Quantum Dissipation Theory And Its Application To Spectroscopies

Quantum dissipation refers to the reduced dynamics of a system embedded in environment (bath). The latter consists of macroscopic degrees of freedom whose effects on the system should be treated in a statistical manner. Consequently, the system of primary interest undergoes energy relaxation and dephasing processes, evolving eventually to the thermal equilibrium state. The key quantity in quantum dissipation theory is the reduced density operator. The development of quantum dissipation theory has involved diversified fields of research, such as nuclear magnetic resonance, quantum optics, molecular spectroscopy, condensed phase physics, and chemical physics. Optical spectroscopy provides a powerful tool in the detection and understanding of molecular structures, interactions, and dynamics. We present the efficient quantum dissipation theory to study spectroscopies in the thesis.In the thesis, We exploit the hierarchical equations of motion (HEOM) formalism of quantum dissipation theory by Prof. Yan's group in Hong Kong University of Science and Technology as a foundation. Nevertheless, an explicit HEOM construction relies on the choice of the statistical environment basis set that expands the environment correlation functions into its complex memory conponents. The environment correlation function is dictated by the fluctuation-dissipation theorem, involving the Fourier transform of the product of the spectral density and Bose Function. We request the best statistical environment basis set for an efficient HEOM construction and its practical applications. The conventional HEOM construction involves the Matsubara spectrum decomposition (MSD) for the Bose function. However, MSD is notorious for its slow convergence. The resulting HEOM is rather expensive and limited largely to simple systems with Drude dissipations. We have shown recently that the Pade spectral decomposition (PSD) is the best sum-over-poles (SOP) scheme for the Bose function.In Chapter 1, we introduce the theoretical background of QDT, including the reduced system description, the correlation and response functions versus linear response theory, with emphasis on key concepts and fluctuation-dissipation theorem.In chapter 2, we summarize the establishment of the exact and nonperturbative HEOM of QDT, via the calculus on the influence functional path integral. We implement the PSD scheme to establish the corresponding PSD-HEOM. For environment spectral density, we adopt the multiple Brownian oscillators (MBO) model. It can describe optically actively vibronic coupling via underdamped Brownian oscillator mode, and also energy fluctuation via strongly overdamped Drude dissipation. We also propose a hierarchical quantum master equation (HQME) approach, which adopts a modified semiclassical Drude model.In chapter 3, we use HEOM and HQME, which are introduced in chapter 2 to calculate the linear absorption and emission spectrum of a two-level system (TLS). For the same bath cut-off frequency y, along with the bigger solvent reorganizationλ, the linear absoption and emission spectrum get wider, strength get smaller, the spectroscopic Stokes shift get bigger. The reason is the effect of bath on the system is intense, the electron can transfer to the higher vibrational energy levels, so the Stokes shift get larger. Compare to the HQME and HEOM, the discrepancy seems not to matter. For the same solvent reorganizationλ, along with the bigger bath cut-off frequency y, the linear absoption and emission spectrum get narrower, the spectroscopic Stokes shift get smaller. The bigger bath cut-off frequency y is, the more quickly bath get equilibrium state. The reason is the effect of bath on the system is weak, the electron can only transfer to the lower vibrational energy levels, so the Stokes shift get smaller. We also propose a criterion to estimate the performance of HQME. For the TLS system, the initial steady state solution of HEOM can be obtained analytically. If without considering the initial system-bath coupling, the response function is zero. We demonstrate the linear spectroscopies by the complete second-order correlated driving-dissipation equations (CODDE).In chapter 4, we use HEOM to demonstrate the transient stimulated and spontaneous emissions spectroscopies of a two-level system. We present in detail a highly efficient numerical method to evaluate the key quantity in our spectroscopic theory—field-dressed response function. Our newly developed numberical method is based on a mixed Schrodinger/Heisenberg picture of the field-dressed response function, which reduced the two-dimensional time-grid problem almost to two one-dimensional time-grid problems, so it costs little time to calculate.1. Pump-probe field on the sequential instance:(1) Shot time pump field, wave packet will have relaxation on excited state. So the stimulated emissionα_ω,td) get red shitλ→-λ.(2) Long time pump field, pump light will choose a narrow frequency to excitated. So the narrow wave packet will have relaxation on excited state. The stimulated emissionα (ω>td) get wide and red shit 0→-λ.2. Pump-probe field on the coherent instance:(1) shot time pump field, note that the stimulated emissionα_[ω,td) has some significant negative values in some frequency region. In fact, the concept of being emissive may only be physical correct for the sequentialα_S (ω,td) contribution. This implies thatα_C(ω,td) may be more properly called as the stimulated emission Raman contribution. The negative values inα_C(ω,td) thus indicate the underlying conherent Raman processes. But the stimulated emissionα_ω,td get red shitλ→-λ.(2) long time pump field, have the same conclusion as shot time pump field. The stimulated emissionα_ω,td get wide and red shit 0→-λ.3. At six representing delay times comparison among the ordinary fluorescence SE(ω,td) and the stimulated emissionα_ω,td. SE andα are only different in the short time regime, but evolve to be identical as the results of dissipation that suppresses the memory effect. At the long time regime both SE andα coincide with the stationary emission spectrum.In Chapter 5, we use HEOM to study the transient absorption spectroscopies in the pump-probe scenario of some models monomer and dimer exciton systems. For a monomer, the vibrational versus electronic coherence will be demonstrated, so we adopt the multiple Brownian oscillators model for environment spectral density. In the experiment we can measure optically active phonon by the pump-probe, we also demonstrate the HEOM approach to correlated system-environment coherence. Turn to a dimer, we only consider the Drude spectral density. While S (td) remains as the single-exciton state particle emission, S+(td) contains now not just the ground-state hole absorption, but also the single-exciton state particle reabsorption.In Chapter 6, we summarize the thesis, and comment on the future work concerning both the theoretical and application aspects of quantum dissapation theory. We like to emphasis here that HEOM is by far the most numerically tractable formalism for exact quantum dynamics under arbitrary Gaussian bath influence at finite temperature. The explicit HEOM construction depends on the way of decomposing bath influence into complex memory components. This is about the statistical bath basis set representation of HEOM quantum dissipation theory. The proposed PSD-MBO scheme is likely the best. We have also verified the established minimum bath basis set criterions. In most of the numerical demonstrations presented in this thesis, only one PSD pole is sufficient, while about five MSD poles are required in the same cases. As the total number of ADOs is concerned, the present HEOM resembles a full configuration interaction formalism in the system-bath coherence space. An efficient filtering algorithm which exists for Drude dissipations needs to be developed further to include the general MBO cases.