Quantum State Transitions Research Articles

The fewest switches surface hopping as an optimisation problem

Several ways of defining the probabilities of quantum state transitions in nonadiabatic trajectory surface hopping simulations have been proposed and successfully applied to date. Despite their success, there is a question about the uniqueness of the ways to define such probabilities – some formulations require mathematically-motivated but still ad hoc assumptions to resolve the otherwise under-determined problem. In this work, I present a new approach (termed FSSH-3) to define the hop proposal probabilities. Unlike other approaches, it does not require any ad hoc assumptions and is based on the least squares optimisation of certain functionals combined with particular choices of initial conditions for the target variables. A comprehensive comparative study of several established surface hopping methodologies is conducted using several multiple-state model Hamiltonians. The recently reported formulation of the FSSH-2 method is extended to the case of multiple states and validated. It is demonstrated that the performance of all studied methods, including the new FSSH-3 (in two variants) is robust with respect to integration time step used but only if local diabatisation approach is used. Under such conditions, all methods yield nearly identical results, in excellent agreement with fully quantum simulations, even with sufficiently large integration time steps.

Reformulating the Quantum Uncertainty Relation through Geometric Illustrations

The uncertainty principle stands as a fundamental tenet within the realm of quantum theory. In this study, we embark on a reexamination of an emerging variant of the uncertainty relation within both pure and mixed quantum systems, leveraging a geometric elucidation. Subsequently, an enhancement to this relation is achieved by the incorporation of a surface angle denoted as θ , thereby transforming it from an inequality into an equation. Notably, this surface angle encapsulates the dynamics inherent in quantum state transitions. Complementing our analysis, a series of calculations are conducted, yielding results that offer an intuitive elucidation of the uncertainty relation across distinct quantum states. Consequently, this method bears significance as a pivotal visual insight within the domain of quantum information and measurement.

Estimation of optimal control for two-level and three-level quantum systems with bounded amplitude

Abstract A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state transitions are studied as illustration. Comparisons between numerical and analytical results are made, and deviations are significantly small. For the three-level system, two critical time points are determined with high accuracy, and optimal controls are obtained for different durations. The shape of optimized control field is simple and does not switch frequently, thus are easy to implement in experiment. In addition, we compare our method with the chopped random basis (CRAB), and the performance of our method is much better than that of CRAB. Our scheme is of importance in estimating the quantum speed limit and optimal control for cases in which analytical solution is absent.

A LINDBLADIAN OPERATOR FOR OPEN SYSTEM THERMALIZATION, WITH APPLICATIONS

A general phenomenological expression is provided, within the frame of the Gorini-Kossakowski-Sudarshan-Lindblad formalism, for the time (t) development of the density operator ρ(t) during thermalization, namely the process such that an open system with arbitrary initial states, when coupled to a thermal bath, ρ (t -> ∞) takes up a Gibbsian form. The theory is applied to a molecular vibrating system, to a semi-classical vibronic entity, and may be applied to the excitation probabilities in a condensed state’s phonon system and to arbitrarily large-scale systems (reaching as far as global warming). A sideline is to an entropy-decreasing Maxwell-demon type quantum state transition. While the prescription may not be unique, it gives rise to an experimentally testable non-monotonicity in the system’s information entropy. The calculated entropy maximum found for an electronic doublet is interpreted as a “transient democratization” of the states and, though lacking a formal proof, a conjecture is proposed for the occurrence of maxima in general instances.

Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger’s preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of interstate phase differences in a deterministic, rather than random, process of multiphoton absorption. Alternate halves of the Rabi cycle exhibit phase reversals much like the classical beats of coupled oscillators. For non-zero detuning, population inversion does not occur because the exciting field drifts out of the proper phase before inversion is complete. A close correspondence with classical, coupled oscillator beats offers insights for interpretation of deterministic quantum dynamics and suggests an experimental test for the correctness of this picture depending on the long-time phase stability of exciting fields.

State control strategy of open quantum systems by reverse engineering: via homodyne-based feedback control

Quantum state transition is the core content of quantum control. This paper presents a control scheme of the state evolution path based on feedback control and reverse engineering design. To achieve high-precision state transition, we first adopt a homodyne-based feedback control strategy to form a closed-loop system. Then, based on the idea of reverse engineering design, the state evolution path of the system is planned and designed by considering the influence of environment decoherence on the state evolution. Numerical simulation results show that the control pulse based on planning design can drive the system from any initial state to the desired target state, and the coherence of the system is effectively protected during state transition.

