We study the effects of a laser on the splitting of the lowest electronic states of a pair of two-dimensional (2D) GaAs-(Ga,Al)As coupled quantum dots, in the presence of a homogeneous external magnetic field. The interaction of light with the 2D quantum dots is treated within a dressed-band approach in which a two-band scheme is used to model the GaAs bulk semiconductor whereas the interaction with the laser field is treated through the renormalization of the semiconductor energy gap and conduction/valence effective masses. This approach is valid far from resonances and has been successfully used to treat other confined semiconductor heterostructures. We focus our attention on the splitting of the lowest singlet and triplet states and on their double occupation probability. We analyze the exchange coupling (J) in the effective Heisenberg model as a function of the laser field and its detuning, as well as of the magnetic field (B) within the Heitler-London approximation of molecular physics. We find that due to the electronic confinement the laser may play a role similar to the external magnetic field in the qualitative behavior of the exchange parameter J. Furthermore, the presence of the laser may assure both the sizable exchange coupling and the vanishingly small double occupation probability required for efficient quantum computer operations, even in the absence of an external magnetic field. Besides being of fundamental interest, these features may be used as an efficient two-qubit gate control.
We study the effects of a laser on the splitting of the lowest electronic states of a pair of two-dimensional (2D) GaAs-(Ga,Al)As coupled quantum dots, in the presence of a homogeneous external magnetic field. The interaction of light with the 2D quantum dots is treated within a dressed-band approach in which a two-band scheme is used to model the GaAs bulk semiconductor whereas the interaction with the laser field is treated through the renormalization of the semiconductor energy gap and conduction/valence effective masses. This approach is valid far from resonances and has been successfully used to treat other confined semiconductor heterostructures. We focus our attention on the splitting of the lowest singlet and triplet states and on their double occupation probability. We analyze the exchange coupling (J) in the effective Heisenberg model as a function of the laser field and its detuning, as well as of the magnetic field (B) within the Heitler-London approximation of molecular physics. We find that due to the electronic confinement the laser may play a role similar to the external magnetic field in the qualitative behavior of the exchange parameter J. Furthermore, the presence of the laser may assure both the sizable exchange coupling and the vanishingly small double occupation probability required for efficient quantum computer operations, even in the absence of an external magnetic field. Besides being of fundamental interest, these features may be used as an efficient two-qubit gate control.
We theoretically study a double-quantum-dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer, with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope-function approach in the current scheme, and also the merits of various quantum-chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent-field method, the molecular-orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic-field control, and error correction.
We consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling J in the effective Heisenberg model as a function of magnetic (B) and electric fields, and of the interdot distance a within the Heitler-London approximation of molecular physics. This result is refined by using sp hybridization, and by the Hund-Mulliken molecular-orbit approach, which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on B and a due to the long-range Coulomb interaction. We find that the exchange J changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear-spin polarization and/or by magnetic fields.
We theoretically consider the effects of having unintentional charged impurities in laterally coupled two-dimensional double (GaAs) quantum-dot systems, where each dot contains one or two electrons and a single charged impurity. Using molecular orbital and configuration interaction methods, we calculate the effect of the impurity on the two-electron energy spectrum of each individual dot as well as on the spectrum of the coupled-double-dot two-electron system. We find that the singlet-triplet exchange splitting between the two lowest-energy states, both for the individual dots and the coupled-dot system, depends sensitively on the location of the impurity and its coupling strength (i.e. the effective charge). A strong electron-impurity coupling breaks down the equality of the two doubly occupied singlets in the left and the right dots, leading to a mixing between different spin singlets. As a result, the maximally entangled qubit states are no longer fully obtained in the zero-magnetic-field case. Moreover, a repulsive impurity results in a triplet-singlet transition as the impurity effective charge increases or the impurity position changes. We comment on the impurity effect in spin qubit operations in the double-dot system based on our numerical results.
We discuss the microscopic modeling of exchange interactions between double semiconductor quantum dots used as spin qubits. Starting from a reference full configuration interaction (CI) calculation for the two-particle wave functions, we build a reduced basis set of dressed states that can describe the ground-state singlets and triplets over the whole operational range with as few as 100 basis functions (as compared to a few thousands for the full CI). This enables fast explorations of the exchange interactions landscape as well as efficient time-dependent simulations. We apply this methodology to a double hole quantum dot in germanium and discuss the physics of exchange interactions in this system. We show that the net exchange splitting results from a complex interplay among interdot tunneling, Coulomb exchange, and correlations. We analyze, moreover, the effects of confinement, strains, and Rashba interactions on the anisotropic exchange and singlet-triplet mixings at finite magnetic field. We finally illustrate the relevance of this methodology for time-dependent calculations on a singlet-triplet qubit.
In this work, we develop a physically transparent Coulomb-interaction model from simplification of a general many-body theory and apply this model to study interacting electron dynamics for transient occupation and quantum coherence in both single and double quantum dots under laser irradiation. Our theory considers self-consistently the Coulomb-renormalized Rabi coupling to light by using an induced optical-depolarization field, corresponding to dynamical exchange interaction between two electrons within the same quantum dot. Meanwhile, we employ evanescent-field coupling for dynamical Coulomb interaction between two electrons in different quantum dots based on a surface-plasmon model. In particular, we explore the quantum interference between a pair of laser-induced quantum coherence in three-level quantum-dot systems, which gives rise to indirect transition of electrons for sum- and difference-frequency transient optical responses. By varying laser frequency detuning, the control of laser-dressed electronic states becomes possible and can be utilized for switching among off-state, partial, and complete on-states. This study will be useful for controlling the phase entanglement of two laser-dressed states of quantum dots, as well as for enhancing the electro-optical performance through sum- and difference-frequency transitions in many optoelectronic devices.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.