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AIP conference proceedings

Dynamical control of electronic states in AC-driven quantum dots

C. E. Creffield

Published Jan 1, 2005• 0 citations
Publisher

Abstract

We investigate the dynamics of two interacting electrons moving in a one‐dimensional array of quantum dots, under the influence of an ac field. The quantum dot array is modeled as a single‐band tight‐binding model of Hubbard‐type, and the system is analyzed by means of the Floquet approach. Our results show that the system exhibits two distinct regimes of behavior, depending on the ratio of the strength of the driving field to the inter‐electron Coulomb repulsion. When the ac‐field dominates an effect termed coherent destruction of tunneling occurs at certain frequencies, in which transport along the array is suppressed. In the other, weak‐driving, regime we find the surprising result that the two electrons can bind together into a single composite particle — despite the strong Coulomb repulsion between them — which can then be controlled by the ac field in an analogous way. We show how calculation of the system’s Floquet quasienergies explains these results, and thus how ac fields can be used to control the time evolution of entangled states in mesoscopic devices.

DOI
10.1063/1.1994351

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We investigate the dynamics of two interacting electrons moving in a one‐dimensional array of quantum dots, under the influence of an ac field. The quantum dot array is modeled as a single‐band tight‐binding model of Hubbard‐type, and the system is analyzed by means of the Floquet approach. Our results show that the system exhibits two distinct regimes of behavior, depending on the ratio of the strength of the driving field to the inter‐electron Coulomb repulsion. When the ac‐field dominates an effect termed coherent destruction of tunneling occurs at certain frequencies, in which transport along the array is suppressed. In the other, weak‐driving, regime we find the surprising result that the two electrons can bind together into a single composite particle — despite the strong Coulomb repulsion between them — which can then be controlled by the ac field in an analogous way. We show how calculation of the system’s Floquet quasienergies explains these results, and thus how ac fields can be used to control the time evolution of entangled states in mesoscopic devices.
We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to a transition of the Floquet quasienergy from real to complex values and results in decaying probabilities for the particle to be in the double well. By combining analytical solutions in the high-frequency approximation with numerical calculations based on an accurate model, we exhibit quantum-dynamical behavior of the particle such as Floquet oscillation, coherent destruction of tunneling, quasi-NOON-state population, partial one-particle tunneling, and the decay of the probabilities of occupation, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results suggest an experimental method for testing quantum motion in an open system by adjusting the driving field.
We investigate the quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasienergies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasienergy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second-quantized model, we find also a triangular structure in the quantum quasienergy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasienergies is further explored by a semiclassical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasienergies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.
We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba-Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.
We describe time-dependent single-electron transport through quantum dots in the Coulomb blockade regime. Coherent dynamics of a single charge qubit in a double quantum dot is discussed with full one-qubit manipulation. Strength of decoherence is controlled with the applied voltage, but uncontrolled decoherence arises from electron–phonon coupling and background fluctuations. Then energy-relaxation dynamics is discussed for orbital and spin degree of freedom in a quantum dot. The electron–phonon interaction and spin–orbit coupling can be investigated as the dissipation problem. Finally, charge detection measurement is presented for statistical analysis of single-electron tunnelling transitions and for a sensitive qubit read-out device.
Coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding approximation. In the high-frequency regime within or without multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the special Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. Applying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.
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.