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arXiv:cond-mat/0412503 · Physical Review B

Charge qubit dynamics in a double quantum dot coupled to phonons

Zhuo-Jie Wu, Ka‐Di Zhu, Xiao-Zhong Yuan, Yiwen Jiang, Hang Zheng

Published May 31, 2005• 52 citations
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Abstract

The dynamics of charge qubit in a double quantum dot coupled to phonons is investigated theoretically in terms of a perturbation treatment based on a unitary transformation. The dynamical tunneling current is obtained explicitly. The decoherence induced by acoustic phonons is analyzed in detail after a derivation of spectral density. It is shown that the contribution from deformation potential coupling is comparable to that from piezoelectric coupling in small dots and large tunneling rates. A possible decoupling mechanism is predicted.

DOI
10.1103/physrevb.71.205323

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The dynamics of charge qubit in a double quantum dot coupled to phonons is investigated theoretically in terms of a perturbation treatment based on a unitary transformation. The dynamical tunneling current is obtained explicitly. The decoherence induced by acoustic phonons is analyzed in detail after a derivation of spectral density. It is shown that the contribution from deformation potential coupling is comparable to that from piezoelectric coupling in small dots and large tunneling rates. A possible decoupling mechanism is predicted.
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We investigate the dynamics of a double quantum dot charge qubit which is coupled to piezoelectric acoustic phonons, appropriate for GaAs heterostructures. At low temperatures, the phonon bath induces the non-Markovian dynamical behavior of the oscillations between the two charge states of the double quantum dot. Upon applying the numerically exact quasiadiabatic propagator path-integral scheme, the reduced density matrix of the charge qubit is calculated, thereby avoiding the Born-Markov approximation. This allows a systematic study of the dependence of the QQQ factor on the lattice temperature, on the size of the quantum dots, as well as on the interdot coupling. We calculate the QQQ factor for a recently realized experimental setup and find that it is two orders of magnitudes larger than the measured value, indicating that the decoherence due to phonons is a subordinate mechanism.
We study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born--Markov approximation. After including appropriate form factors, we find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. We calculate the dependence of the QQQ factor on lattice temperature, quantum dot size, and interdot coupling. Our results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.
We have studied the dynamics of charge qubit with the static bias by a perturbation treatment based on unitary transformations. The approach can be practiced for various forms of the spectral density and the usual Ohmic and piezoelectric spectra are used in our calculations. Analytical results of the quantum dynamics, described by the population inversion P(t)P(t)P(t), are obtained together with the damping rate and the oscillation frequency. We find that a weak coupling of the qubit to the environment leads to a higher coherence oscillation frequency and a longer coherence time. For a fixed tunneling between the double quantum dots, the finite bias enhances the oscillation frequency effectively but its effect on the damping rate is relatively small. This is a possible way to maintain quantum coherence.
The decoherence dynamics of two charge qubits in a double quantum dot is investigated theoretically. We consider the quantum dynamics of two interacting electrons in a vertically coupled quantum dot driven by an external electric field. We derive the equations of motion for the density matrix, in which the presence of an electron confined in the double dot represents one qubit. A Markovian approach to the dynamical evolution of the reduced density matrix is adopted. We evaluate the concurrence of two qubits in order to study the effect of acoustic phonons on the entanglement. We also show that the disentanglement effect depends on the double dot parameters and increases with the temperature.