Quantum Master Equation Research Articles

Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation.

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

Emergence of prethermal states in a driven dissipative system through cross-correlated dissipation

Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-1/2 system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently reported fluctuation-regulated quantum master equation (Chakrabarti A. and Bhattacharyya R., Phys. Rev. A 97 (2018) 063837), to show that the predicted dynamics can successfully explain the experimentally observed features of the transient and prethermal regime.

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

Quantum classical approach to spin and charge pumping and the ensuing radiation in terahertz spintronics: Example of the ultrafast light-driven Weyl antiferromagnet Mn3Sn

The interaction of a femtosecond laser pulse with magnetic materials has been intensely studied for more than two decades in order to understand ultrafast demagnetization in single magnetic layers or terahertz emission from their bilayers with nonmagnetic spin-orbit (SO) materials. However, in contrast to well-understood spin and charge pumping by dynamical magnetization in spintronic systems driven by microwaves or current injection, analogous processes in light-driven magnets and radiation emitted by them remain largely unexplained due to the multiscale nature of the problem. Here we develop a multiscale quantum-classical formalism---where conduction electrons are described by quantum master equation (QME) of the Lindblad type, classical dynamics of local magnetization is described by the Landau-Lifshitz-Gilbert (LLG) equation, and incoming light is described by classical vector potential, while outgoing electromagnetic radiation is computed using the Jefimenko equations for retarded electric and magnetic fields---and apply it to a bilayer of antiferromagnetic Weyl semimetal ${\mathrm{Mn}}_{3}\mathrm{Sn}$, hosting noncollinear local magnetization, and SO-coupled nonmagnetic material. Our $\mathrm{QME}+\mathrm{LLG}+$Jefimenko scheme makes it possible to understand how a femtosecond laser pulse directly generates spin and charge pumping and electromagnetic radiation by the ${\mathrm{Mn}}_{3}\mathrm{Sn}$ layer, including both odd and even high harmonics (of the pulse center frequency) up to order $n\ensuremath{\le}7$. The directly pumped spin current then exerts spin torque on local magnetization whose dynamics, in turn, pumps additional spin and charge currents radiating in the terahertz range. By switching on and off LLG dynamics and SO couplings, we unravel which microscopic mechanism contributes the most to emitted terahertz radiation---charge pumping by local magnetization of ${\mathrm{Mn}}_{3}\mathrm{Sn}$ in the presence of its own SO coupling is far more important than standardly assumed (for other types of magnetic layers) spin pumping and subsequent spin-to-charge conversion within the adjacent nonmagnetic SO-coupled material.

Full counting statistics and coherences: Fluctuation symmetry in heat transport with the unified quantum master equation.

Recently, a "unified" quantum master equationwas derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equationdescribes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equationto investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equationgives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equationto those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.

Bespoke pulse design for robust rapid two-qubit gates with trapped ions

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.

Strong-coupling magnetophononics: Self-blocking, phonon-bitriplons, and spin-band engineering

Magnetophononics, the modulation of magnetic interactions by driving infrared-active lattice excitations, is emerging as a key mechanism for the ultrafast dynamical control of both semiclassical and quantum spin systems by coherent light. We demonstrate that, in a quantum magnet with strong spin-phonon coupling, resonances between the driven phonon and the spin excitation frequencies exhibit an intrinsic self-blocking effect, whereby only a fraction of the available laser power is absorbed by the phonon. Using the quantum master equations governing the nonequilibrium steady states of the coupled spin-lattice system, we show how self-blocking arises from the self-consistent alteration of the resonance frequencies. We link this to the appearance of mutually repelling collective spin-phonon states, which in the regime of strong hybridization become composites of a phonon and two triplons. We then identify the mechanism and optimal phonon frequencies by which to control a global nonequilibrium renormalization of the lattice-driven spin excitation spectrum and demonstrate that this effect should be observable in ultrafast THz experiments on a number of known quantum magnetic materials.

Investigating the Association Reactions of HOCH2CO and HOCHCHO with O2: A Quantum Computational and Master Equation Study

Glycolaldehyde, HOCH2CHO, is an important multifunctional atmospheric trace gas formed in the oxidation of ethylene and isoprene and emitted directly from burning biomass. The initial step in the atmospheric photooxidation of HOCH2CHO yields HOCH2CO and HOCHCHO radicals; both of these radicals react rapidly with O2 in the troposphere. This study presents a comprehensive theoretical investigation of the HOCH2CO + O2 and HOCHCHO + O2 reactions using high-level quantum chemical calculations and energy-grained master equation simulations. The HOCH2CO + O2 reaction results in the formation of a HOCH2C(O)O2 radical, while the HOCHCHO + O2 reaction yields (HCO)2 + HO2. Density functional theory calculations have identified two open unimolecular pathways associated with the HOCH2C(O)O2 radical that yield HCOCOOH + OH or HCHO + CO2 + OH products; the former novel bimolecular product pathway has not been previously reported in the literature. Master equation simulations based on the potential energy surface calculated here for the HOCH2CO + O2 recombination reaction support experimental product yield data from the literature and indicate that, even at total pressures of 1 atm, the HOCH2CO + O2 reaction yields ∼11% OH at 298 K.

