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

Abstract

Quantum control of the wave function of two interacting electrons confined in quasi-onedimensional 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 avoided crossings 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.PACS numbers: 78.67.Hc The control of quantum systems is a fundamental challenge in physical chemistry, nanoscience, and quantum information processing [1,2]. Quantum control is the manipulation of the temporal evolution of a system in order to obtain a desired target state or value of a certain physical observable. From the experimental point of view, the techniques of quantum control are highly developed in the area of magnetic resonance, and more recently great progress has been made in quantum chemistry thanks to the development of ultrafast laser pulses [3].Coherent control in semiconductor quantum dots has become an active field of research in the last 15 years. Early works on electron localization in double well systems spurred intense theoretical activity. In a seminal paper, Grossmann et al. [4] showed that, by applying an appropriate AC electric field, the tunneling of the electron between the wells could be coherently destroyed, thereby maintaining an existing localization in one of the wells. Shortly after, Bavli and Metiu [5] found ways to, starting from the delocalized ground state, localize the electron wave function and then to preserve the localization with a precisely taylored time-dependent electric field. A large body of literature followed these pioneering works. A decade later, the first steps in the theoretical exploration of localization and control of two interacting electrons in quantum dots were made [6,7,8]. Whereas Zhang and Zhao studied a model two-level system, Tamborenea and Metiu studied a more realistic multi-level system inspired by quasi-one-dimensional semiconductor nanorods. The study of two-electron localization and control in double dots has remained active ever since [9,10,11,12,13].In this Letter we propose an efficient method to control the wave function of two interacting electrons confined in quasi-one-dimensional nanorods [8,14]. The control method is based on the knowledge of the energy spectrum as a function of an external uniform electric field. The method requires that the system behaves locallynear avoided level crossings-as the Landau-Zener (LZ) two-level model [15]. This fact is exploited to navigate the spectrum using slow (adiabatic) and rapid (diabatic) changes of the external control parameter. Although this characteristic may seem rather restrictive, it is, in fact, a general ...

Time-optimal control fields for quantum systems with multiple avoided crossings

“…This situation is of interest in a wide variety of quantum mechanical systems, such as molecular dipoles interacting with electric fields [33,34], ultracold atoms in optical lattices [35], Rydberg atoms [36] and superconducting qubits [37]. Using this particular interaction between the states of the system, we generate initial guesses for the control protocols using piecewise-constant functions derived from previous studies [38,39]. In a recent work, we studied the QSL time for these protocols by using QOC, and showed that the calculated QSL time is in general smaller than the sum of the optimal times for each avoided crossing [40].…”

Controlled high-fidelity navigation in the charge stability diagram of a double quantum dot

“…Since the seminal Letter of Grossmann et al [8] a number of theoretical and experimental works have addressed the issue of controlling the localization of an electron state in a double well potential [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. These various control strategies include the use of analytically wellestablished phenomena like the paradigmatic LandauZener (LZ) transition [12][13][14], Landau-Zener-Stückelberg interferometry [15,16], the composite pulse (CP) protocol and several other two-level control strategies [12,[24][25][26][27], and OCT [18][19][20][21][22][23].…”

“…These various control strategies include the use of analytically wellestablished phenomena like the paradigmatic LandauZener (LZ) transition [12][13][14], Landau-Zener-Stückelberg interferometry [15,16], the composite pulse (CP) protocol and several other two-level control strategies [12,[24][25][26][27], and OCT [18][19][20][21][22][23]. For the experimental control strategies, as can be seen in [10,[15][16][17], the first stage is the measurement of the charge stability diagram (CSD).…”

Optimal control of a charge qubit in a double quantum dot with a Coulomb impurity

“…In recent years there has been an increasing interest in controlling quantum phenomena in molecular systems and nanodevices [8,9,10,11,12,13,14,15], due to the possibility to modify the wave function of the system through the appropriate tailoring of external fields such as laser pulses. Coherent quantum control of electrons in quantum dots exposed to electromagnetic radiation is of great interest in many technological applications from charge transport devices to quantum information [16,17,18].…”