Minimal Evolution Time Research Articles

Understanding two-photon double ionization of helium from the perspective of the characteristic time of dynamic transitions

By using the B-spline numerical method, we investigate a two-photon double-ionization (TPDI) process of helium in a high-frequency laser field with its carrier frequency ranging from 1.6 to 3.0 a.u. and the pulse duration ranging from 75 to 160 attoseconds. We found that there exists a characteristic time tc for a TPDI process, such that the pattern of energy distribution of two ionized electrons presents a peak or two, depending respectively on whether the pulse duration is shorter or longer than tc. Especially, when the pulse duration is larger than tc, the TPDI spectrum shows a double-peak structure which is attributed to the fact that most of the electron–electron Coulomb interaction energy is acquired by a single electron during their oscillation around the nucleus before the two electrons leave, and hence the double-peak structure cannot be identified as a signal of sequential ionization. Additionally, if the carrier frequency is less than the ionization energy of He+, i.e. that carrier frequency is in the so called correlated region, tc is not a fixed value, and it increases as the carrier frequency decreases; while if the carrier frequency is greater than the ionization energy of He+, i.e. the carrier frequency is in the so called non-correlated region, tc is fixed at about 105 attoseconds. We further found that, for a helium-like ion in its ground state, the characteristic time for when the carrier frequency is larger than the ionization energy of the second electron has a key relation with the Coulomb interaction energy between the two electrons, which can be expressed as , a type of quantum mechanical uncertainty relation between time and energy. In addition, this relation can be attributed to the existence of a minimal evolution time from the ground state to a double ionization state with two electrons carrying different energies. These results may shed light on a deeper understanding of many-electron quantum dynamical processes.

Quantum speed limit time for the damped Jaynes-Cummings and Ohmic-like dephasing models in Schwarzschild space-time

Quantum theory sets the bound on the minimal evolution time between initial and final states of the quantum system. This minimal evolution time can be used to specify the maximal speed of the evolution in open and closed quantum systems. Quantum speed limit is one of the interesting issue in the theory of open quantum systems. One may investigate the influence of the relativistic effect on the quantum speed limit time. When several observers are placed in different inertial or non-inertial frames, or in Schwarzschild space-time, the relativistic effect should be taken into account. In this work, the quantum speed limit time in Schwarzschild space-time will be studied for two various model consist of damped Jaynes-Cummings and Ohmic-like dephasing. First, it will be observed that how quantum coherence is affected by Hawking radiation. According to the dependence of quantum speed limit time on quantum coherence and the dependence of quantum coherence on relative distance of quantum system to event horizon R_{0}, it will be represented that the quantum speed limit time in Schwarzschild space-time is decreased by increasing R_{0} for damped Jaynes-Cummings model and conversely. It is increased by increasing R_{0} for Ohmic-like dephasing model.

Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels

The minimal evolution time between two distinguishable states is of fundamental interest in quantum physics. Very recently Mirkin et al. argue that some most common quantum-speed-limit (QSL) bounds which depend on the actual evolution time do not cleave to the essence of the QSL theory as they grow indefinitely but the final state is reached at a finite time in a damped Jaynes-Cummings (JC) model. In this paper, we thoroughly study this puzzling phenomenon. We find the inconsistent estimates will happen if and only if the limit of resolution of a calculation program is achieved, through which we propose that the nature of the inconsistency is not a violation to the essence of the QSL theory but an illusion caused by the finite precision in numerical simulations. We also present a generic method to overcome the inconsistent estimates and confirm its effectiveness in both amplitude-damping and phase-damping channels. Additionally, we show special cases which may restrict the QSL bound defined by "quantumness".

Generalized Geometric Quantum Speed Limits

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the non uniqueness of a bona fide measure of distinguishability defined on the quantum state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

Minimal evolution time and quantum speed limit of non-Markovian open systems.

We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized Hamiltonian and dissipator. For a non-Markovian quantum open system, the possible evolution time between two arbitrary states is not unique, among the set of which we find that the minimal one and its QSL can decrease more steeply by adjusting the coupling strength of the dissipator, which thus provides potential improvements of efficiency in many quantum physics and quantum information areas.

The initial-state dependence of the quantum speed limit

The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with a structural environment is investigated. We define a new bound for the quantum speed limits. It is shown that the non-Markovianity and the population of the excited state can fail to signal the quantum evolution acceleration, but the initial-state dependence is an important factor. In particular, we find that different quantum speed limits could produce contradictory predictions on the quantum evolution acceleration.

Quantum speed limit for arbitrary initial states

The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.

Quantum Speed Limit for Non-Markovian Dynamics

We derive a Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply these results to the damped Jaynes-Cummings model and demonstrate that the corresponding bound is tight. We further show that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.

Quantum Speed Limit for Physical Processes

The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.