Quantum dynamics, master equation and equilibrium for a qubit coupled to a thermal boson field.

Abstract We demonstrate that system-agnostic physics-informed neural networks can efficiently learn the dynamical solution of quantum master equations, as compared to problem-specific numerical solvers, with respect to accuracy, stability of training convergence, robustness towards bath parameters or initial conditions, and equivalent convergence times for the non-Markovian evolution of two-level quantum systems. We study cases of quantum dot systems driven by external electromagnetic fields and coupled to an acoustic phonon environment, and analyze two problem setups, the evolution of Bloch vectorized coupled differential equations obtained from a Lindblad master equation and the evolution of a non-Markovian master equation obtained from the Nakajima-Zwanzig formulation. We implement a fully connected physics-informed neural network architecture to solve the two problems. We also use the same methodology to solve the inverse problem of estimation of bath parameters in a supervised fashion, but with a very limited number of noisy samples.

We present an experimental and theoretical study of the interplay between ultrafast electron dynamics and librational dynamics in liquid nitrobenzene. A femtosecond ultraviolet pulse and two femtosecond near-infrared pulses interact with nitrobenzene molecules, generating a four-wave mixing nonlinear signal measured in the Optical Kerr Effect geometry. The signal is measured to be nonzero only at negative time delays, corresponding to the near-infrared pulses arriving before the ultraviolet pulse. We perform time-dependent Quantum Master Equation calculations with classical libration to simulate the experiment. The simulations support the conclusion that the near-infrared pulses launch librational motion while creating electronic coherences resulting in a libration-modulated electronic nonlinear response. The analysis of the phase-matched four-wave mixing signals suggests a nonparametric process leaving the molecules in an excited electronic state, providing new insight into ultrafast nonlinear optical interactions in liquids and advancing toward probing ultrafast electronic coherences in complex molecular liquids.

Microscopic master equations have gained traction for the dissipative treatment of molecular spin and solid-state systems for quantum technologies. Single-particle approximations are often invoked to treat these systems, which can lead to unphysical evolution when combined with master equation approaches. We present a mathematical constraint on the system-environment parameters to ensure microscopically derived Markovian master equations preserve fermionic, N-representable statistics when applied to reduced systems. We demonstrate these constraints for the recently derived unified master equation and the universal Lindblad equation, along with the Redfield master equation for cases when positivity issues are not present. For operators that break the constraint, we explore the addition of Pauli factors to recover N-representability. This work promotes feasible applications of novel microscopic master equations for realistic chemical systems.

Weak unitary symmetries of open quantum dynamics: beyond quantum master equations

Controlling light-matter interactions is emerging as a powerful strategy to enhance the performance of organic light-emitting diodes (OLEDs). By embedding the emissive layer in planar microcavities or other modified optical environments, excitons can couple to photonic modes, enabling new regimes of device operation. In the weak-coupling regime, the Purcell effect can accelerate radiative decay, while in the strong-coupling regime, excitons and photons hybridize to form entirely new energy eigenstates with altered dynamics. These effects offer potential solutions to key challenges in OLEDs, such as triplet accumulation and efficiency roll-off, yet demonstrations in the strong-coupling case remain sparse and modest. To systematically understand and optimize photodynamics across the different coupling regimes, we develop a unified quantum master equation model for microcavity OLEDs. Applying the model, we identify the conditions under which each coupling regime performs optimally. Strikingly, we find that maximizing the coupling strength does not necessarily maximize internal quantum efficiency. Instead, the efficiency depends on a delicate balance between material and cavity parameters.

In this work, we explore the range of validity of the semiclassical approximation of a quantum master equation designed to describe the c c ¯ dynamics in a quark-gluon plasma at various temperatures, in the quantum Brownian regime. We perform a comparative study of various properties, e.g., the charmonia yield, of the Wigner density obtained both with the Lindblad equation and with the associated semiclassical Fokker-Planck equation. The semiclassical description is found to reproduce with a remarkable accuracy the results obtained through the full quantum description. We show that, to a large extent, this can be attributed to the nonunitary components of the dynamics that result from the contact of the c c ¯ subsystem with the thermal quark-gluon bath, leading to a rapid classicalization of the subsystem.