Theory and computation of Markovian quantum antenna systems

We describe a general framework for the modeling and analysis of Markovian quantum antenna systems viewed as a special problem in quantum stochastic dynamics. The quantum radiator, which can be used to spatially direct radiated quantum states in future quantum communication systems, is modeled as an open quantum system capable of controlling the composition of its radiation modes through external source manipulations while in continuous interaction with the surrounding thermal and random environments. Our analysis and computational methods are based on deploying the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation to account for environment-induced jump processes such as quantum dissipation and decoherence. We construct a definition of the quantum antenna directivity inspired by the corresponding formulas in classical antenna theory and present several versions of the quantum directivity formula. As a computational example, we study the flow of the density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, which is evolved in time using the quantum master equation. It is shown that by manipulating the amplitude and phase excitations of individual quantum dots, one may significantly enhance the directive radiation properties of the Markovian quantum antenna system.

Hydration shell effects in ac-driven single-molecule junctions

We propose a quantum-mechanical model to calculate the current through a single molecular junction immersed in a solvent and surrounded by a thin shell of bound water under an applied ac voltage. The solvent plus hydration shell are captured by a dielectric continuum model for which the resulting spectral density is determined. Here the dielectric properties, e.g., the Debye relaxation time and the dielectric constant, of the bulk solvent and the hydration shell as well as the shell thickness directly enter. We determine the charge current through the molecular junction under an ac voltage in the sequential tunneling regime where we solve a quantum master equation by a real-time diagrammatic technique. Interestingly, the Fourier components of the charge current show an exponential-like decline when the hydration shell thickness increases. Finally, we apply our findings to binary solvent mixtures with varying volume fractions and find that the current is highly sensitive to both the hydration shell thickness as well as the volume fraction of the solvent mixture, giving rise to possible applications as shell and concentration sensors on the molecular scale.

Quantum nonstationary phenomena of spin systems in collision models

We investigate the non-stationary phenomenon in a tripartite spin-1/2 system in the collision model (CM) framework. After introducing the dissipation through the system-environment collision for both Markovian and non-Markovian cases, we find the emergence of long-time oscillation in the dynamics of the system and the synchronization among subsystems. We connect the CM description and the quantum master equation in the continuous time limit and explain the existence of the stable oscillation by means of Liouvillian spectrum analysis. The time-dependence of the thermal property and the correlations are investigated, in particular we discuss the possibility of violation of the Landauer's principle in non-Markovian dynamics. In addition, we find that the imperfection of collective dissipation can be compensated by the randomness of the interaction sequence in our CM.

Particle and thermal transport through one dimensional topological systems via Lindblad formalism

We apply the Lindblad quantum master equation to two examples of one-dimensional topological systems, the Su-Schrieffer-Heeger (SSH) model and Kitaev chain, to study their particle and thermal transport. The steady-state properties are obtained by decomposing fermions into Majorana fermions and extracting their correlation functions. We focus on the particle and thermal currents flowing through the bulk when the system is driven by two reservoirs coupled to the two ends. The ratio of the currents of the SSH model from the topological and trivial regimes with the same bandwidth demonstrates suppression of transport due to the edge states, which couple to the reservoirs but do not participate in transport. A similar comparison cannot be performed for the Kitaev chain because the topological and trivial regimes have different bandwidths, and the edge states are less significant away from the transition. Therefore, the results contrast different topological properties in quantum transport.

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the Bose–Einstein condensate-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model (Myers et al 2022 New J. Phys. 24 025001). Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

Robust quantum control with disorder-dressed evolution

Quantum control pulses, used to produce desired states in quantum technology applications, can be problematically sensitive to disorder. Here, the authors develop a systematic approach to finding quantum control pulses that are robust in realistic scenarios by translating disorder into a quantum master equation and maximizing the purity of the resulting density matrix.

Nonequilibrium dynamics of axionlike particles: The quantum master equation

We study the non-equilibrium dynamics of Axion-like particles (ALP) coupled to Standard Model degrees of freedom in thermal equilibrium. The Quantum Master Equation (QME) for the (ALP) reduced density matrix is derived to leading order in the coupling of the (ALP) to the thermal bath, but to \emph{all} orders of the bath couplings to degrees of freedom within or beyond the Standard Model other than the (ALP). The (QME) describes the damped oscillation dynamics of an initial misaligned (ALP) condensate, thermalization with the bath, decoherence and entropy production within a unifying framework. The (ALP) energy density $\mathcal{E}(t)$ features two components: a ``cold'' component from the misaligned condensate and a ``hot'' component from thermalization with the bath, with $\mathcal{E}(t)= \mathcal{E}_{c}\,e^{-\gamma(T)\,t}+\mathcal{E}_{h}(1-e^{-\gamma(T)\,t})$ thus providing a ``mixed dark matter'' scenario. Relaxation of the (ALP) condensate, thermalization, decoherence and entropy production occur on similar time scales. An explicit example with (ALP)-photon coupling, valid post recombination yields a relaxation rate $\gamma(T)$ with a substantial enhancement from thermal emission and absorption. A misaligned condensate is decaying at least since recombination and on the same time scale thermalizing with the cosmic microwave background (CMB). Possible consequences for birefringence of the (CMB) and (ALP) contribution to the effective number of ultrarelativistic species and galaxy formation are discussed.

