研究了自旋为1的系统在绝对值为常数的磁场中的量子速降线问题。这样的系统使我们有可能详细检查论文的陈述[A.卡利尼{ \it等人}，物理修订版信函{ \bf 96}，060503（2006），D. C. Brody，D. W. Hook，J.Phys.A { \bf 39}，L167，（2006）]，{ \it，实现具有最小通过时间的演化的状态向量沿着由初始和最终状态向量跨越的子空间演化。}用显式例子证明了量子速降线的存在性，它具有最小的可能时间，但其状态向量在演化过程中{ \em离开}初始和最终状态向量所张成的子空间.这是选择更多约束的哈密顿量的结果，然后在一般的量子速降线问题中假设，但值得注意的是，尽管这样的演化更复杂，它仍然是时间最优的。这对于实验可能是重要的，其中具有所有允许参数的一般哈密顿量难以实现，但依赖于磁场的约束哈密顿量可以实现。然而，对于预约束哈密顿量，并非所有的最终状态都是可访问的。目前的结果并不矛盾的量子最速线问题的一般陈述，但提供了新的见解如何实现时间最优通道。
英文摘要：
We study quantum brachistochrone problem for the spin-1 system in a magnetic field of a constant absolute value. Such system gives us a possibility to examine in detail the statement of papers [A. Carlini {\it et al.}, Phys. Rev. Lett. {\bf 96}, 060503 (2006), D. C. Brody, D. W. Hook, J. Phys. A {\bf 39}, L167, (2006)] that {\it the state vectors realizing the evolution with the minimal time of passage evolve along the subspace spanned by the initial and final state vectors.} Using explicit example we show the existence of quantum brachistochrone with minimal possible time, but the state vector of which, during the evolution {\em leaves} the subspace spanned by the initial and final state vectors. This is the result of the choice of more constrained Hamiltonian then assumed in the general quantum brachistochrone problem, but what is worth noting, despite that such evolution is more complicated it is still time optimal. This might be important for experiment, where general Hamiltonian with the all allowed parameters is difficult to implement, but constrained one depending on magnetic field can be realized. However for pre-constrained Hamiltonian not all final states are accessible. Present result does not contradict general statement of the quantum brachistochrone problem, but gives new insight how time optimal passage can be realized.
We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the most brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with the fidelities over 99.2% on the spin state of nitrogen-vacancy center are realized with average durations shortened by 74.9%, comparing with conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds 96.5% on the hybrid spin registers. With these fast high-fidelity gates available, we implement quantum entanglement-enha…
Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising interaction
Chouaïb Doukkali University（舒艾卜杜卡利大学）；Mohammed V University in Rabat（拉巴特穆罕默德五世大学）；Ibn Zohr University（伊本·佐赫尔大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Prince Sultan University（苏丹王子大学）；Menoufia University（门尤菲亚大学）
Comprehending the connections between the geometric, topological, and dynamical structures of integrable quantum systems with quantum phenomena exploitable in quantum information tasks, such as quantum entanglement, is a major problem in geometric information science. In this work we investigate these issues in a physical system of $\mathcal{N}$ interacting spin-$\mathtt{s}$ under long-range Ising model. We discover the relevant dynamics, identify the corresponding quantum phase space and we derive the associated Fubini-Study metric. Through the application of the Gauss-Bonnet theorem and the …
Fermionic systems differ from bosonic ones in several ways, in particular that the time-reversal operator $T$ is odd, $T^2=-1$. For $PT$-symmetric bosonic systems, the no-signaling principle and the quantum brachistochrone problem have been studied to some degree, both of them controversially. In this paper, we apply the basic methods proposed for bosonic systems to {\it fermionic} two- and four-dimensional $PT$-symmetric Hamiltonians, and obtain several surprising results: We find - in contrast to the bosonic case - that the no-signaling principle is upheld for two-dimensional fermionic Hamil…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal quantum state control. We establish compact mechanisms for achieving time dependent unitary evolution, and present new calculation methods for time-ordered exponential operators. A powerful modification of the brachistochrone technique is presented that allows solution of a class of problems via matrix decomposition of the Hamiltonian. These techniques allow us t…
We study suppression of nonadiabatic transitions during adiabatic generation of a cat-like state (a superposition of different size cat states) and a spin squeezed state in a bosonic Josephson junction. In order to minimize the adiabatic error, we use quantum adiabatic brachistochrone, which enables us to track a geometrically efficient path in parameter space under given conditions without requiring additional terms. For creation of a cat-like state, divergence of the quantum geometric tensor associated with gap closing at the critical point is avoided because of the parity conservation. The …
In this paper, we briefly discuss the methodology for simulating a quantum computer which performs Shor's algorithm on a 7-qubit system to factorise 15. Using this simulation and the overlooked quantum brachistochrone method, we devised a Monte Carlo algorithm to calculate the expected time a theoretical quantum computer could perform this calculation under the same energy conditions as current working quantum computers. We found that, experimentally, a nuclear magnetic resonance quantum computer would take $1.59 \pm 0.04$ s to perform our simulated computation, whereas the expected optimal ti…
Single magnetic molecules may be the smallest functional magnets. An electric-field controllable spin state of magnetic molecules is of fundamental importance for applications while its realization remains challenging. To date the observed spin-electric interaction based on spin-orbit coupling or spin dipole coupling is useful to tune fine spin structures but too weak to flip the spin state. In this work, we propose a new mechanism to realize enhanced spin-electric coupling and flip the spin states by tuning the spin superexchange between local spins. Using first-principles calculations and He…
By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the non-relativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic field and an effective spin-orbit interaction generated by the spin connection. Geometrically, the pseudo-magnetic field is proportional to the Gaussian curvature and the effective spin-orbit interaction is determined by the Weingarten curvature tensor. Particularly, we find that the pseudo-magnetic field and the effective spin-orbit interaction can be employed to separ…
We investigate the formation of magnetic Bose polaron, an impurity atom dressed by spin-wave excitations, in a one-dimensional spinor Bose gas. In terms of an effective potential model the impurity is strongly confined by the host excitations which can even overcome the impurity-medium repulsion leading to a self-localized quasi-particle state. The phase diagram of the attractive and self-bound repulsive magnetic polaron, repulsive non-magnetic (Fr{\" o}hlich-type) polaron and impurity-medium phase-separation regimes is explored with respect to the Rabi-coupling between the spin components, sp…
An unusual regime for liquid-state nuclear magnetic resonance (NMR) where the magnetic field strength is so low that the $J$-coupling (intramolecular spin-spin) interactions dominate the spin Hamiltonian opens a new paradigm with applications in spectroscopy, quantum control, and in fundamental-physics experiments, including searches for well-motivated dark-matter candidates. An interesting possibility is to bring this kind of "extreme NMR" together with another one---single nuclear spin detected with a single-spin quantum sensor. This would enable single-molecule $J$-spectroscopy.
