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Manipulations with open quantum systems (such as qubits) are fundamental for any quantum technology. They are the focus of studies involving optimal control theory. Usually, control is achieved through the use of time-dependent external fields when driven system evolution is simulated employing the Davies construction (second-order Markov quantum master equation formulation). As a weak (second order) coupling scheme, the Davies construction is limited in its ability to account for bath-induced coherences. To overcome the limitation, we utilize the nonequilibrium Green’s function method and demonstrate that accounting for the coherences makes a qualitative impact on quantum control studies. We find that accounting for the coherences is especially important when dealing with system evolution involving mixed states.
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The development of experimental techniques at the nanoscale has enabled the performance of spectroscopic measurements on single-molecule current-carrying junctions. These experiments serve as a natural intersection for the research fields of optical spectroscopy and molecular electronics. We present a pedagogical comparison between the perturbation theory expansion of standard nonlinear optical spectroscopy and the (non-self-consistent) perturbative diagrammatic formulation of the nonequilibrium Green’s functions method (which is widely used in molecular electronics), highlighting their similarities and differences. By comparing the two approaches, we argue that the optical spectroscopy of open quantum systems must be analyzed within the more general Green’s function framework.more » « less
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We study the applicability of the Liouvillian exceptional points (LEPs) approach to nanoscale open quantum systems. A generic model of the driven two-level system in a thermal environment is analyzed within the nonequilibrium Green’s function (NEGF) and Bloch quantum master equation formulations. We derive the latter starting from the exact NEGF Dyson equations and highlight the qualitative limitations of the LEP treatment by examining the approximations employed in its derivation. We find that the non-Markov character of evolution in open quantum systems does not allow for the introduction of the concept of exceptional points for a description of their dynamics. Theoretical analysis is illustrated with numerical simulations.more » « less
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The infrared response of a system of two vibrational modes in a cavity is calculated by an effective non-Hermitian Hamiltonian derived by employing the nonequilibrium Green's function (NEGF) formalism. Degeneracies of the Hamiltonian (exceptional points, EPs) widely employed in theoretical analysis of optical cavity spectroscopies are used in an approximate treatment and compared with the full NEGF. Qualitative limitations of the EP treatment are explained by examining the approximations employed in the calculation.more » « less
