Spin-resolved counting statistics as a sensitive probe of spin correlation in transport through a quantum dot spin valve.

We investigate the noise in spin transport through a single quantum dot (QD) tunnel coupled to ferromagnetic (FM) electrodes with noncollinear magnetizations. Based on a spin-resolved quantum master equation, auto- and cross-correlations of spin-resolved currents are analyzed to reveal the underlying spin transport dynamics and characteristics for various polarizations. We find the currents of majority and minority spins could be strongly autocorrelated despite uncorrelated charge transfer. The interplay between tunnel coupling and the Coulomb interaction gives rise to an exchange magnetic field, leading to the precession of the accumulated spin in the QD. It strongly suppresses the bunching of spin tunneling events and results in a unique double-peak structure in the noise of the net spin current. The spin autocorrelation is found to be susceptible to magnetization alignments, which may serve as a sensitive tool to measure the magnetization directions between the FM electrodes.

Dynamics of the spin-boson model: The effect of bath initial conditions.

The dynamics of the (sub-)Ohmic spin-boson model under various bath initial conditions is investigated by employing the Dirac-Frenkel time-dependent variational approach with the multiple Davydov D1 Ansatz in the interaction picture. The validity of our approach is carefully checked by comparing the results with those of the hierarchy equations of motion method. By analyzing the features of nonequilibrium dynamics, we identify the phase diagrams for different bath initial conditions. We find that for the spectral exponent s < sc, there exists a transition from coherent to quasicoherent dynamics with increasing coupling strengths. For sc < s ≤ 1, the coherent to incoherent crossover occurs at a certain coupling strength and the quasicoherent dynamics emerges at much larger couplings. The initial preparation of the bath has a considerable influence on the dynamics.

Emission spectral non-Markovianity in qubit-cavity systems in the ultrastrong coupling regime.

We study the emission spectra of the dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectral features under different qubit-cavity coupling strengths and system initial conditions.

Lamb Shift and the Vacuum Rabi Splitting in a Strongly Dissipative Environment.

We study the vacuum Rabi splitting of a qubit ultrastrongly coupled to a high-Q cavity mode and a radiation reservoir. Three methods are employed: a numerically exact variational approach with a multiple Davydov ansatz, the rotating-wave approximation (RWA), and the transformed RWA. Agreement between the variational results and the transformed RWA results is found in the regime of validity of the latter, where the RWA breaks down completely. We illustrate that the Lamb shift plays an essential role in modifying the vacuum Rabi splitting in the ultrastrong coupling regime, leading to off-resonant qubit-cavity coupling even though the cavity frequency equals the bare transition frequency of the qubit. Specifically, the emission spectrum exhibits one broad low-frequency peak and one narrow high-frequency peak in the presence of relatively weak cavity-qubit coupling. As the cavity-qubit coupling increases, the low-frequency peak narrows while the high-frequency peak broadens until they have similar widths.

Dynamics of the two-spin spin-boson model with a common bath.

Dynamics of the two-spin spin-boson model in the presence of Ohmic and sub-Ohmic baths is investigated by employing a multitude of the Davydov D1 trial states, also known as the multi-D1 Ansatz. Its accuracy in dynamics simulations of the two-spin SBM is improved significantly over the single D1 Ansatz, especially in the weak to moderately strong coupling regime. Validity of the multi-D1 Ansatz for various coupling strengths is also systematically examined by making use of the deviation vector which quantifies how faithfully the trial state obeys the Schrödinger equation. The time evolution of population difference and entanglement has been studied for various initial conditions and coupling strengths. Careful comparisons are carried out between our approach and three other methods, i.e., the time-dependent numerical renormalization group (TD-NRG) approach, the Bloch-Redfield theory, and a method based on a variational master equation. For strong coupling, the multi-D1 trial state yields consistent results as the TD-NRG approach in the Ohmic regime while the two disagree in the sub-Ohmic regime, where the multi-D1 trial state is shown to be more accurate. For weak coupling, the multi-D1 trial state agrees with the two master-equation methods in the presence of both Ohmic and sub-Ohmic baths, but shows considerable differences with the TD-NRG approach in the presence of a sub-Ohmic bath, calling into question the validity of the TD-NRG results at long times in the literature.