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arXiv:cond-mat/0404364

Phonon impact on the coherent control of quantum states in semiconductor quantum dots

Anna Grodecka, Lucjan Jacak, Paweł Machnikowski, Katarzyna Roszak

Published Apr 15, 2004• 5 citations
arXivHTMLPDF

Abstract

This chapter is devoted to the recent theoretical results on the optical quantum control over charges confined in quantum dots under influence of phonons. We show that lattice relaxation processes lead to decoherence of the confined carrier states. The theoretical approach leading to a uniform, compact description of the phonon impact on carrier dynamics, perturbative in phonon couplings but applicable to arbitrary unperturbed evolution, is described in detail. Next, some applications are presented: phonon damping of Rabi oscillations in quantum dots and phonon-induced error of a single-qubit gate for an excitonic quantum dot qubit as well as for a semiconductor quantum dot spin qubit operated via a STIRAP transfer.

DOI
10.48550/arxiv.cond-mat/0404364

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This chapter is devoted to the recent theoretical results on the optical quantum control over charges confined in quantum dots under influence of phonons. We show that lattice relaxation processes lead to decoherence of the confined carrier states. The theoretical approach leading to a uniform, compact description of the phonon impact on carrier dynamics, perturbative in phonon couplings but applicable to arbitrary unperturbed evolution, is described in detail. Next, some applications are presented: phonon damping of Rabi oscillations in quantum dots and phonon-induced error of a single-qubit gate for an excitonic quantum dot qubit as well as for a semiconductor quantum dot spin qubit operated via a STIRAP transfer.
This Chapter contains a review of the recent results, both experimental and theoretical, related to optical control of carriers confined in semiconductor quantum dots. The physics of Rabi oscillations of exciton and biexciton occupations, as well as time-domain interference experiments are discussed. Next, the impact of carrier--phonon interaction in a semiconductor structure is described and modern methods of theoretical description of the carrier--phonon kinetics and of the resulting dephasing are presented.
This paper studies the carrier-phonon dynamics in the optical control of the spin states in a single doped semiconductor quantum dot by means of a perturbation theory describing the open system evolution under arbitrary driving and a correlation expansion technique. This paper considers the phonon-induced decoherence accompanying a single-qubit gate: an arbitrary rotation between two selected electron spin states performed via stimulated adiabatic Raman transitions and virtual excitation of a trion state. The error of the quantum gate as well as the population and coherence dynamics is calculated depending on the driving duration and detuning and study the possible reduction of the phonon decoherence.
We analyse various phonon-assisted mechanisms which contribute to the decoherence of excitonic qubits in quantum dot systems coupled by the Förster-type transfer process. We show the significant loss of coherence accompanied by dissipation due to charge carrier oscillations between qubit states by using a model of one-phonon assisted Förster-type transfer process. We obtain explicit expressions for the relaxation and dephasing times for excitonic qubits interacting with acoustic phonons via both deformation potential and piezoelectric coupling. We compare the decoherence times of the GaAs/AlGaAs material system with half times of concurrence decay in a 2$\otimes$2 bipartite mixed excitonic qubit system. We extend calculations to determine the influence of phonon mediated interactions on the non-unitary evolution of Berry phase in quantum dot systems.
We show that the interaction between carriers confined in a quantum dot and the surrounding lattice under external driving of carrier dynamics has a dynamical, resonant character. The quality of Rabi oscillations in such a system depends on the relation between nonlinear spectral characteristics of the driven dynamics and the spectral density of effectively coupled lattice modes (phonon frequencies and density of states). For a large number of Rabi oscillations within a fixed time (allowed by, e.g., exciton recombination) the spectrum of the dynamics extends towards high frequencies, coming into resonance with acoustic and optical phonons. Thus, this resonant lattice response strongly restricts the possibility of fully coherent control over the charge state in a quantum dot.
The paper discusses coherent control of charge and spin states of a biexciton system in a quantum dot via coherent two-photon transitions. Rabi oscillations between the ground state of a quantum dot and the biexciton state, as well as oscillations between the two single-exciton states induced by laser pulses with different circular or linear polarizations are studied. The effect of phonon-induced decoherence on these processes is described. System properties and driving conditions that lead to optimal coherent control are identified. It is shown that proper optimization allows one to control the two-qubit biexciton system via two-photon transitions with a high fidelity.