Since the birth of quantum mechanics, there has been a long fascination of the role of quantum effects in the evolution of biological systems, which has inspired decoding quantum coherence effects in photosynthetic systems. In photosynthetic complexes, the pigments do not exist in isolation; they interact with their surrounding protein environment. However, the strength of this system-bath coupling can vary, and one must be careful in characterizing it (with many complexes actually in an intermediate coupling regime). This review will summarize the studies toward unraveling excitonic energy transfer in photosynthetic systems, examining the influence of electronic and vibronic coherence and system-bath interactions on transfer efficiency in photosynthetic protein complexes. The review first examines the absorption properties of chlorophylls and the structural organization of protein complexes, highlighting their role in facilitating ultrafast-energy and charge-transfer processes. It also introduces the principles of multidimensional coherent spectroscopy (a nonlinear four-wave-mixing technique) and related ultrafast spectroscopic methods, which provide key insights into these processes. We also discuss theoretical approaches and models (quantum master equations and other quantum dissipative models) used to simulate the evolution of electronic coherence in photosynthetic systems. Additionally, the review considers recent advancements in both natural and artificial photosynthetic systems, focusing on the critical role of system-bath interactions and dissipation in protein environments. These dynamics are shown to direct energy transfer effectively, overcoming the fragility of quantum coherence under physiological conditions.

Abstract The Bloch equation which first inspired the field of open quantum systems, was conceived by pure physical reasoning. Since then, the Lindblad (GKLS) form of a quantum master equation, its most general mathematical representation, became an established staple in
the open quantum systems toolbox. It allows the description of a multitude of quantum phenomena, however its universality comes at a cost – without additional constraints, the resultant dynamics are not necessarily thermodynamically consistent, and the equation itself lacks an intuitive interpretation. We present a mathematically equivalent form of the Lindblad master equation under a single constraint of strict energy conservation, which reinstates physical intuition, separating the system dynamics into its elemental parts: thermal mixing, dephasing, and energy relaxation. The analytical capabilities of the formalism are illustrated by calculating the fixed point of the dynamics and exploring the conditions for canonical invariance in quantum systems.

Abstract The repeated interaction model provides a framework for emulating and analyzing the dynamics of open quantum systems. We explore here the dynamics generated by this protocol in a system that is simultaneously coupled to two baths through noncommuting system operators. One bath is made to couple to nondiagonal elements of the system, thus it induces dissipative dynamics, while the other couples to diagonal elements, and by itself it generates pure dephasing. By solving the problem analytically exactly, we show that when both baths act concurrently, a strong systembath coupling gives rise to nonadditive effects in the dynamics. A prominent signature of this nonadditivity is the characteristic slowing down of population relaxation, driven by the influence of the dephasing bath. Beyond dynamics, we investigate the thermodynamic behavior of the model. Previous studies, using quantum master equations, showed that strong system-bath coupling created bath-cooperativity in this model, allowing heat exchange to the dephasing (diagonally coupled) bath. We find instead that, under the repeated interaction scheme, heat flows exclusively to the dissipative bath (coupled through nondiagonal elements). Our results highlight the need for a deeper understanding of the types of open quantum system dynamics and steady-state phenomena that emerge within the repeated interaction framework and the relation of this protocol to other common open quantum system techniques.

Chiral molecular junctions offer a promising platform for realizing chiral-induced spin selectivity (CISS), where spin filtering occurs without external magnetic fields. Here, we investigate spin transport in such junctions by combining quantum master equation (QME) methods for purely electronic dynamics with surface hopping (SH) and mean-field Ehrenfest (MF) approaches to incorporate electron-phonon coupling. To the best of our knowledge, this is the first study employing the SH method to investigate spin dynamics in molecular junctions. For low-frequency nuclear vibrations and weak molecule-lead coupling, the SH method is particularly suitable and outperforms MF. Our results show that transient spin polarization emerges but eventually vanishes. Bias, molecular length, and SOC govern the dynamics─higher bias enhances current but reduces polarization, while longer molecules and stronger SOC amplify it. Electron-phonon coupling modifies current-voltage responses, enhancing currents at moderate bias and suppressing them at high bias. However, the extent to which electronic and vibrational effects interplay in influencing CISS remains unclear, highlighting the need for further investigation. These findings underscore the complex relationship between electronic and vibrational interactions in CISS and suggest directions for future research in molecular spintronics.