P‐82: Prediction Methodology for the Optical Properties of QDs with Arbitrary 3D Shape

Recently, researchers have strived to enhance the optical characteristics of Quantum Dots (QDs) by carefully tailoring the QD material composition, shape and size. In this endeavor, simulation proves an invaluable tool to assess and optimize the QD structure. In this paper, the optical properties of QD structures are explored, taking into account the complex band structure of the QD and its geometric structure, as well as the probability of quantum state transitions. In order to perform this analysis the In‐house Simulator (DaVinci_QD), based on 3D FEM, was developed and applied. We demonstrate that the DaVinci_QD simulator exhibits good agreement with experiment, providing confidence that the tool be applied to predict optical characteristics with accuracy. The simulator is applied to state‐of�the‐art QDs that are currently under development, offering additional insight to aid in the analysis of optical measurements and revealing paths to further performance enhancement. In this way, simulation can replace experiment and QD structures can be optimized rapidly.

Fluctuation-dissipation relations for thermodynamic distillation processes.

The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterize optimal thermodynamic distillation processes, and then we prove a relation between the amount of free energy dissipated in such processes and the free-energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or an arbitrary number of independent energy-incoherent systems, and they allow not only for a state transformation but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure, and thermodynamically free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N.

Ultrafast intraband Auger process in self-doped colloidal quantum dots

Summary Investigating the separate dynamics of electrons and holes has been challenging, although it is critical for the fundamental understanding of semiconducting nanomaterials. n-Type self-doped colloidal quantum dots (CQDs) with excess electrons occupying the low-lying state in the conduction band (CB) have attracted a great deal of attention because of not only their potential applications to infrared optoelectronics but also their intrinsic system that offers a platform for investigating electron dynamics without elusive contributions from holes in the valence band. Here, we show an unprecedented ultrafast intraband Auger process, electron relaxation between spin-orbit coupling states, and exciton-to-ligand vibrational energy transfer process that all occur exclusively in the CB of the self-doped β-HgS CQDs. The electron dynamics obtained by femtosecond mid-infrared spectroscopy will pave the way for further understanding of the blinking phenomenon, disproportionate charging in light-emitting diodes, and hot electron dynamics in higher quantum states coupled to surface states of CQDs.

Quantum Entanglement Results from Quantum State Transition at Fast-Than-Light Speed with Matter Wave’s Phase Velocity

The quantum entanglement, that violates the local realism and other classical physics theories, leads to various counterintuitive phenomena, is a primary feature of quantum mechanics and probably results from the quantum state’s conservation and the quantum state’s transition with the matter wave’s phase velocity at the fast-than-light speed. The quantum state transition of entangled particles proceeds with the phase velocity, while the observer measures the process with the electromagnetic or the light speed. This speed difference makes the causality law no longer fully valid everywhere except in certain areas.

Mathematics of the classical and the quantum

Newtonian and Schrödinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. The Newtonian dynamics was shown to be the Schrödinger dynamics of states constrained to a submanifold of the space of states, identified with the classical phase space of the system. Quantum observables are identified with vector fields on the space of states. The commutators of observables are expressed through the curvature of the space. The resulting embedding of the Newtonian and Schrödinger dynamics into a unified geometric framework is rigid in the sense that the Schrödinger dynamics is a unique extension of the Newtonian one. Under the embedding, the normal distribution of measurement results associated with a classical measurement implies the Born rule for the probability of transition of quantum states. The mathematics of the discovered relationship between the classical and the quantum is reviewed and investigated here in detail and applied to the process of measurement of spin and position observables.

Coulomb Blockade Spectroscopy of a MoS2 Nanotube

Low‐temperature transport spectroscopy measurements on a quantum dot lithographically defined in a multiwall MoS2 nanotube are demonstrated. At T = 300 mK, clear Coulomb blockade is observed, with charging energies in the range of 1 meV. In single‐electron tunneling, discrete conductance resonances are visible at finite bias. Additionally, a magnetic field perpendicular to the nanotube axis reveals clear indications of quantum state transitions, with effective g factors consistent with published theoretical predictions.

