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Physical Review A

Demonstration of pure geometric universal single-qubit operation on two-level atoms

Hiromitsu Imai, Atsuo Morinaga

Published Jul 2, 2008• 7 citations
Publisher

Abstract

With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.

DOI
10.1103/physreva.78.010302

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Physical Review A•Feb 9, 2009•3 citations
With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.
The geometric manipulation of the quantum states of two-level atoms with two laser-controlled resonant $\ensuremath{\pi}$ pulses with a relative phase difference was evaluated using a time-domain atom interferometer comprising a cold sodium atom ensemble and two copropagating two-photon Raman pulses. It was verified that the relative phase shift between two states is double the control phase difference and that the rotation around the axis 3 of the Bloch sphere can be controlled by geometric manipulation.
The quantum states of cold ensemble of two-level atoms were rotated around axis 2 on the Bloch sphere geometrically using a laser-controlled resonant pulse sequence with pulse areas of $\ensuremath{\pi}∕2$, $\ensuremath{\pi}$, and $\ensuremath{\pi}∕2$, whose central pulse has a relative phase difference of $\ensuremath{\pi}+\ensuremath{\delta}∕2$. It was ascertained that the population probability of the excited state varies according to a sinusoidal function of $\ensuremath{\delta}$ within an uncertainty of 1%. Hybrid operations of two-level atoms were realized combining the geometrical operation with the Rabi excitation around axis 2 or the time evolution around axis 3.
We demonstrate two types of basic Bloch vector rotations in thulium ion ensemble embedded in yttrium aluminum garnet crystal based on our previous work that designed the appropriate Hamiltonians driving Bloch vector rotations through geometric evolution in two-level atom. The angles of the geometric rotations were controlled by the relative phases of the laser pulses driving the rotations. The rotation angles were measured using photon echoes and compared with the corresponding theoretical values. The operation fidelity was calculated for both demonstrated rotations that resulted in average values of 94.00 and 99.96%, respectively. The schemes to improve the operation fidelity will be discussed.