Valence Orbitals Driving the Spin Dynamics in a Rare-Earth Single-Atom Magnet.

We combine spin-polarized scanning tunneling microscopy with quantum master equation analysis to investigate the spin dynamics of the single atom magnet Dy on graphene/Ir(111). By performing reading and writing experiments, we show that the strongly spin polarized 5d6s valence shells, as well as their intra-atomic exchange coupling to the 4f shell, determine the pathways for magnetization relaxation and thus the spin dynamics. The good quantum number that determines which states are stable and which mechanisms for reversal exist in a given crystal field is the atomic total angular momentum J_{z}^{tot} and not the commonly considered J_{z}^{4f} of the 4f shell only.

Vertex algebras and quantum master equation

We contribute to study the two dimensional chiral conformal field theories that arise from chiral deformations of free theories such as the $\beta \gamma$‑system, bc‑system and chiral bosons. Our method is based on the effective Batalin–Vilkovisky quantization theory. We establish an exact correspondence between renormalized quantum master equations for chiral deformations and Maurer–Cartan equations for the Lie algebra of modes of chiral vertex algebras. The generating functions on the torus are proven to have modular property with mild holomorphic anomaly. As an application, we construct an exact solution of quantum B‑model (BCOV theory) in complex one dimension that solves the full higher genus mirror symmetry conjecture on elliptic curves.

All-optical polarization-state engineering in quantum cavity optomagnonics

We theoretically propose an optical polarization-state engineering based on a cavity optomagnonic platform in the full quantum regime. Here, the optomagnonic interaction can be realized in an yttrium iron garnet (YIG) sphere, which supports both two traveling-photon modes with orthogonal linear polarizations [i.e., horizontally ($H$-) and vertically ($V$-) polarized photon modes] and a Kittel magnon mode. In our scheme, the magnons mediate the photons during polarization conversions, and break the time-reversal symmetry in mutual interconversions. Through a triple resonance between the magnon mode, $H$-polarized, and $V$-polarized photon modes within the YIG optomagnonic cavity, we demonstrate an all-optical scheme to manipulate the optical polarization behaviors by adjusting an external driving laser, finding that the polarization states of the output light can be well mapped to the whole Poincar\'e sphere and a large polarization rotation of the output light with photon antibunching and superbunching can be achieved easily for a range of realistic parameters. We find the strong discrepancy in the polarization response between the exact numerical calculation using the full quantum master equation and the semiclassical approximation. In addition, we reveal the magnon-induced broken time-reversal symmetry, which connects the quantum cavity optomagnonics to the classical magneto-optical effect. Our obtained results have potential application in quantum polarization-state engineering, and also offer a further understanding for cavity optomagnonics at the quantum level.

Nonequilibrium fluctuations in boson transport through squeezed reservoirs

We investigate the effect of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a bosonic site. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under an equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing. The odd and even cumulants saturate at two different but unique values which are identified analytically. Under maximum squeezing of one bath, the saturation value of the cumulants is solely governed by other bath’s properties. Further, squeezing always increases the magnitude of the even cumulants in comparison to the unsqueezed case. The saturation values of the even cumulants become independent of squeezing as soon as one bath is squeezed to its limit. This is in contrast to what is observed for the odd cumulants. The even cumulants are symmetric with respect to exchanging the left and right squeezing parameters while the affinity is found to be antisymmetric.

Optomechanical effects in nanocavity-enhanced resonant Raman scattering of a single molecule

In this article, we address the optomechanical effects in surface-enhanced resonant Raman scattering (SERRS) from a single molecule in a nano-particle on mirror (NPoM) nanocavity by developing a quantum master equation theory, which combines macroscopic quantum electrodynamics and electron-vibration interaction within the framework of open quantum system theory. We supplement the theory with electromagnetic simulations and time-dependent density functional theory calculations in order to study the SERRS of a methylene blue molecule in a realistic NPoM nanocavity. The simulations allow us not only to identify the conditions to achieve conventional optomechanical effects, such as vibrational pumping, non-linear scaling of Stokes and anti-Stokes scattering, but also to discovery distinct behaviors, such as the saturation of exciton population, the emergence of Mollow triplet side-bands, and higher-order Raman scattering. All in all, our study might guide further investigations of optomechanical effects in resonant Raman scattering.