We theoretically analyze the Photosystem II reaction center using a quantum master equation approach, where excitonic and charge-transfer rates are computed at the Redfield and Förster levels with realistic spectral densities. The focus is on ergotropy, the maximum work extractable from a quantum state without energy loss. We compute the ergotropy by constructing passive states in a thermodynamic sense. Among the electron transfer pathways, those involving charge separation between ChlD1 and PheD1, as well as a route passing through three sequential charge-separated states, yield higher ergotropy, suggesting greater capacity for work extraction, akin to quantum energy capacitors. A third pathway, bypassing the ChlD1, PheD1 pair, shows a significantly reduced ergotropy. These differences arise from population-induced transitions between active and passive regimes. Our findings highlight how biological systems may exploit nonequilibrium population structures to optimize energy conversion, connecting quantum thermodynamic principles to biological energy harvesting.

Spectral degeneracies in Liouvillian generators of dissipative dynamics generically occur as exceptional points, where the corresponding non-Hermitian operator becomes nondiagonalizable. Steady states, i.e., zero modes of Liouvillians, are considered a fundamental exception to this rule since a no-go theorem excludes nondiagonalizable degeneracies there. Here, we demonstrate that the crucial issue of diverging timescales in dissipative state preparation is largely tantamount to an asymptotic approach toward the forbidden scenario of an exceptional steady state in the thermodynamic limit. With case studies ranging from NP-complete satisfiability problems encoded in a quantum master equation to the dissipative preparation of a symmetry protected topological phase, we reveal the close relation between the computational complexity of the problem at hand, and the finite size scaling toward the exceptional steady state, exemplifying both exponential and polynomial scaling. Formally treating the weight W of quantum jumps in the Lindblad master equation as a parameter, we show that exceptional steady states at the physical value W=1 may be understood as a critical point hallmarking the onset of dynamical instability.

Magnets have recently emerged as promising candidates for quantum computing, particularly using topologically-protected nanoscale spin textures. While the quantum dynamics of such spin textures has been theoretically studied, direct experimental evidence of their nonclassical behavior remains an open challenge. To address this, we propose to employ Brillouin light scattering (BLS) as a method to probe the quantum nature of skyrmions in frustrated magnets. We show that, for a specific geometry, classical skyrmions produce symmetric sidebands in the BLS spectrum, whereas quantum skyrmions exhibit a distinct asymmetry arising from vacuum fluctuations of their rotation. By studying the photon-skyrmion interaction, we calculate the BLS spectrum using a quantum master equation and show that sideband asymmetry serves as a robust witness of energy level quantization. We find that this asymmetry is pronounced at low temperatures, and can be controlled by input laser power. These findings establish a concrete protocol for the optical detection of nonclassical features in spin textures, paving the way for exploring their role in quantum applications.

Understanding the coherent properties of electron spins driven by electric fields is crucial for their potential application in quantum-coherent nanoscience. In this work, we address two distinct driving mechanisms in electric-field-driven electron spin resonance as implemented in scanning tunneling spectroscopy. We study the origin of the driving field using a single-orbital Anderson impurity, connected to polarized leads and biased by a voltage modulated on resonance with a spin transition. By mapping the quantum master equation into a system of equations for the impurity spin, we identify two distinct driving mechanisms. Below the charging thresholds of the impurity, electron spin resonance is dominated by a magnetically exchange-driven mechanism or field-like torque. Conversely, above the charging threshold spin-transfer torque caused by the spin-polarized current through the impurity drives the spin transition. Only the first mechanism enables coherent quantum spin control, while the second one leads to fast decoherence and spin accumulation towards a non-equilibrium steady state. The electron spin resonance signals and spin dynamics vary significantly depending on which driving mechanism dominates, highlighting the potential for optimizing quantum-coherent control in electrically driven quantum systems.

