We propose a method which combines the quantum-classical mapping approach to surface hopping (MASH) with the dissipative quantum dynamics of the Lindblad master equation. Like conventional surface-hopping methods, our approach is based on classical trajectories coupled to the dynamics of a quantum subsystem. However, instead of evolving the subsystem wavefunction according to the time-dependent Schrödinger equation, we use stochastic quantum trajectories derived from secular Redfield theory. This enables the simulation of open quantum systems coupled simultaneously to Markovian quantum baths and anharmonic non-Markovian classical degrees of freedom. Applications to the spin--boson model and to the cavity-enhanced fluorescence of an electronically nonadiabatic molecule show excellent agreement with fully quantum-mechanical benchmarks.
We discuss hybrid master equations of composite systems which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested, its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement
Canonical coupling between classical and quantum systems cannot result in reversible equations, rather it leads to irreversible master equations. Coupling of quantized non-relativistic matter to gravity is illustrated by a simplistic example. The heuristic derivation yields the theory of gravity-related decoherence proposed longtime ago by Penrose and the author.
Based on the recent experiments on the hybrid quantum system of a superconducting microwave cavity coupling strongly to an inhomogeneous broadening spin ensemble under an external driving field, we use the exact master equation approach to investigate its non-Markovian decoherence dynamics. Here the spin ensemble is made by negatively charged nitrogen-vacancy (NV) defects in diamond. Our exact master equation theory for open systems depicts the experimental decoherence results and reveals the mechanism how the decoherence induced by the inhomogeneous broadening is suppressed in the strong-coup…
Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron-temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an ea…
The interaction among the components of a hybrid quantum system is often neglected when considering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical predictions, as has been shown for cavity-QED and optomechanical systems in the ultrastrong-coupling regime. To deal with these cases, master equations with dissipators retaining the interaction between these components have been derived for the quantum Rabi model and for the standard optomechanical Hamiltonian. In this article, we go beyond these previous der…
We present a theoretical study of the resonance fluorescence spectra of an optically driven quantum dot placed near a single metal nanoparticle. The metallic reservoir coupling is calculated for an 8-nm metal nanoparticle using a time-convolutionless master equation approach where the exact photon reservoir function is included using Green function theory. By exciting the system coherently near the nanoparticle dipole mode, we show that the driven Mollow spectrum becomes highly asymmetric due to internal coupling effects with higher-order plasmons. We also highlight regimes of resonance squeez…
We investigate quantum heat transfer and thermal management in the nonequilibrium qubit-phonon hybrid system by applying the quantum master equation embedded with phononic coherent state. We obtain the steady state heat flow by tuning the arbitrary qubit-phonon coupling strength, which particularly exhibits the power-law scaling behavior and the turnover behavior in the weak and strong coupling regimes, respectively. Moreover, we analyze the negative differential thermal conductance and thermal rectification, which becomes profound with weak qubit-phonon interaction and large temperature bias.…
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environme…
We consider the problem of the measurement of a system occurring during a finite time interval, while environmentally-induced noise decreases the system-state coherence. We assume a Markovian measuring device and, therefore, use a Lindbladian description for the measurement dynamics. For studying the case of noise produced by a non-Markovian environment, whose definition does not include the measuring apparatus, we use the Redfield approach to the interaction between system and environment. In the present hybrid theory, to trace out the environmental degrees of freedom, we introduce an analyti…
Dynamics of a state of interest coupled to a non-Markovian environment is studied for the first time by concatenating the non-Markovian quantum state diffusion (QSD) equation and the Feshbach projection operator partitioning technique. An exact one-dimensional stochastic master equation is derived as a general tool for controlling an arbitrary component of the system. We show that the exact one-dimensional stochastic master equation can be efficiently solved beyond the widely adapted second-order master equations. The generality and applicability of this hybrid approach is justified and exempl…
A comparison of different master equations for driven-dissipative dynamics in composite quantum systems: Dispersive readout in structured electromagnetic environments
Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law must be a completely positive and norm preserving map. We prove that if the dynamics is memoryless, there are two classes of these dynamics, one which features finite sized jumps in the classical phase space and one which is continuous. We find the most general form of each class of classical-quantum master equation. This is achieved by applying the complete…
We propose a level-resolved protocol in a hybrid architecture for connecting a superconducting qubit and a magnon mode contained within a microwave cavity (resonator) to generate the local and global entangled states, enabling a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Exploiting the high-degree of controllability in such a hybrid qubit-photon-magnon system, we derive effective Hamiltonians at the second- or the third-order resonant points by virtue of the strong counter-rotating interactions between the resonator and the qubit…
We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illu…
We describe a method for simulating exciton dynamics in protein-pigment complexes, including effects from charge transfer as well as fluorescence. The method combines the hierarchical equations of motion, which are used to describe quantum dynamics of excitons, and the Nakajima-Zwanzig quantum master equation, which is used to describe slower charge transfer processes. We study the charge transfer quenching in light harvesting complex II, a protein postulated to control non-photochemcial quenching in many plant species. Using our hybrid approach, we find good agreement between our calculation …
