Vibrational decoherence of a "breathing sphere" oscillator in a thermal Lennard-Jones bath is examined using a classical analog approach. The equivalence between this approach and the linearized semiclassical initial value representation (IVR) is established and the method is exploited to produce a useful computational strategy that can efficiently evaluate the time dependence of the decoherence in these systems. A comparison between Harmonic and Morse "breathing sphere" models is presented and the rate of decoherence is found to depend on the choice of model, the initial state of the oscillator, the initial conditions of the bath (temperature, density), and the choice of quantity measuring the decoherence rate. The results are used to examine the utility of the Caldeira-Leggett model in this realistic system.
Vibrational decoherence of a "breathing sphere" oscillator in a thermal Lennard-Jones bath is examined using a classical analog approach. The equivalence between this approach and the linearized semiclassical initial value representation (IVR) is established and the method is exploited to produce a useful computational strategy that can efficiently evaluate the time dependence of the decoherence in these systems. A comparison between Harmonic and Morse "breathing sphere" models is presented and the rate of decoherence is found to depend on the choice of model, the initial state of the oscillator, the initial conditions of the bath (temperature, density), and the choice of quantity measuring the decoherence rate. The results are used to examine the utility of the Caldeira-Leggett model in this realistic system.
The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.
Effective descriptions accounting for the evolution of quantum systems that are acted on by a bath are desirable. As the number of bath degrees of freedom increases and full quantum simulations turn out computationally prohibitive, simpler models become essential to understand and gain an insight into the main physical mechanisms involved in the system dynamics. In this regard, vibrational decoherence of an I2 diatomics is tackled here within the framework of Markovian quantum state diffusion. The I2 dynamics are analyzed in terms of an effective decoherence rate, Λ, and the specific choice of the initial state, in particular, Gaussian wave packets and two-state superpositions. It is found that, for Markovian baths, the relevant quantity regarding decoherence is the product of friction (η) and temperature (T); there is no distinction between varying one or the other. It is also observed that decoherence becomes faster as the energy levels involved in the system state correspond to higher eigenvalues. This effect is due to a population redistribution during the dynamical process and an eventual irreversible loss of the initial coherence. These results have been compared with those available in the literature from more detailed semiclassical IVR simulations, finding a good agreement.
ABSTRACT: The concept of open quantum system is very broad and it is related to the ability of measuring only certain degree of freedoms of a particular system. Although this idea is relatively simple, the separation between the system of interest, the degree of freedoms that are accesible experimentally, and the reservoir, the degree of freedoms that are not accesible experimentally, is not always clear. For instance, in molecular systems, electronic spectroscopy has access only to electronic degree of freedoms so that the nuclear and vibrational degree of freedom become the reservoir, this makes its description not trivial. This scenario leads to have non-trivial and structured reservoirs and to develop powerful tools to analyze them. The hallmark of non-trivial and structured reservoirs is the non-Markovian dynamics. By translating the Feynman and Vernon influence functional approach into phase-space representation, we develop two theories of semiclassical evolution of the Wigner function of the system of interest that incorporate non-Markovian dynamics and highly non-trivial quantum effects such as non-locality of quantum mechanics: (i) We translate the Caldeira-Leggett model into phase-space representation of quantum mechanics and (ii) we consider the possibility of having non-linear baths and therefore, truly quantum reservoirs. During the last forty years the study of energy loss and coherence in quantum systems has been based on the Ullersma-Caldeira-Leggett model, a model that describes the environment of quantum systems of interest as a collection of harmonic oscillators with classical evolution. We constructed this model in the Wigner-Weyl representation of quantum mechanics and discuss the classical nature of the evolution of the bath modes and the semiclassical evolution of the central system. As an application of the semiclassical Wigner propagator, the non-Markovian time evolution under the Morse potencial is analyzed. There, it is clear how decohering processes shrink the propagator to smaller regions of phase space implying that the dynamics become more local, i.e., more classical. The current level of experimentation and control of physical systems have called into question the validity of the model in, one hand, molecular systems (e.g. photosynthetic complexes immersed in solvents, chemical systems in liquid phase or gas and manipulated with intense laser pulses) and, in the other hand, solid state systems (e.g. Josephson junctions, spins in quantum dots or "spinning ice"). Given the importance of these systems in the development of new quantum technologies and in the understanding of quantum phenomena in mesoscopic systems, it has become necessary to develop new models of the environment and efficient methodologies with quantitative prediction power. However, some of them are artificial modifications of the Ullersma-Caldeira-Leggett model without solid and clean physical support. Here we formulated a general framework that allows the study of quantum correlations in quantum systems in the presence of non-harmonic thermal baths (e.g. baths formed by strongly coupled diatomic molecules). This formulation will allow a more precise and quantitative description of processes such as the transport of excitons in photosynthetic complexes, the transfer of heat in solid state devices, among others. Results clearly show the non-classical time dynamics of the bath modes. The implementation of this particular theory remains, however, as a challenge.
The effect of chaotic bath dynamics on the decoherence of a quantum system is examined for the vibrational degrees of freedom of a diatomic molecule in a realistic, constant temperature collisional bath. As an example, the specific case of I(2) in liquid xenon is examined as a function of temperature, and the results compared with an integrable xenon bath. A crossover in behavior is found: The integrable bath induces more decoherence at low bath temperatures than does the chaotic bath, whereas the opposite is the case at the higher bath temperatures. These results, verifying a conjecture due to Wilkie, shed light on the differing views of the effect of chaotic dynamics on system decoherence.
We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically, we show that the effects of the low-dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high-temperature regime of the Caldeira-Leggett model.
The forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is used to study quantum coherence effects in the time-dependent probability distribution of an anharmonic vibrational coordinate and its quenching when coupled to a thermal bath. It is shown that the FB-IVR accurately reproduces the detailed quantum coherent structure in the weak coupling regime, and also describes how this coherence is quenched with an increase of the system–bath coupling and/or the bath temperature. Comparisons are made with other approximations and the physical implications are discussed.