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International Journal of Theoretical Physics

The Coherence Time of Quantum Rod Qubit

Chun-Yu Cai, Cui-Lan Zhao, Jing‐Lin Xiao

Published Sep 18, 2014• 1 citation
Publisher
DOI
10.1007/s10773-014-2324-1

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We study the tipping time of a quantum mechanical rod that is constrained to move in a plane in a gravitational potential. The initial state of the center of mass of the rod is localized within the base of support of the rod. The tipping time is found to increase exponentially with the height H of the rod as C1t0 exp[C2(H/H0)9], where C1 and C2 are dimensionless constants of order one, t0 is the time scale of the motion, and H0 is the length scale of the rod. We show that the tipping time cannot be obtained using the uncertainty principle alone, and compare our result to that obtained using the Wentzel–Kramers–Brillouin approximation.

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ABSTRACT A confinement‐engineered design framework is developed for CdSe quantum‐rod qubits by treating the radius and aspect ratio as independent control parameters. The qubit is encoded in the two lowest axially confined orbital states; finite‐barrier and dielectric‐mismatch corrections () shift the coherence ridge by only nm without altering the Pareto topology, as confirmed by a new corrected sub‐panel (Figure 3b). Phonon‐induced relaxation is modeled through deformation‐potential, piezoelectric, and Fröhlich channels within a Born–Markov framework whose validity is verified throughout the design space. Mapping the full plane reveals a coherence ridge near nm, , where the phonon‐relaxation‐limited approaches 100 ns at 4 K as an upper bound. The optically driven Rabi frequency increases with rod length, producing a Pareto trade‐off between coherence and gate speed. A four‐parameter sensitivity analysis (Table and Figure ) confirms the ridge and Pareto topology are robust to parameter variations. A Monte Carlo analysis with log‐normal size distributions (Figure ) validates the fabrication robustness metric and confirms the target nm, . A speed‐favored Pareto knee near nm, achieves GHz with ns and gate fidelities –0.99 after DRAG pulse shaping. An experimental control protocol and scalability limitations are discussed.
The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one. Under the condition of strong electron—longitudinal optical phonon coupling in the rod, we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method. This quantum rod system may be used as a two-level qubit. When the electron is in the superposition state of the ground and first-excited states, the probability density of the electron oscillates in the rod with a certain period. It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod, whereas it is a decreasing function of the electron—phonon coupling strength.
We study the tipping time of a quantum mechanical rod that is constrained to move in a plane in a gravitational potential. The initial state of the center of mass of the rod is localized within the base of support of the rod. The tipping time is found to increase exponentially with the height H of the rod as C1t0 exp[C2(H/H0)9], where C1 and C2 are dimensionless constants of order one, t0 is the time scale of the motion, and H0 is the length scale of the rod. We show that the tipping time cannot be obtained using the uncertainty principle alone, and compare our result to that obtained using the Wentzel–Kramers–Brillouin approximation.