Quantum Master Equation Research Articles

Dynamics of high-dimensional quantum systems coupled to a harmonic bath. General theory and implementation via multiconfigurational wave packets and truncated hierarchical equations for the mean-fields.

Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system-bath interactions, where a large number of degrees of freedom must be explicitly considered.

Connected sum for modular operads and Beilinson–Drinfeld algebras

Modular operads relevant to string theory can be equipped with an additional structure, coming from the connected sum of surfaces. Motivated by this example, we introduce a notion of connected sum for general modular operads. We show that a connected sum induces a commutative product on the space of functions associated to the modular operad. Moreover, we combine this product with Barannikov’s non-commutative Batalin–Vilkovisky structure present on this space of functions, obtaining a Beilinson–Drinfeld algebra. Finally, we study the quantum master equation using the exponential defined using this commutative product.

BRST covariant phase space and holographic Ward identities

This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether’s second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian Ward identity for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST-BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical -matrix under asymptotic symmetries. Holographic anomalies for the boundary Ward identity are studied and found to be solutions of a codimension one Wess-Zumino consistency condition. Such solutions are studied in the context of extended BMS symmetry. Their existence clarifies the status of the 1-loop correction to the subleading soft graviton theorem.

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

Quantum control of polariton emission in a microcavity-quantum well system under magnetic field

In this work, a quantum dissipative model is employed to investigate the influence of a perpendicular magnetic field on the photoluminescence (PL) spectrum of a quantum well embedded within a microcavity. This model incorporates both the exact electron-hole interaction within the semiconductor and the light-matter coupling between the fundamental photonic mode and the fermionic particles. The loss and pumping mechanisms are described using the quantum master equation, and the PL spectrum is determined via the quantum regression theorem. Our findings demonstrate that the magnetic field acts as a control mechanism in the polariton emission energy, the emission linewidth and the intensity distribution along the emission line. Finally, it is observed that the magnetic field can redistribute the density matrix occupations leading to modifications in the average number of polaritons in the system.

Extended perturbative approach including Redfield and Förster limits for qualitative analysis of exciton dynamics in any photosynthetic light harvesting and reaction center

According to many reports, the various structures of photosynthetic light-harvesting/reaction-center complexes and their molecular-dynamics simulations necessitate a numerically efficient and quality-conserved theory of excitation energy transfer and exciton relaxation in large pigment systems. Although exciton dynamics depend on various parameters, such as exciton coupling strength, exciton–phonon coupling, site energy values for each pigment, and temperature, classifying the transition mechanism for any Hamiltonian into perturbatively delocalized or localized theories is challenging. In this study, perturbative quantum master equations of a reduced density matrix for any orthogonal transformation similar to the coherent modified Redfield theory are derived. Our approach qualitatively conserves the dynamics of relevant perturbative approximations in each limiting case. As an application, any orthogonal transformation of a relevant system is optimized using the average of the square of interactions between orthogonal state transitions. The numerical results for two pigment systems are compared with the limiting formalisms of the modified Redfield and Förster theory.

Quantum Bernoulli noises approach to quantum master equations and applications to Ehrenfest-type theorems

This paper investigates the regularity properties of quantum master equations with unbounded coefficients within the space of square-integrable complex-valued Bernoulli functionals. Initially, we demonstrate the existence of a unique regular solution to the linear stochastic Schrödinger equation driven by cylindrical Brownian motions. Subsequently, we establish the existence of regular solutions for the autonomous linear quantum master equation and provide a probabilistic representation of this solution in terms of the stochastic Schrödinger equation. Finally, by taking the expectation of some observables with respect to the solution of the quantum master equation, we derive a system of differential equations that describe the evolution of the mean values of certain quantum observables.

Non-equilibrium rate theory for polariton relaxation dynamics.

We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

On the existence of heterotic-string and type-II-superstring field theory vertices

We consider the problem of the existence of heterotic-string and type-II-superstring field theory vertices in the product of spaces of bordered surfaces parameterizing the left- and right-moving sectors of these theories. It turns out that this problem can be solved by proving the existence of a solution to the BV quantum master equation in moduli spaces of bordered spin-Riemann surfaces. We first prove that for arbitrary genus ▪, ▪ Neveu–Schwarz boundary components, and ▪ Ramond boundary components such solutions exist. We also prove that these solutions are unique up to homotopy in the category of BV algebras. Furthermore, we prove that there exists a map in this category under which these solutions are mapped to fundamental classes of Deligne-Mumford stacks of associated punctured spin-Riemann surfaces. These results generalize the work of Costello on the existence of a solution to the BV quantum master equations in moduli spaces of bordered Riemann surfaces which, through the work of Sen and Zwiebach, are related to the existence of bosonic-string vertices, and their relation to fundamental classes of Deligne-Mumford stacks of associated punctured Riemann surfaces. Using the existence of solutions to the BV quantum master equation in moduli spaces of spin-Riemann surfaces, we prove that heterotic-string and type-II-superstring field theory vertices, for arbitrary genus ▪ and an arbitrary number of any type of boundary components, exist. Furthermore, we prove the existence of a solution to the BV quantum master equation in spaces of bordered N=1 super-Riemann surfaces for arbitrary genus ▪, ▪ Neveu–Schwarz boundary components, and ▪ Ramond boundary components.

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems.

