A relationship between the time scales of quantum coherence loss and short-time solvent response for a solute/bath system is derived for a Gaussian wave packet approximation for the bath. Decoherence and solvent response times are shown to be directly proportional to each other, with the proportionality coefficient given by the ratio of the thermal energy fluctuations to the fluctuations in the system-bath coupling. The relationship allows the prediction of decoherence times for condensed phase chemical systems from well-developed experimental methods.
A relationship between the time scales of quantum coherence loss and short-time solvent response for a solute/bath system is derived for a Gaussian wave packet approximation for the bath. Decoherence and solvent response times are shown to be directly proportional to each other, with the proportionality coefficient given by the ratio of the thermal energy fluctuations to the fluctuations in the system-bath coupling. The relationship allows the prediction of decoherence times for condensed phase chemical systems from well-developed experimental methods.
We introduce a general but simple relation between the timescale for quantum coherence loss and the initial fluctuations of operators that couple a quantum system with a surrounding bath. The relation allows the prediction and measurement of early time decoherence dynamics for any open quantum system, through purity, without reconstructing the system's many-body density matrix. It is applied to predict the decoherence time for basic models-the Holstein chain, spin-boson and Caldeira-Legget models-commonly employed to capture electronic, vibrational, and vibronic dynamics in molecules. Such development also offers a practical platform to test the ability of approximate quantum dynamics methods to capture decoherence. In particular, a class of mixed quantum-classical schemes for molecular dynamics where the bath is treated classically, such as Ehrenfest dynamics, are shown to correctly capture short-time decoherence when the initial conditions are sampled from the Wigner distribution. These advances provide a useful platform to develop decoherence times for molecular processes and to test approximate molecular dynamics methods.
A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent-state semiclassical wave-packet method which avoids singularity issues arising in the usual Green's function approach. We discuss the general conditions under which it is approximately correct to discuss quantum decoherence in terms of a ``dephasing'' picture and we derive semiclassical expressions for the phase and phase distribution. Remarkably, an effective system wavefunction emerges whose norm measures the decoherence and is equivalent to a density-matrix formulation.
In this work, we examine how the structure of system-bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath's frequencies. For initially unentangled qubit-bath states, Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit-bath interaction strength, and bath correlation time. Initial system-bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. However, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Furthermore, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic line shape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system-bath dynamics even when there is no inhomogeneity in the initial conditions.
We develop a generalized quantum Fokker-Planck theory in a non-Gaussian-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength of system-bath coupling and the other two are chosen to interpolate smoothly the solvation dynamics between the long- and short-time regimes. The fluctuation-dissipation relation in this model bath is analyzed in detail. Based on this model bath, we derive two sets of coupled Fokker-Planck equations. These two equation sets are equivalent in the second order of system-bath coupling but different in the higher orders. The corresponding reduced Liouville equation in one set of the Fokker-Planck formulation is characterized by a memory relaxation kernel, while that in the other is by a local-time relaxation tensor. Each resulting set of Fokker-Planck equations involves only the reduced density operator and a series of well-characterized Hilbert-space relaxation operators. The present theory is valid for arbitrary time-dependent Hamiltonians and is applicable to the study of quantum coherence and relaxation in various dynamic systems.
We study the effect of initial correlations on the short-time decoherence of a particle linearly coupled to a bath of harmonic oscillators. We analytically evaluate the attenuation coefficient of the superposition of two wave packets both for a free and a harmonically bound particle, with and without initial thermal correlations between the particle and the bath. While short-time decoherence appears to be independent of the system in the absence of initial correlations, we find on the contrary that, for initial thermal correlations, decoherence becomes system dependent even for times much shorter than the characteristic time of the system. The temperature behavior of this system dependence is discussed.
Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an ``open'' quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with noncondensed modes gradually smears out the condensate phase, with a variance growing as At2+Bt+C at long times t, and we give a quantitative prediction for A, B, and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.