Quantum Relaxation Processes Research Articles

Experimental study of rotational relaxation for D2(1,12) in collisions with N2.

The rotational relaxation behavior of D2(1,12) in a D2-N2 mixture was investigated using coherent anti-Stokes Raman scattering (CARS) technique. The rovibrational level v = 1 and J = 12 of D2 was selectively excited through stimulated Raman pumping while monitoring the temporal evolution of population for D2(1, J ≤ 12) molecules using time-resolved CARS spectroscopy. The results demonstrate that the rotational relaxation processes of D2(1,12) encompass both multi-quantum relaxation and continuous single-quantum relaxation. When α, the molar ratio of N2, is less than 0.5, D2(1,12) predominantly undergoes a single quantum relaxation process transition. However, when α ≥ 0.5, the multi-quantum relaxation mechanism gradually predominates. The total rotational relaxation rate coefficients of D2(1,12) collisions with N2 and D2 at 295K were determined to be 3.974 × 10-14 and 1.179 × 10-14cm3s-1, respectively. The temperature dependence of rotational relaxation rate of D2(1,12) was investigated within the temperature range of 295-453K. With increasing temperature, the dominant relaxation process exhibited an accelerated behavior, while the minor relaxation process remained largely unaffected. The rotational temperature of the D2molecule at various N2 molar ratios was determined through the utilization of Boltzmann plots. The rotational temperature undergoes a rapid decline within 2 μs, corresponding to the near-resonant rotation-vibration relaxation process of D2(1,12) collisions with N2. The system reaches a quasi-equilibrium state when the delay time is 3 μs. The findings of this study can serve as a valuable empirical basis for further validation of the kinetic theory and simulation.

Quantum relaxation processes in microtubule tryptophan system

The paper investigates the mechanism of quantum relaxation in a microtubule tryptophan chain on the basis of the Born–Markov formalism. The tryptophans are considered as a system of interacting electric dipoles. Each dipole is represented as a two-level pseudo-spin system. Decoherence and dissipation processes have been investigated. The tunneling effect impact on quantum relaxation time has been considered. Decoherence time in relation to the environment impact has been obtained. Decoherence time dependence on temperature has been determined.

Quantum relaxation effects in Microtubules

The paper investigates quantum dynamics of a system of microtubule tubulins electric dipole moments. Electric dipoles represent two-level pseudo-spin systems, with one of the two polarized tubulin states corresponding to each of a pseudo-spin one. The pseudo-spin system behavior with time has been analyzed on basis of the Born–Markov formalism. The decoherence and dissipation processes caused by pseudo-spin–boson interaction have been considered. The problem of a possible signal propagation mechanism in the microtubule dipole–dipole system, which can be exclusively quantum in nature, has been discussed. It has been determined that the decoherence time depends considerably on dissipative processes in microtubules. Thus, the decoherence time in case of weak dissipation or absence of it equals 10−11–10−10 s. The decoherence time in the presence of dissipation process has been found to be 1.86⋅10−13 s. The temperature dependence of decoherence process has been considered. It has been stated that temperature values are the major factor influencing the dissipation-less decoherence time. The results obtained in the paper make it possible to describe the microtubule as a system in which quantum relaxation processes are important and comparable in time with those occurring in bio systems.

Single-atom verification of the information-theoretical bound of irreversibility at the quantum level

Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state. Furthermore, we carry out experimental verification of this information-theoretical bound by means of a single spin embedded in an ultracold trapped $^{40}$Ca$^{+}$ ion. Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.

Kramers degeneracy and relaxation in vanadium, niobium and tantalum clusters

In this work we use magnetic deflection of V, Nb, and Ta atomic clusters to measure their magnetic moments. While only a few of the clusters show weak magnetism, all odd-numbered clusters deflect due to the presence of a single unpaired electron. Surprisingly, for the majority of V and Nb clusters an atomic-like behavior is found, which is a direct indication of the absence of spin–lattice interaction. This is in agreement with Kramers degeneracy theorem for systems with a half-integer spin. This purely quantum phenomenon is surprisingly observed for large systems of more than 20 atoms, and also indicates various quantum relaxation processes, via Raman two-phonon and Orbach high-spin mechanisms. In heavier, Ta clusters, the relaxation is always present, probably due to larger masses and thus lower phonon energies, as well as increased spin–orbit coupling.

Nonadiabatic Dynamics in Atomistic Environments: Harnessing Quantum-Classical Theory with Generalized Quantum Master Equations.

The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.

Sensing of molecules using quantum dynamics

We design sensors where information is transferred between the sensing event and the actuator via quantum relaxation processes, through distances of a few nanometers. We thus explore the possibility of sensing using intrinsically quantum mechanical phenomena that are also at play in photobiology, bioenergetics, and information processing. Specifically, we analyze schemes for sensing based on charge transfer and polarization (electronic relaxation) processes. These devices can have surprising properties. Their sensitivity can increase with increasing separation between the sites of sensing (the receptor) and the actuator (often a solid-state substrate). This counterintuitive response and other quantum features give these devices favorable characteristics, such as enhanced sensitivity and selectivity. Using coherent phenomena at the core of molecular sensing presents technical challenges but also suggests appealing schemes for molecular sensing and information transfer in supramolecular structures.

Separation and conversion dynamics of nuclear-spin isomers of gaseous methanol.