A hybrid quantum-classical filtering problem, where a qubit system is disturbed by a classical stochastic process, is investigated. The strategy is to model the classical disturbance by using an optical cavity. Relations between classical disturbances and the cavity analog system are analyzed. The dynamics of the enlarged quantum network system, which includes a qubit system and a cavity system, are derived. A stochastic master equation for the qubit-cavity hybrid system is given, based on which estimates for the state of the cavity system and the classical signal are obtained. The quantum ext…
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the approaches of master equation and covariance matrix, we discuss the respective squeezing effects in detail and find that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is …
The implementation of a single magnon level quantum manipulation is one of the fundamental targets in quantum magnetism with a significant practical relevance for precision metrology, quantum information processing, and quantum simulation. Here, we demonstrate theoretically the feasibility of using a hybrid ferromagnet-superconductor quantum system to prepare a single magnon source based on magnon blockade effects. By numerically solving the quantum master equation, we show that the second-order correlation function of the magnon mode depends crucially on the relation between the qubit-magnon …
We investigate steady-state thermal transport and photon statistics in a nonequilibrium hybrid quantum system, in which a qubit is longitudinally and quadratically coupled to an optical resonator. Our calculations are conducted with the method of the quantum dressed master equation combined with full counting statistics. The effect of negative differential thermal conductance is unravelled at finite temperature bias, which stems from the suppression of cyclic heat transitions and large mismatch of two squeezed photon modes at weak and strong qubit-resonator hybridizations, respectively. The gi…
The recent development of hybrid cQED allows one to study how cavity photons interact with a system driven out of equilibrium by fermionic reservoirs. We study here one of the simplest combination : a double quantum dot coupled to a single mode of the electromagnetic field. We are able to couple resonantly the charge levels of a carbon nanotube based double dot to cavity photons. We perform a microwave read out of the charge states of this system which allows us to unveil features of the out of equilibrium charge dynamics, otherwise invisible in the DC current. We extract relaxation rate, deph…
Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition (BD) approach that exploits multiple feasible solutions of the master problem (MP) to generate multiple valid cuts is adapted, so as to be used as an HQC solver for general mixed-integer linear programming (MILP) problems. The use of different cut selection criteria and strategies to manage the size of the MP by eliciting a subset of cuts to be added in each …
The problem of a driven quantum system coupled to a bath and coherently driven is usually treated using either of two approaches: Employing the common secular approximation in the lab frame (as usually done in the context of atomic physics) or in the rotating frame (prevailing in, e.g., the treatment of solid-state qubits). These approaches are applicable in different parts of the parameter space and yield different results. We show how to bridge between these two approaches by working in the rotating frame without employing the secular approximation with respect to the driving amplitude. This…
Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system-bath dissipation. Here by exemplifying in a nonequilibrium qubit-phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system-bath dissipation. By using coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, steady state heat current and current fluctuations will be significantly suppre…
We introduce a hybrid tripartite quantum system for strong coupling between a semiconductor spin, a mechanical phonon, and a microwave photon. Consisting of a piezoelectric resonator with an integrated diamond strain concentrator, this system achieves microwave-acoustic and spin-acoustic coupling rates $\sim$MHz or greater, allowing for simultaneous ultra-high cooperativities ($\sim 10^3$ and $\sim 10^2$, respectively). From finite-element modeling and master equation simulations, we estimate photon-to-spin quantum state transfer fidelities exceeding 0.97 based on separately demonstrated devic…
We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and its lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm performance of our scheme by numerically solving the quantum optical master equation including sources of noise. The eff…
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantu…
We provide a microscopic derivation for the non-Markovian master equation for an atom-cavity system with cavity losses and show that they can induce population trapping in the atomic excited state, when the environment outside the cavity has a non-flat spectrum. Our results apply to hybrid solid state systems and can turn out to be helpful to find the most appropriate description of leakage in the recent developments of cavity quantum electrodynamics.
Hybrid quantum systems seek to combine the strength of its constituents to master the fundamental conflicting requirements of quantum technology: fast and accurate systems control together with perfect shielding from the environment, including the measurements apparatus, to achieve long quantum coherence. Excellent examples for hybrid quantum systems are heterogeneous spin systems where electron spins are used for readout and control while nuclear spins are used as long-lived quantum bits. Here we show that joint initialization, projective readout and fast local and non-local gate operations a…
Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach. And then, we consider the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent work [Phys. Rev. Lett. 120, 030403], the authors concluded that the dynamic…
Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamic…
We study the dynamics of a mechanical resonator parametrically coupled to a driven dissipative quantum emitter in the ultra-strong coupling regime. We show that this regime is fully compatible with a semi-classical treatment, and we derive master equations for the emitter and the resonator. We show that the fluctuations of the driven emitter's population induce the non-symmetrical scattering of the mechanical quadratures. At long timescales, such scattering back-acts on the emitter, which eventually decouples from the driving light. This optical noise at the quantum limit is observable with st…
We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific structure. The role of the quantum algorithm is to find integer solutions to subproblems appearing in Branch-and-Price. Obtaining optimal or near-optimal integer solutions to these subproblems can increase the quality of solutions and reduce the depth and branching factor of the Branch-and-Price algorithm and hence reduce the overall running time. We investigate…