Structure and properties of nature clathrate and its application in energy and enviromental science

Clathrate hydrates are energy and environmental related materials for energy storage and extraction, as well as for waste gas sequestration. The three general structures of natural clathrates, structure I, structure Ⅱ and structure H are reviewed in the aspects of stability, cage size, and preferred guest molecule encapsulation. Neutron scattering technique has its unique advantage of clathrate hydrates characterization, such as large bulk property determination, penetration of high pressure vessel and the clathrate sample inside, sensitive to light elements (clathrate hydrates mainly containing C, H, and O atoms). Neutron diffraction and inelastic neutron scattering of clathrate hydrates are covered on the abilities of H/D atoms positions and anisotropic thermal parameters, pressure-temperature-dependent guest molecule occupancy, the disordered distributions of guest molecules and the nuclear density distributions, the thermodynamic and kinetic process of formation and decomposition, the translational and rotational vibration models of guest molecules and their quantum state transitions. Using CO<sub>2</sub> to gently replace CH<sub>4</sub> in methane hydrate is one of the most attractive exploiting schemes for its benefits to both geologic hazard consideration and cost efficiency (energy extraction and CO<sub>2</sub> sequestration).

Parameters adaptive adjustment strategy of quantum communication channel in free-space based on software-defined quantum communication

Quantum communication in free space will be disturbed by natural environment, such as fog, dust, and rain, which is a difficult problem in the construction of quantum communication system. In order to solve this problem and improve the survivability of quantum communication system, we propose an adaptive parameter adjustment strategy for free-space quantum communication based on software-defined quantum communication (SDQC). Firstly, we propose a software-defined quantum communication model based on the idea of software defined networks. The architecture of SDQC is divided into four layers: transport layer, access layer, control layer, and management layer. The SDQC system sends the link information to the preset program at a management level through the real-time monitoring of channel state by the access layer. According to the link information, the management level issues instructions to the control layer to adjust the parameters such as the initial quantum state and the existence time of single quantum state, in order to improve the quantum entanglement and fidelity. Secondly, we analyze the relationship between quantum fidelity and parameters in SDQC system under three noise channels, i.e. depolarization channel, spontaneous amplitude decay channel, and phase damping channel. In the depolarized channel, the quantum fidelity <i>F</i> decreases with the increase of the error probability <i>P</i><sub>d</sub> of the qubit. When the error probability of qubit is certain, the system has the maximum quantum fidelity with the value of parameter <i>x</i> is 0.5. In the spontaneous amplitude decay channel, the quantum fidelity <i>F</i> decreases with the increase of the quantum state transition probability <i>p</i><sub>t</sub>. When the transition probability of quantum state is certain, the higher the value of parameter <i>x</i>, the higher the fidelity will be. In the phase-damped channel, the quantum fidelity <i>F</i> decreases with the increase of the probability <i>p</i><sub>c</sub> with which the qubit and the background interference equivalent quantum state have complete elastic scattering. When the probability is certain, the larger the value of |1/2 – <i>x</i>|, the higher the quantum fidelity of the system will be. Finally, we study the optimal values of SDQC system parameters under different environmental disturbances. The simulation results show that the optimal parameters of SDQC system are different when the parameters of three noise channels, namely depolarization, spontaneous amplitude decay and phase damping, are different. The system adaptively selects the initial quantum state and the existence time of single quantum state according to the environmental change and business demand, so that the quantum fidelity is always at the peak in the communication process. This strategy effectively improves the adaptability and comprehensive immunity of the quantum communication system.

Free and bound entanglement dynamics in qutrit systems under Markov and non-Markov classical noise

We investigate in detail the dynamics of decoherence, free and bound entanglements, and the conversion from one to another (quantum state transitions), in a two non-interacting qutrits system initially entangled and subject to independents or a common classical noise. Both Markovian and non-Markovian environments are considered. Furthermore, isotropic and bound entangled states for qutrits systems are considered as initial states. We show the efficiency of the formers over the latters against decoherence, and in preserving quantum entanglement. The loss of coherence increases monotonically with time up to a saturation value depending upon the initial state parameter and is stronger in a collective Markov environment. For the non-Markov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is deduced depending on both the peculiar characteristics of the noise, the physical setup and the initial state of the system. We demonstrate distillability sudden death for conveniently selected parameters in bound entangled states; meanwhile, it is completely absent for isotropic states, where entanglement sudden death is avoided for dynamic noise independently of the noise regime and the physical setup. Our results indicate that distillability sudden death under the Markov/non-Markov noise considered can be avoided depending upon the physical setup.