All symmetrical molecules with non-zero nuclear spin exist in nature as nuclear-spin isomers (NSIs). However, owing to the lack of experimental information, knowledge is rare about interconversions of NSIs of gaseous molecules with torsional symmetry. Here we report our separation and conversion observations on NSI-torsion-specific transition systems of gaseous methanol from a light-induced drift experiment involving partially spatial separation of the ortho and para isomers. We find that vibrationally excited molecules of the methanol spin isomer have a smaller collision cross-section than their ground-state counterparts. Interconversion of the enriched ortho isomer with the para isomer, which is generally considered improbable, has been quantitatively studied by sensitive detections of the spectral intensities. Rather counterintuitively, this reveals that the interconversion is inhibited with increasing pressure. Our results suggest that the spin conversion mechanism in methanol is via a quantum relaxation process with the quantum Zeno effect induced by molecular collisions.

Nuclear spin conversion in diatomic molecules

A mechanism of the internal interaction in dimers that mixes different nuclear spin modifications has been proposed. It has been shown that the intramolecular current associated with transitions between electronic terms of different parities can generate different magnetic fields on nuclei, leading to transitions between spin modifications and to the corresponding changes in rotational states. In the framework of the known quantum relaxation process, this interaction initiates irreversible conversion of nuclear spin modifications. The estimated conversion rate for nitrogen at atmospheric pressure is quite high (10−3–10−5 s−1).

Order in de Broglie–Bohm quantum mechanics

A usual assumption in the so-called de Broglie–Bohm approach to quantum dynamics is that the quantum trajectories subject to typical ‘guiding’ wavefunctions turn to be quite irregular, i.e. chaotic (in the dynamical systems’ sense). In this paper, we consider mainly cases in which the quantum trajectories are ordered, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a Hénon–Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie–Bohm formalism, namely the influence of order on the so-called quantum relaxation effect. We show that the existence of regular trajectories poses restrictions on the quantum relaxation process and give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.

Quantum quench influenced by an excited-state phase transition

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear cut evidence of the ESQPT effects is presented in integrable models, while in the nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

Characterization and quantification of the role of coherence in ultrafast quantum biological experiments using quantum master equations, atomistic simulations, and quantum process tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.

The stochastic Baker-Hausdorff formula and its applications to quantum relaxation processes

In this paper, we consider the stochastic analog of the Baker-Hausdorff formula for operators satisfying the canonical commutation relations. This formula can be used to obtain an exact solution to the problem of the dynamics of a quantum system interacting with the environment.

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. Herein, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis the influence of nonequilibrium fluctuations and periodic electrical fields on quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.

Quantum relaxation and Poincaré recurrences

We study the quantum relaxation process in open dynamical systems with completely chaotic or mixed classical phase space. We show that quantum effects modify the decay rate of Poincaré recurrences P ( t ). In particular, the exponent p of the algebraic decay P ( t )∝1/ t p is shown to have the universal value p =1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.

Relaxation process in a regime of quantum chaos

We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale t_q. This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time: t_q ~ g^alpha where g is the conductance of the system and the exponent alpha is close to 1/2. As a result, quantum and classical decay probabilities remain close up to values P ~ exp(-sqrt(g)) similarly to the case of open disordered systems.

Spin relaxation. The renormalized operator cumulant approach

Two-level systems under the influence of external noise are generic models of quantum relaxation processes. The spin 1/2 particle in a stochastic magnetic field is one of the best known examples. Interesting effects are observed if the noise is colored as is the case in most applications. The time-ordered operator cumulant expansion forms a convenient approach to this problem. Recently, a renormalization procedure has been proposed which corresponds to a partial summation of the naive expansion and hence constitutes an essential improvement over the second cumulant considered usually. For colored noise of intermediate strength and correlation time this approach is used to derive renormalized expressions for the transverse (T2) and longitudinal (T1) relaxation time and the frequency shift. In this parameter region, the ratioT1/T2=α is found to deviate substantially from its value α=2 valid for white noise exactly and for colored noise in the second cumulant approximation. This corroborates and extends results of Budimir and Skinner obtained by including the second and fourth cumulant only. However, their truncated expansion is shown to lead to unphysical results in the intermediate parameter region treated still correctly by the renormalized expansion.

On the consistent description of quantum relaxation processes: The harmonic oscillator

On the consistent description of quantum relaxation processes: The harmonic oscillator

Dressed particle description of a quantum relaxation process

Ullersma's model of the damped harmonic oscillator is considered. It is whown that the bare phonon description of the corresponding quantum relaxation process can be transformed into a description which no longer shows the essential peculiarities of the original model and which allows the definition of physical particles.

On the consistent description of quantum relaxation processes: The harmonic oscillator

The quantum-mechanical description of a relaxation process is critically reviewed. The initially reversible “universe” consists of a harmonic oscillator (system) interacting with N further harmonic oscillators (heat bath). The coupling is linear in both, system- and bath-coordinates. The underlying dynamical equations are exactly solvable. A reasonable quantum-mechanical treatment of relaxation processes should guarantee that for all times the canonical commutation relations deviate only in a higher order of the coupling constant from their reversible values. A hierarchy of descriptions with decreasing quantum-mechanical consistency is formulated and discussed: 1. (i) the exact irreversible solution in connection with a decoupling of system and bath at t = 0; 2. (ii) the exact irreversible solution in connection with a conditional thermal average at t = 0; 3. (iii) a semi-Markovian stochastic differential equation (SDE), where the dissipation is described by a single parameter while the fluctuation (i.e. the correlation function of the stochastic force includes the information on the continuous bath-spectrum; 4. (iv) a complete Markovian SDE; dissipation and fluctuation are characterized by one single parameter. For the Drude model the descriptions (i)–(iii) are equivalent in relation to consistent results of first order in the dissipative parameters. On the contrary, description (iv) is unsuitable in the quantum-mechanical regime.