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Register a new userTime-optimal synthesis of SU(2) transformations for a spin-1/2 system
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Authors
A. D. Boozer
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We consider a quantum control problem involving a spin-1/2 particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the x-y plane, serves as a control parameter that can be varied to govern the evolution of the system. We analytically solve for the time dependence of the control parameter that will synthesize a given target SU(2) transformation in the least possible amount of time, and we show that the time-optimal solutions have a simple geometric interpretation in terms of the fiber bundle structure of SU(2). We also generalize our time-optimal solutions to a control problem that includes a constant bias field along the z axis, and to the case of inhomogeneous control, in which a single control parameter governs the evolution of an ensemble of spin-1/2 systems.
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We present measurements of a topological property, the Chern number ($C_mathrm{1}$), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract $C_mathrm{1}$ from the nonadiabitic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition $C_mathrm{1} = 1 rightarrow 0$. Our measurement of $C_mathrm{1}$ is quantized to within 2 percent on either side of the transition.
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We report the realization of a novel degenerate Fermi mixture with an SU(2)*SU(6) symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb with the nuclear spin I=1/2 and 173Yb with I=5/2 below the Fermi temperature T_ F as 0.46T_F for 171Yb and 0.54T_F for 173Yb. The same scattering lengths for different spin components make this mixture featured with the novel SU(2)*SU(6) symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the SU(2)*SU(6) Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.
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