Interplay between Landau-Zener transition dynamic and quantum phase transition in dissipative spin chain with Dzyaloshinsky-Moriya interaction

The paper investigates the transition dynamic of a two-level system coupled uniformly to a general XY dissipative spin-chain environment with the Dzyaloshinsky-Moriya interaction. The collective effect of the spin-chain environment is studied and we obtained the exact expression of the final occupation of the system. It is observed that the increase of the decay parameter favors a shortcut to adiabaticity. In the absence of decay, the transition probability oscillations are modulated in time by the renormalized Landau-Zener (LZ) parameter that we derived. We found that in the vicinity of the critical point of the environment, depending on the strength of the system-environment coupling, the decay of the population transfer can be tailored by tuning the other parameters of the model. The critical point and thus the occurrence of the phase transition are observed to be independent of these parameters. It is shown that this quantum state transition is related to the occurrence of the quantum phase transitions in the chain. The adiabatic change for the magnetization observed in some magnetic molecules may be due to the number of spin involved in the chain, the anisotropy parameter of the chain or the external magnetic field strength.

Higher Quantum State Transitions in Colloidal Quantum Dot with Heavy Electron Doping

Electron occupation in the lowest quantized state of the conduction band (1Se) in the colloidal quantum dot leads to the intraband transition in steady-state (1Se-1Pe). The intraband transition, solely originating from the quantum confinement effect, is the unique property of semiconducting nanocrystals. To achieve the electron occupation in 1Se state in the absence of impurity ions, nonthiol ligand passivated HgS colloidal quantum dots are synthesized. The nonthiol ligand passivated HgS quantum dot exhibits strong steady-state intraband transition in ambient condition and enables a versatile ligand replacement to oxide, acid, and halide functional ligands, which was not achievable from conventional HgS or HgSe quantum dots. Surprisingly, the atomic ligand passivation to HgS colloidal quantum dot solution efficiently maintains the electron occupation at 1Se of HgS CQDs in ambient condition. The electron occupation in 1Se of HgS CQD solid film is controlled by surface treatment with charged ions, which is ...

Quantum Zeno effect in the strong measurement regime of circuit quantum electrodynamics

We observe the quantum Zeno effect—where the act of measurement slows the rate of quantum state transitions—in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following amplifier. Under simultaneous strong measurement and qubit drive, the qubit undergoes a series of quantum jumps between states. These jumps are visible in the experimental measurement record and are analyzed using maximum likelihood estimation to determine qubit transition rates. The observed rates agree with both analytical predictions and numerical simulations. The analysis methods are suitable for processing general noisy random telegraph signals.

Can quantum coherent solar cells break detailed balance?

Carefully engineered coherent quantum states have been proposed as a design attribute that is hypothesized to enable solar photovoltaic cells to break the detailed balance (or radiative) limit of power conversion efficiency by possibly causing radiative recombination to be suppressed. However, in full compliance with the principles of statistical mechanics and the laws of thermodynamics, specially prepared coherent quantum states do not allow a solar photovoltaic cell—a quantum threshold energy conversion device—to exceed the detailed balance limit of power conversion efficiency. At the condition given by steady-state open circuit operation with zero nonradiative recombination, the photon absorption rate (or carrier photogeneration rate) must balance the photon emission rate (or carrier radiative recombination rate) thus ensuring that detailed balance prevails. Quantum state transitions, entropy-generating hot carrier relaxation, and photon absorption and emission rate balancing are employed holistically and self-consistently along with calculations of current density, voltage, and power conversion efficiency to explain why detailed balance may not be violated in solar photovoltaic cells.

Robustness of controlled quantum dynamics

The control of multilevel quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can cause an otherwise optimal field to deviate from controlling desired quantum state transitions and reaching a particular objective. An accurate analysis of robustness is thus essential in understanding and achieving model-based quantum control, such as in the control of chemical reactions based on ab initio or experimental estimates of the molecular Hamiltonian. In this paper, theoretical foundations for quantum control robustness analysis are presented from both a distributional perspective---in terms of moments of the transition amplitude, interferences, and transition probability---and a worst-case perspective. Based on this theory, analytical expressions and a computationally efficient method for determining the robustness of coherently controlled quantum dynamics are derived. The robustness analysis reveals that there generally exists a set of control pathways that are more resistant to destructive interferences in the presence of control field and system parameter uncertainty. These robust pathways interfere and combine to yield a relatively accurate transition amplitude and high transition probability when uncertainty is present.