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arXiv:cond-mat/0703192 · Physical Review Letters

Coherent Control of Interacting Electrons in Quantum Dots via Navigation in the Energy Spectrum

Gustavo E. Murgida, Diego A. Wisniacki, P. I. Tamborenea

Published Jul 20, 2007• 41 citations
arXivHTMLPDF

Abstract

Quantum control of the wave function of two interacting electrons confined in quasi-one-dimensional double-well semiconductor structures is demonstrated. The control strategies are based on the knowledge of the energy spectrum as a function of an external uniform electric field. When two low-lying levels have an avoided crossing, our system behaves dynamically to a large extent as a two-level system. This characteristic is exploited to implement coherent control strategies based on slow (adiabatic passage) and rapid (diabatic Landau-Zener transition) changes of the external field. We apply this method to reach desired target states that lie far in the spectrum from the initial state.

DOI
10.1103/physrevlett.99.036806

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•Jan 1, 2012•0 citations
Quantum control of the wave function of two interacting electrons confined in quasi-one-dimensional double-well semiconductor structures is demonstrated. The control strategies are based on the knowledge of the energy spectrum as a function of an external uniform electric field. When two low-lying levels have an avoided crossing, our system behaves dynamically to a large extent as a two-level system. This characteristic is exploited to implement coherent control strategies based on slow (adiabatic passage) and rapid (diabatic Landau-Zener transition) changes of the external field. We apply this method to reach desired target states that lie far in the spectrum from the initial state.
Abstract Semiconductor quantum dots are ideal candidates for quantum information applications in solid-state technology. However, advanced theoretical and experimental tools are required to coherently control, for example, the electronic charge in these systems. Here we demonstrate how quantum optimal control theory provides a powerful way to manipulate the electronic structure of coupled quantum dots with an extremely high fidelity. As alternative control fields we apply both laser pulses as well as electric gates, respectively. We focus on double and triple quantum dots containing a single electron or two electrons interacting via Coulomb repulsion. In the two-electron situation we also briefly demonstrate the challenges of timedependent density-functional theory within the adiabatic local-density approximation to produce comparable results with the numerically exact approach.
We propose an efficient control protocol for charge transfer in a double quantum dot. We consider numerically a two-dimensional model system, where the quantum dots are subjected to time-dependent electric fields corresponding to experimental gate voltages. Our protocol enables navigation in the charge stability diagram from a state to another through controllable variation of the fields. We show that the well-known adiabatic Landau-Zener transition-when supplemented with a time-dependent field tailored with optimal control theory-can remarkably improve the transition speed. The results also lead to a simple control scheme obtained from the experimental charge stability diagram that requires only a single parameter. Eventually, we can achieve the ultrafast performance of the composite pulse protocol that allows the system to be driven at the quantum speed limit.
Quantum state preparation through external control is fundamental to established methods in quantum information processing and in studies of dynamics. In this respect, excitons in semiconductor quantum dots are of particular interest, since their coupling to light allows them to be driven into a specified state using the coherent interaction with a tuned optical field, such as an external laser pulse. We propose a protocol, based on adiabatic rapid passage, for the creation of entangled states in an ensemble of pairwise coupled two-level systems, such as an ensemble of coupled quantum dots. We show by quantitative analysis using realistic parameters for semiconductor quantum dots that this method is feasible where other approaches are unavailable. Furthermore, this scheme can be generically transferred to some other physical systems, including circuit QED, nuclear and electron spins in solid-state environments, and photonic coupled cavities.
We analyze the dynamics of a ground state two-level system built on the spatial distribution of the system wave function and designed to be well-separated from the remainder of the state space. With a total of two operative electrons on a planar array of quantum dots coupled capacitively to a set of external voltage gates, the system is modeled using an extended Hubbard Hamiltonian. The voltage dependence of the low-energy singlet and triplet states is analyzed, respectively, using the Feshbach formalism. Coherent operation of the array is studied with respect to single quantum bit operations. One quantum gate is implemented via voltage controls, while for the necessary second quantum gate, a uniform external magnetic field is introduced. The Aharonov-Bohm phases on the closed loop tunnel connections in the array are used to effectively suppress the tunneling, despite a constant tunneling amplitude in the structure. This allows one to completely stall the qubit in any arbitrary quantum superposition, providing full control of this interesting quantum system.
We investigate the utilization of external magnetic field for the manipulation of the quantum states in a two-electron double quantum dot. The singlet and triplet states are coupled through the hyperfine interaction between the electrons and surrounding nuclei. When the magnetic field is changed as a function of time, the singlet-triplet transition is possible for certain values of magnetic field, when the singlet state becomes degenerate with the triplet state. The transition probability depends on the sweeping speed of the magnetic field through the averaged Landau-Zener formula. We evaluate proper time scales for efficient control of the quantum dot, evaluate the singlet probabilities for different time-dependent magnetic fields, and study the average of the final singlet probability, averaged over the orientations of the nuclear spins surrounding the quantum dot.
In this thesis, the coherent interaction of single semiconductor quantum dots and ultrafast optical pulses is studied. Under certain conditions, localized exciton transitions in quantum dots can be seen as semi-isolated two-level systems. While this description is sufficient for the explanation of some observations in coherent experiments, it is sometimes necessary to explicitly consider coupling of the discreet quantum states confined to the dot with the environment. We start out from simple, classical examples of coherent spectroscopy and then turn towards experiments where the interaction with the vicinity of the dot becomes an important factor. First, a novel method for transient differential reflectivity spectroscopy of single quantum systems is introduced. It is a pure far-field optical technique which does not require any sophisticated sample preparation steps which makes it applicable to a broad range of structures. Pump pulses excite the sample structure and probe pulses read out the pump-induced changes in the system after a variable delay time. In the case of a single dipole, the signal is given in the form of the spectral inteferogram between the backscattered wave from the particle and the probe light which is reflected at the sample surface. This form of homodyne detection amplifies the weak scattered wave from the particle and thus makes this kind of spectroscopy for single quantum dots feasible. In the remainder of this thesis our spectroscopic method is applied to either characterize the coherent properties of single quantum dots, to prepare and read-out a desired quantum state or to deliberately manipulate them. Coherence times and oscillator strengths are determined for localized exciton transitions. Arbitrary population states can be written by driving coherent population oscillations using resonant pulses, while entangled superpositions of two exciton states in a single dot are investigated by quantum beats on transient differential spectra. We finally exploit the interaction between the dot and a nearby absorbing layer to switch the dot's absorption spectrum on ultrafast timescales via light-induced transient electric fields.