Efficient entanglement operator for a multi-qubit system

In liquid-state NMR quantum computation, a selective entanglement operator between qubits 2 and 3 of a three-qubit molecule is conventionally realized by applying a pair of short $\pi$-pulses to qubit 1. This method, called refocusing, is well suited for heteronuclear molecules. When the molecule is homonuclear, however, the $\pi$-pulses applied to qubit 1 often induce unwanted $z$-rotations on qubits 2 and 3, even if the $z$-components of qubits 2 and 3 are left unchanged. This phenomenon is known as the transient Bloch-Siegert effect, and compensation thereof is required for precise gate operation. We propose an alternative refocusing method, in which a weak square pulse is applied to qubit 1. This technique has the advantage of curbing the Bloch-Siegert effect, making it suitable for both hetero- and homonuclear molecules.Comment: 11 pages, 4 figure

Topological Vortex Formation in BEC under Gravitational Field

Topological phase imprinting is a unique technique for vortex formation in a Bose-Einstein condensate (BEC) of alkali metal gas, in that it does not involve rotation: BEC is trapped in a quadrupole field with a uniform bias field which is reversed adiabatically leading to vortex formation at the center of the magnetic trap. The scenario has been experimentally verified by MIT group employing $^{23}$Na atoms. Recently similar experiments have been conducted at Kyoto University, in which BEC of $^{87}$Rb atoms has been used. In the latter experiments they found that the fine-tuning of the field reverse time $T_{\rm rev}$ is required to achieve stable vortex formation. Otherwise, they often observed vortex fragmentations or a condensate without a vortex. It is shown in this paper that this behavior is attributed to the heavy mass of the Rb atom. The confining potential, which depends on the eigenvalue $m_B$ of the hyperfine spin \bv{F} along the magnetic field, is now shifted by the gravitational field perpendicular to the vortex line. Then the positions of two weak-field-seeking states with $m_B=1$ and 2 deviate from each other. This effect is more prominent for BEC with a heavy atomic mass, for which the deviation is greater and, moreover, the Thomas-Fermi radius is smaller. We found, by solving the Gross-Pitaevskii equation numerically, that two condensates interact in a very complicated way leading to fragmentation of vortices, unless $T_{\rm rev}$ is properly tuned.Comment: 7 pages, 3 figures submitted to PR