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Physical Review B

Controlled rotation in a double quantum dot structure

Emmanuel Paspalakis, Z. Kis, Evangelos Voutsinas, A. F. Terzis

Published Apr 19, 2004• 77 citations
Publisher

Abstract

The coherent manipulation of a double quantum dot system by an external driving field is analyzed. Using a controlled rotation method a general superposition state of the lower states is formed. Several interaction schemes are discussed and analytic results are presented. These are found to agree very well with the results of numerical simulations.

DOI
10.1103/physrevb.69.155316

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The coherent manipulation of a double quantum dot system by an external driving field is analyzed. Using a controlled rotation method a general superposition state of the lower states is formed. Several interaction schemes are discussed and analytic results are presented. These are found to agree very well with the results of numerical simulations.
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We analyze coherent spin rotations in a dc biased double quantum dot driven by crossed dc and ac magnetic fields. In this configuration, spatial delocalization due to interdot tunneling competes with intradot spin rotations induced by the time dependent magnetic field, giving rise to a complicated time dependent behavior of the tunneling current. When the Zeeman splitting has the same value in both dots and spin flip is negligible, the electrons remain in the triplet subspace performing coherent spin rotations and current does not flow. This electronic trapping is removed either by finite spin relaxation or when the Zeeman splitting is different in each quantum dot. In the last case, we will show that by applying a resonant bichromatic magnetic field, the electrons become trapped in a coherent superposition of states and electronic transport is blocked. Then, manipulating ac magnetic fields allows one to drive electrons to perform coherent spin rotations which can be unambiguously detected by direct measurement of the tunneling current.
A method of coherent manipulation of the electron tunneling in quantum dots is proposed, which utilizes the quantum interference in nonadiabatic double crossing of the discrete energy levels. In this method, we need only a smoothly varying gate voltage to manipulate electrons, without a sudden switching on and off. A systematic design of a smooth gate pulse is presented with a simple analytic formula to drive the two-level electronic state to essentially an arbitrary target state, and numerical simulations for complete transfer of an electron is shown for coupled double quantum dots and an array of quantum dots. Estimation of the manipulation time shows that the present method can be employed in realistic quantum dots.
The coherent time evolution of electrons in double quantum dots (DQDs) induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven DQDs are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation, we obtain the energy- and time-resolved electron transfer through the device that resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.