اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTime-optimal synthesis of SU(2) transformations for a spin-1/2 system
78
0
0.0
(
0
)
تأليف
A. D. Boozer
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 o
f 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.
In this work we demonstrate new BCH-like relations involving the generators of the su(1, 1), su(2) and so(2, 1) Lie algebras. We use our results to obtain in a straightforward way the composition of an arbitrary number of elements of the correspondin
g Lie groups. In order to make a self-consistent check of our results, as a first application we recover the non-trivial composition law of two arbitrary squeezing operators. As a second application, we show how our results can be used to compute the time evolution operator of physical systems described by time-dependent hamiltonians given by linear combinations of the generators of the aforementioned Lie algebras.
We consider extension of the standard model $SU(2)_l times SU(2)_h times U(1)$ where the first two families of quarks and leptons transform according to the $SU(2)_l$ group and the third family according to the $SU(2)_h$ group. In this approach, the
largeness of top-quark mass is associated with the large vacuum expectation value of the corresponding Higgs field. The model predicts almost degenerate heavy $W$ and $Z$ bosons with non-universal couplings, and extra Higgs bosons. We present in detail the symmetry breaking mechanism, and carry out the subsequent phenomenology of the gauge sector. We compare the model with electroweak precision data, and conclude that the extra gauge bosons and the Higgs bosons whose masses lie in the TeV range, can be discovered at the LHC.
In this paper we revisit the isomorphism $SU(2)otimes SU(2)cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generaliz
ed from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