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

Computation of biological conductance with Liouville quantum master equation

Recent experiments have revealed that single proteins can display high conductivity, which stays finite for low temperatures, decays slowly with distance, and exhibits a rich spatial structure featuring highly conducting and strongly insulating domains. Here, we intruduce a new formula by combining the density matrix of the Liouville-Master Equation simulating quantum transport in nanoscale devices, and the phenomenological model of electronic conductance through molecules, that can account for the observed distance- and temperature dependence of conductance in proteins. We demonstrate its efficacy on experimentally highly conductive extracellular cytochrome nanowires, which are good candidates to illustrate our new approach by calculating and visualizing their electronic wiring, given the interest in the arrangement of their conducting and insulating parts. As proteins and protein nanowires exhibit significant potential for diverse applications, including energy production and sensing, our computational technique can accelerate the design of nano-bioelectronic devices.

Coherent Acoustic Control of Defect Orbital States in the Strong-Driving Limit

We use a bulk acoustic wave resonator to demonstrate coherent control of the excited orbital states in a diamond nitrogen-vacancy (NV) center at cryogenic temperature. Coherent quantum control is an essential tool for understanding and mitigating decoherence. Moreover, characterizing and controlling orbital states is a central challenge for quantum networking, where optical coherence is tied to orbital coherence. We study resonant multiphonon orbital Rabi oscillations in both the frequency and time domain, extracting the strength of the orbital-phonon interactions and the coherence of the acoustically driven orbital states. We reach the strong-driving limit, where the physics is dominated by the coupling induced by the acoustic waves. We find agreement between our measurements, quantum master-equation simulations, and a Landau-Zener transition model in the strong-driving limit. Using perturbation theory, we derive an expression for the orbital Rabi frequency versus the acoustic drive strength that is nonperturbative in the drive strength and agrees well with our measurements for all acoustic powers. Motivated by continuous-wave spin-resonance-based decoherence protection schemes, we model the orbital decoherence and find good agreement between our model and our measured few-to-several-nanoseconds orbital decoherence times. We discuss the outlook for orbital decoherence protection. Published by the American Physical Society 2024

Efficient Microwave Photon-to-Electron Conversion in a High-Impedance Quantum Circuit.

We demonstrate an efficient and continuous microwave photon-to-electron converter with large quantum efficiency (83%) and low dark current. These unique properties are enabled by the use of a high kinetic inductance disordered superconductor, granular aluminium, to enhance light-matter interaction and the coupling of microwave photons to electron tunneling processes. As a consequence of strong coupling, we observe both linear and nonlinear photon-assisted processes where two, three, and four photons are converted into a single electron at unprecedentedly low light intensities. Theoretical predictions, which require quantization of the photonic field within a quantum master equation framework, reproduce well the experimental data. This experimental advancement brings the foundation for high-efficiency detection of individual microwave photons using charge-based detection techniques.

Coherent feedback ground state cooling of the mechanical resonator in quadratic optomechanical system assisted by an atomic ensemble

We propose a scheme for cooling a mechanical resonator to its ground state in a quadratic optomechanical system, assisted by an atomic ensemble in the unresolved sideband regime. The system features an auxiliary cavity directly coupled to an optical cavity, with a portion of the optical cavity’s output field being fed back through an asymmetric beam splitter. Utilizing quantum Langevin and master equations, we derive the optical fluctuation spectrum, the cooling rate, and the mean phonon number of the mechanical resonator. Our results demonstrate that the feedback mechanism substantially enhances the cooling rate. Furthermore, under optimal cooling conditions, the mechanical resonator achieves ground state cooling even with weaker optomechanical coupling strengths and higher auxiliary cavity dissipation rates, thereby mitigating the experimental constraints associated with these parameters. Additionally, we provide the feasible ranges for optomechanical coupling strength and atomic decay rates. Our findings suggest promising avenues for quantum manipulation in nonlinear systems and its applications in macroscopic optical devices.

Adding stubs to quantum string field theories

Generalizing recent work by Schnabl-Stettinger and Erbin-Fırat, we outline a universal algebraic procedure for ‘adding stubs’ to string field theories obeying the BV quantum master equation. We apply our results to classical and quantum closed string field theory as well as to open-closed string field theory. We also clarify several aspects of the integration-out process in the co-algebraic formulation of string field theory at the quantum level.

Adaptive spiking, itinerancy, and quantum effects in artificial neuron circuit hardware with niobium–hafnium oxide-niobium memristor devices inserted

To improve artificial intelligence/autonomous systems and help with treating neurological conditions, there is a requirement for the discovery and design of artificial neuron hardware that mimics the advanced functionality and operation of the neural networks available in biological organisms. We examine experimental artificial neuron circuits that we designed and built in hardware with memristor devices using 4.2 nm of hafnium oxide and niobium metal inserted in the positive and negative feedback of an oscillator. At room temperature, these artificial neurons have adaptive a spiking behavior and hybrid non-chaotic/chaotic modes. When networked, they output with strong itinerancy, and we demonstrate a four-neuron learning network and modulation of signals. The superconducting state at 8.1 K results in Josephson tunneling with signs that the hafnium oxide ionic states are influenced by quantum control effects in accordance with quantum master equation calculations of the expectation values and correlation functions with a calibrated time-dependent Hamiltonian. These results are of importance to continue advancing neuromorphic hardware technologies that integrate memristors and other memory devices for many biological-inspired applications and beyond that can function with adaptive-itinerant spiking and quantum effects in their principles of operation.

Coherent control from quantum commitment probabilities.

We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail.

Entropy variances of pure coherent states in the diffusion channel

Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system’s complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

The Quantum A∞-relations on the elliptic curve

We define and prove the existence of the Quantum A∞-relations on the Fukaya category of the elliptic curve, using the notion of the Feynman transform of a modular operad, as defined by Getzler and Kapranov. Following Barannikov, these relations may be viewed as defining a solution to the quantum master equation of Batalin-Vilkovisky geometry.