This doctoral dissertation is concerned with the study of quantum dynamics where finite dimensional systems (typically two-level `qubits') interact with or through a set of bosonic modes, in various different configurations. Our main focus is on identifying and investigating signatures of quantum coherence emerging between the qubits in such dynamical situations. We first present a toy model where two qubits are encoded in the single-excitation subspace of the global system and study the average fidelity of a controlled-Z (CZ) quantum gate mediated by the bosonic modes. Next, we turn to analytically intractable spin-boson like models, by adopting the Multi-configurational Ehrenfest (MCE) method. We apply MCE to the study of the Choi fidelity of a CZ gate between two distant qubits, mediated by sets of bosonic modes (including sets which represent discretization of bath's continua) under different coupling Hamiltonians. The testing of the MCE method is then pushed further by a comparative analysis with full variational approaches and adiabatic path integral techniques in a case of super-Ohmic spin-boson model. Finally, we determine a general error bound applicable to most approximated treatments of unitary quantum evolutions, and suitable to compare MCE with other numerical techniques for the study of spin-boson dynamics.This doctoral dissertation is concerned with the study of quantum dynamics where finite dimensional systems (typically two-level `qubits') interact with or through a set of bosonic modes, in various different configurations. Our main focus is on identifying and investigating signatures of quantum coherence emerging between the qubits in such dynamical situations. We first present a toy model where two qubits are encoded in the single-excitation subspace of the global system and study the average fidelity of a controlled-Z (CZ) quantum gate mediated by the bosonic modes. Next, we turn to analytically intractable spin-boson like models, by adopting the Multi-configurational Ehrenfest (MCE) method. We apply MCE to the study of the Choi fidelity of a CZ gate between two distant qubits, mediated by sets of bosonic modes (including sets which represent discretization of bath's continua) under different coupling Hamiltonians. The testing of the MCE method is then pushed further by a comparative analysis with full variational approaches and adiabatic path integral techniques in a case of super-Ohmic spin-boson model. Finally, we determine a general error bound applicable to most approximated treatments of unitary quantum evolutions, and suitable to compare MCE with other numerical techniques for the study of spin-boson dynamics.

Jul 28, 20121 citation

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths

Andrés Montoya−Castillo, David R. Reichman

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

arXiv:1610.04243The Journal of Chemical PhysicsJan 12, 201717 citations

Quantum Path Interference through Incoherent Motions in Multilevel Quantum Systems

Xin Chen

Quantum path interferences or resonances in multilevel dissipative quantum systems play an important and intriguing role in the transport processes of nanoscale systems. Many previous minimalistic models used to describe the quantum path interference driven by incoherent fields are based on the approximations including the second order perturbation for the weak coupling limit, the ad-hoc choices of two-time correlation functions and $\it{etc}$ . On the other hand, the similar model to study the non-adiabatic molecular electronic excitation have been extensively developed and many efficient quantum molecular dynamics simulation schemes, such as the Ehrenfest scheme, have been proposed. In this paper, I aim to propose an unified model, extend the Ehrenfest scheme to study the interactions of system-light and system-phonon simultaneously and gain insight into and principles of the roles of quantum path interferences in the realistic molecular systems. I discuss how to derive the time-dependent stochastic Schr $\ddot{o}$ dinger equation from the Ehrenfest scheme as a foundation to discuss the detailed balance for the weak coupling limit and therefore the quantum correction in the Ehrenfest scheme. Different from the master equation technique, the Ehrenfest scheme doesn't need any specific assumptions about spectral densities and two time correlation functions. With simple open two-level and three-level quantum systems, I show the effect of the quantum path interference on the steady state populations. Currently I only focus on the role of the phonon thermal reservoir. The electromagnetic field (solar light) will be modeled as a thermal reservoir and discussed in detail in the future paper.Quantum path interferences or resonances in multilevel dissipative quantum systems play an important and intriguing role in the transport processes of nanoscale systems. Many previous minimalistic models used to describe the quantum path interference driven by incoherent fields are based on the approximations including the second order perturbation for the weak coupling limit, the ad-hoc choices of two-time correlation functions and $\it{etc}$. On the other hand, the similar model to study the non-adiabatic molecular electronic excitation have been extensively developed and many efficient quantum molecular dynamics simulation schemes, such as the Ehrenfest scheme, have been proposed. In this paper, I aim to propose an unified model, extend the Ehrenfest scheme to study the interactions of system-light and system-phonon simultaneously and gain insight into and principles of the roles of quantum path interferences in the realistic molecular systems. I discuss how to derive the time-dependent stochastic Schr$\ddot{o}$dinger equation from the Ehrenfest scheme as a foundation to discuss the detailed balance for the weak coupling limit and therefore the quantum correction in the Ehrenfest scheme. Different from the master equation technique, the Ehrenfest scheme doesn't need any specific assumptions about spectral densities and two time correlation functions. With simple open two-level and three-level quantum systems, I show the effect of the quantum path interference on the steady state populations. Currently I only focus on the role of the phonon thermal reservoir. The electromagnetic field (solar light) will be modeled as a thermal reservoir and discussed in detail in the future paper.

arXiv:1305.4197May 17, 20130 citations

\it{etc}

. On the other hand, the similar model to study the non-adiabatic molecular electronic excitation have been extensively developed and many efficient quantum molecular dynamics simulation schemes, such as the Ehrenfest scheme, have been proposed. In this paper, I aim to propose an unified model, extend the Ehrenfest scheme to study the interactions of system-light and system-phonon simultaneously and gain insight into and principles of the roles of quantum path interferences in the realistic molecular systems. I discuss how to derive the time-dependent stochastic Schr

\ddot{o}

dinger equation from the Ehrenfest scheme as a foundation to discuss the detailed balance for the weak coupling limit and therefore the quantum correction in the Ehrenfest scheme. Different from the master equation technique, the Ehrenfest scheme doesn't need any specific assumptions about spectral densities and two time correlation functions. With simple open two-level and three-level quantum systems, I show the effect of the quantum path interference on the steady state populations. Currently I only focus on the role of the phonon thermal reservoir. The electromagnetic field (solar light) will be modeled as a thermal reservoir and discussed in detail in the future paper.