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arXiv:0909.0064 · Physical Review B

Optical rotation of heavy hole spins by non-Abelian geometrical means

Hui Sun, Xun‐Li Feng, Chunfeng Wu, Jinming Liu, Shangqing Gong, C. H. Oh

Published Dec 3, 2009• 10 citations
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Abstract

A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about $y$ and $z$ axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole-spin-state readout are also possible.

DOI
10.1103/physrevb.80.235404

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A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about yyy and zzz axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole-spin-state readout are also possible.
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We demonstrate coherent optical control of a single hole spin confined to an InAs/GaAs quantum dot. A superposition of hole-spin states is created by fast (10-100 ps) dissociation of a spin-polarized electron-hole pair. Full control of the hole spin is achieved by combining coherent rotations about two axes: Larmor precession of the hole spin about an external Voigt geometry magnetic field, and rotation about the optical axis due to the geometric phase shift induced by a picosecond laser pulse resonant with the hole-trion transition.
A method is proposed for the optical rotation of the spin of an electron in a quantum dot using excited trion states to implement operations significantly faster than those of most existing proposals. Key ingredients are the geometric phase induced by 2pi hyperbolic secant pulses, use of coherently trapped states and use of naturally dark states. Our proposal covers a variety of quantum dots by addressing different parameter regimes. Numerical simulations with typical parameters for InAs self-assembled quantum dots, including their dissipative dynamics, give fidelities of the operations in excess of 99%.
A basic system with important potential applications in quantum technologies is a quantum dot in the Voigt geometry. The spin states of the quantum dot in the Voigt geometry can act as a prototype qubit which can be manipulated by applied optical fields in order to produce the necessary quantum gates. The basic method for spin initialization in a quantum dot in the Voigt geometry is optical pumping. Here, we propose and analyze a new method for the coherent preparation of the quantum dot spin states based on adiabatic control methods. Specifically, we show that the application of two mutually delayed and partially overlapping optical pulses, similar to those used in stimulated Raman adiabatic passage, can lead to initialization of one of the spin states with high fidelity. We also demonstrate that the fidelity of the method may be increased by integrating the quantum dot with a micropillar cavity. Specifically, we show that a preferential Purcell-enhanced decay rate towards the target spin state, in certain cases, increases the fidelity of spin initialization of the adiabatic method. Our results are based on the numerical solution of the relevant density matrix equations for the quantum dot system, either in an isotropic photonic environment or in a micropillar cavity. The calculations presented in this paper are not limited to quantum dots in micropillar cavities. Similar effects can be obtained by other photonic structures as well, as for example, for quantum dots in photonic crystal cavities.
We introduce a non-abelian geometric quantum energy pump realized by a transitionless geometric quantum drive--a time-dependent Hamiltonian supplemented by a counterdiabatic term generated by a prescribed trajectory on a smooth control manifold--that coherently transports states within a degenerate subspace. When the coordinates of the trajectory are independently addressable by external drives, the net energy transferred between drives is set by the non-abelian Berry-curvature tensor. The trajectory-averaged pumping power is separately controlled by the initial state and by the Hamiltonian topology through the Euler class. We outline an implementation with artificial atoms, which are realizable on various platforms including trapped atoms/ions, superconducting circuits, and semiconductor quantum dots. The resulting energy pump can serve as a quantum transducer or charger, and as a metrological tool for measuring phase coherences in quantum states.
We demonstrate optical control of the geometric phase acquired by one of the spin states of an electron confined in a charge-tunable InAs quantum dot via cyclic 2pi excitations of an optical transition in the dot. In the presence of a constant in-plane magnetic field, these optically induced geometric phases result in the effective rotation of the spin about the magnetic field axis and manifest as phase shifts in the spin quantum beat signal generated by two time-delayed circularly polarized optical pulses. The geometric phases generated in this manner more generally perform the role of a spin phase gate, proving potentially useful for quantum information applications.