Reduced purities as measures of decoherence in many-electron systems

Survival of quantum features in the dynamics of a dissipative quantum system and their effect on the state purity

Destruction of the quantum mechanical features of matter by decoherence restricts the applicability of quantum technologies. The limited information of the quantum features (such as coherence) in the basis-dependent observations urges the use of a basis-independent quantity for a better understanding. In this context, the state purity of a quantum system (composed of quantized pigments immersed in a noisy protein environment) is studied with a numerically exact hierarchical equations of motion approach over the wide range of the parameter domain (with the main focus on the nonzero-energy gradient). It is noted that the state purity does not necessarily reflect any significant information about the persistence of quantum features (in the dissipative environment), even when the quantum coherence survives at the steady state in both the localized and the eigenstate basis.

Quantifying Early Time Quantum Decoherence Dynamics through Fluctuations

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.

Quantifying fermionic decoherence in many-body systems

Practical measures of electronic decoherence, called distilled purities, that are applicable to many-body systems are introduced. While usual measures of electronic decoherence such as the purity employ the full N-particle density matrix which is generally unavailable, the distilled purities are based on the r-body reduced density matrices (r-RDMs) which are more accessible quantities. The r-body distilled purities are derivative quantities of the previously introduced r-body reduced purities [I. Franco and H. Appel, J. Chem. Phys. 139, 094109 (2013)] that measure the non-idempotency of the r-RDMs. Specifically, the distilled purities exploit the structure of the reduced purities to extract coherences between Slater determinants with integer occupations defined by a given single-particle basis that compose an electronic state. In this way, the distilled purities offer a practical platform to quantify coherences in a given basis that can be used to analyze the quantum dynamics of many-electron systems. Exact expressions for the one-body and two-body distilled purities are presented and the utility of the approach is exemplified via an analysis of the dynamics of oligo-acetylene as described by the Su-Schrieffer-Heeger Hamiltonian. Last, the advantages and limitations of the purity, reduced purity, and distilled purity as measures of electronic coherence are discussed.

Understanding the Fundamental Connection Between Electronic Correlation and Decoherence

We introduce a theory that exposes the fundamental and previously overlooked connection between the correlation among electrons and the degree of quantum coherence of electronic states in matter. For arbitrary states, the effects only decouple when the electronic dynamics induced by the nuclear bath is pure-dephasing in nature such that [H(S),H(SB)] = 0, where H(S) is the electronic Hamiltonian and H(SB) is the electron-nuclear coupling. We quantitatively illustrate this connection via exact simulations of a Hubbard-Holstein molecule using the Hierarchical Equations of Motion that show that increasing the degree of electronic interactions can enhance or suppress the rate of electronic coherence loss.

Nonadiabatic and Time-Resolved Photoelectron Spectroscopy for Molecular Systems

We quantify the nonadiabatic contributions to the vibronic sidebands of equilibrium and explicitly time-resolved nonequilibrium photoelectron spectra for a vibronic model system of trans-polyacetylene. Using exact diagonalization, we directly evaluate the sum-over-states expressions for the linear-response photocurrent. We show that spurious peaks appear in the Born-Oppenheimer approximation for the vibronic spectral function, which are not present in the exact spectral function of the system. The effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states and also persists when either only initial or final states are replaced by correlated vibronic states. Only when correlated initial and final vibronic states are taken into account are the spurious spectral weights of the Born-Oppenheimer approximation suppressed. In the nonequilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wavepacket motion of the system can be traced in the time-resolved photoelectron spectra as a function of the pump-probe delay.