its external pair of electrodes. Transition between two energy levels of an individual atom/ QD are controlled by the voltage on its electrodes, and by the external laser. Interactions between two atoms/ QDs are performed with the additional help of the cavity mode (using on-resonance condition). Laser frequency, cavity frequency, and energy levels are far off-resonance most of the time, and they are brought to the resonance (using the Stark effect) only at the time of operations. Steps for a controlled-NOT gate between any two atoms/QDs have been described for this model. Our model demands some challenging technological efforts, such as manufacturing single-electron QDs inside a cavity. However, it promises big advantages over other existing models which are currently implemented, and might enable a much easier scale-up, to compute with many more qubits.