We discuss bounds for nonadiabatic transitions from the viewpoints of the adiabatic perturbation theory and the quantum speed limit. We show that the amount of nonadiabatic transitions from the $n$th level to the $m$th level is bounded by a function of the quantum geometric tensor for the $m$th level. We analyze this bound from the viewpoint of the adiabatic perturbation theory. In addition, this bound and the viewpoint of the quantum speed limit suggest nontrivial relationship between the dynamical transformation and the adiabatic transformation. We also derive a universal bound for any nonadiabatic transition. This bound is written in terms of the counterdiabatic Hamiltonian.
We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sub-lattices are suppressed in the nearly-adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.
We propose a scheme which can produce desired nonadiabatic passages for the stimulated Raman transition in three-level systems. The state transfer in the protocol is realized by following the evolution of the dynamical basis itself and no additional coupling field is required. We also investigate the interplay between the present nonadiabatic protocol and the shortcut to adiabaticity. By incorporating the latter technology, we show that alternative passages with less occupancy of the intermediate level could be designed.
We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasi-spins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from nonadiabatic to adiabatic regime. In the adiabatic regime, the quasi-spins trace the time dependent effective magnetic field and then oscillate between spin up and…
We present a means of studying rare reactive pathways in open quantum systems using Transition Path Theory and ensembles of quantum jump trajectories. This approach allows for elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes, as well as the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the tr…
We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely on prior knowledge of transition states or reactive pathways, and thus can provide mechanistic insight into ultrafast relaxation processes in addition to their associated rates. In particular, we formulate a quantum path ensemble using the stochastic realizations of an unravelled quantum master equation, which results in trajectories that can be conditioned o…
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 …
Since the pioneering works by Landau, Zener, Stückelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for engineering quantum systems. Here, we study systematically various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in [Shevchenko, S. N., S. Ashhab, and F. Nori (2010), "Landau-Zener-Stückelberg interferom…
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that pr…
We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in a finite-temperature heat bath. A Born-Markovian quantum master equation is formally derived for the time-dependent system with discrete energy levels. This quantum master equation can be applied to situations with a broad range of driving speeds and bath temperatures and thus be used to study the finite-time quantum thermodynamics even when nonadiabatic transition and dissipation coexist. The dissipative Landau-Zener model is analyzed as an example. The population evolution and transition pro…
Nonadiabatic transitions in non-Hermitian $\mathcal{PT}$-symmetric two-level systems
College of Physics, Sichuan University（四川大学物理学院）；Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University（教育部高能密度物理与技术重点实验室）；Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University（福建省量子信息与量子光学重点实验室，福州大学物理与信息工程学院）
Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. In this paper we propose a control protocol using a tangent-pulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by…
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, $H_I$. Here, we point to the existence of an analytical solution for such a problem for an arbitrary $H_I$ beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotoni…
Accelerating quantum adiabatic evolution with $π$-pulse sequences
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University（清华大学低维量子物理国家重点实验室和物理系）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels a…
The nonadiabatic photodissociation dynamics of alkali halide molecules excited by a femtosecond laser pulse in the gas phase are investigated theoretically, and it is shown that the population of the photoexcited molecules exhibits power-law decay with exponent -1/2, in contrast to exponential decay, which is often assumed in femtosecond spectroscopy and unimolecular reaction theory. To elucidate the mechanism of the power-law decay, a diagrammatic method that visualizes the structure of the nonadiabatic reaction dynamics as a pattern of occurrence of dynamical events, such as wavepacket bifur…
Fermi's golden rule rate expression for transitions due to nonadiabatic derivative couplings in the adiabatic basis
Queens College, City University of New York（纽约市立大学皇后学院）；Graduate Center of the City University of New York（纽约市立大学研究生中心）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
Selective excitation in a three-state system using a hybrid adiabatic-nonadiabatic interaction
绝热耦合区中的啁啾脉冲相互作用导致了$V$型三能级系统能态的循环排列，这一过程被称为三能级啁啾快速绝热通过。在这里，我们表明，在啁啾脉冲的光谱孔可以打开和关闭的两个绝热交叉点的这个过程中，减少系统的一个有效的二能级系统。给定的混合绝热-非绝热跃迁的结果在三能级系统的选择性激发，控制的激光强度和光谱位置的孔，以及啁啾参数的符号。利用整形飞秒激光脉冲和铷原子（$^{85}$ Rb）的三个最低能级（5S $_{1/2}$、5 P $_{1/2}$和5 P $_{3/2}$）进行了实验，实验结果与理论分析的动力学结果吻合较好.结果表明，我们的方法与普通的啁啾RAP相结合，实现了两个激发态之间的绝热跃迁。此外，当与激光束轮廓编程结合使用时，依赖于激光强度的控制可以具有包括选择性激发空间中布置的原子或离子的应用。
Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we de…
Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe
继我们之前的论文Bergeron et al，Smooth quantum dynamics of the mixmaster universe，Phys. Rev. D 92，061302（R）（2015），关于真空Bianchi IX模型和Born-Huang-Oppenheimer框架的量子化，我们提出了模型动力学性质的进一步分析。与深量子机制一致，我们实现了各向异性势的谐波近似。因此，我们得到可管理的动力学方程。我们研究了宇宙弹跳阶段的量子各向异性振荡。忽略量子各向异性态之间的跃迁的反反应，我们得到了解析结果。特别是，我们确定了一个参数，这是与量子模型的动力学性质，并描述了一种相变。一旦参数超过临界值，玻恩-黄-奥本海默近似就失效了。将本结果应用于一个简单的宇宙模型表明，该参数确实超过了其临界值，并且在反弹时产生了巨大的各向异性。这反过来必然导致一个持续的加速扩张阶段，即通货膨胀阶段。应在基于电子振动方法的后续论文中检查反向反应的定量包含。