A thorough understanding of electronic transport through molecular junctions in the presence of molecular vibrations is crucial for the technical progress of molecular electronics. In this work, we first develop a non-Markovian formalism to predict the waiting-time distribution (WTD) in terms of a generalized quantum master equation, which is valid for finite bias and temperatures. This formalism is applied to the investigation of electron transport through a vibrating molecule for different parameters, where the WTDs are analyzed to explore non-Markovian dynamics induced by the coupling between the molecule and the electrodes in the presence of mechanical dampings. This analysis reveals that the WTDs exhibit prominent damped oscillations for a small damping, indicating that electron transport is directly modulated by the periodic motion of the molecular vibration for both Markovian and non-Markovian couplings to the electrodes. However, the periodic oscillations are sustained for a much longer time in the presence of non-Markovian dynamics. This intriguing non-Markovian characteristic is gradually washed out by increasing either the bias or the tunneling length because both decrease the electronic correlation time, leading to an effective reduction of the coupling between molecules and electrodes. In contrast, an increasing tunneling rate gives rise to enhanced non-Markovian signatures in the WTD, which feature a strong first peak as more energy is pumped into the molecular vibrations by frequent electron tunneling events.

The theoretical description of materials' properties driven out of equilibrium has important consequences in various fields such as semiconductor spintronics, nonlinear optics, and continuous and discrete quantum information science and technology. The coupling of a quantum many-body system to an external bath can dramatically modify its dynamics compared to that of closed systems; new phenomena like relaxation and decoherence appear as a consequence of the non-unitary evolution of the quantum system. In addition, electron-electron correlations must be properly accounted for in order to go beyond a simple one-electron or mean-field description of the electronic system. Here, we discuss a first-principles methodology based on the evolution of the electronic density matrix capable of treating electron-environment interactions and electron-electron correlations at the same level of description. The effect of the environment is separated into a coherent contribution, like the coupling to applied external electromagnetic fields, and an incoherent contribution, like the interaction with lattice vibrations or the thermal background of radiation. Electron-electron interactions are included using the nonequilibrium Green's function plus the generalized Kadanoff-Baym ansatz. The obtained non-Markovian coupled set of equations reduces to the ordinary Lindblad quantum master equation form in the Markovian limit.

The article addresses the important and relevant task of remote induction of quantum dynamic scenarios. This involves transferring such scenarios from donor atoms to a target atom. This induction is based on the enhancement of quantum transitions in the presence of multiple photons of the same transition. We use the quantum master equation for the Tavis-Cummings-Hubbard (TCH) model with multiple cavities connected to the target cavity via waveguides. The dependence of the efficiency and transfer of the scenario on the number of donor cavities, the number of atoms in them, and the bandwidth of the waveguides is investigated.

Reliable quantum master equation of the Unruh-DeWitt detector

In ultrafast time-resolved experiments with gas phase molecules, the alignment of the molecular axis relative to the polarization of the interacting laser pulses plays a crucial role in determining the dynamics following this light-matter interaction. The molecular axis distribution is influenced by the interacting pulses and is intrinsically linked to the electronic coherences of the excited molecules. However, in typical theoretical calculations of such interactions, the signal is either calculated for a single molecule in the molecular frame or averaged over all possible molecular orientations to compare with the experiment. Such averaging removes information about anisotropy in the molecular-axis distribution, even though anisotropic contributions can play a significant role in the measured experimental signal. Here, we calculate the laboratory frame transient electronic first-order polarization [P(1)] spectra in terms of separated molecular frame and laboratory frame quantities. The laboratory frame polarizations are compared with orientation-averaged quantum master equation calculations, demonstrating that orientation-averaging captures only the isotropic contributions. We show that our formalism also allows us to evaluate the anisotropic contributions to the spectrum. Finally, we discuss the application of this approach to achieve ultrafast quantum state tomography using transient absorption spectroscopy and field observables in nonlinear spectroscopy.