Born-Markov Approximation Research Articles

The damping and diffusion of atoms moving in a thermal electromagnetic background

The interaction between an atom and the quantized electromagnetic field depends on the position of the atom, leading to a force which is the negative gradient of this interaction. At zero temperature, the mean of this force vanishes, but it has a nonzero value for a thermal electromagnetic background. By applying the Heisenberg equations of motion and the Born–Markov approximation, we obtain the mean and correlation of the force, which show that the center-of-mass motion of the atom is damped and diffused. This approach can be easily extended to multi-level atoms, and it is shown that the damping force and diffusion coefficients are invariant under Galilean transformations. In principle, this effect can be utilized to determine the velocity of the laboratory relative to the thermal background.

Heat currents in qubit systems

There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e. the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born–Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.

Self-consistent dynamical maps for open quantum systems

In several cases, open quantum systems can be successfully described using master equations relying on Born-Markov approximations, but going beyond these approaches has become often necessary. In this work, we introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond these master equations replacing the Born approximation with a self-consistent approximation, known as non-crossing approximation (NCA). These maps are formally similar to master equations, but allow to capture non-perturbative effects of the environment at a moderate extra numerical cost. To demonstrate their capabilities, we apply them to the spin-boson model at zero temperature for both a Ohmic and a sub-Ohmic environment, showing that they can both qualitatively capture its strong-coupling behaviour, and be quantitatively correct beyond standard master equations.

Dynamics of a quantum interacting system: Extended global approach beyond the Born-Markov and secular approximations

Dynamics of a quantum interacting system: Extended global approach beyond the Born-Markov and secular approximations

Collisional dynamics of a few atom quantum system with tunable interaction

The advent of single-atom trapping in optical tweezers and experimental evolution in control, isolation, and manipulation of cold atoms allows us to manifest the few-body physics and its connection with the many-body systems. In cold atom experiments, the universality of few-body physics is majorly governed by the scattering length which makes it an important parameter in determining theoretically calculated loss rates. Here, we numerically study the 3-body collisional dynamics for Cesium atoms using the atom loss model described by Born-Markov approximation. Using the Cs atoms provides us the freedom to vary the scattering length, a, as a function of the magnetic field through Feshbach resonances. We investigate the three-, two-, and one-particle processes in the repulsive interactions regime at different values for a. We find that the probability of one atom remaining in the trap is maximum at B = 26 G corresponding to a = 402.382a 0 and has the highest value amongst the probability of zero-, two-, and three-particle remaining in the trap at same magnetic field after the collision. Our findings leads to high fidelity single atom tweezers which have direct application in creating defect free arrays for quantum information processing purposes.

Entanglement dynamics: Generalized master equation for uniformly accelerated two-level systems

We propose an alternative form for the quantum master equation in the theory of open quantum systems. This alternative formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper times. In the Born-Markov approximation, we consider a quantum massless scalar field coupled with two-level systems. Starting from a separable state, we show the emergence of entanglement harvesting. For different proper accelerations we also verify the entanglement sudden death.

Topological signatures in the entanglement of a topological insulator-quantum dot hybrid

In the present work, we consider a hybrid plexciton composed of a semiconductor quantum dot interacting with a topological insulator nanoparticle subject to an external magnetic field. Due to the topological magnetoelectricity of the nanoparticle, long-living plasmonic surface modes are induced, which are quantized and coupled with the quantum dot through its polarization operator. We consider the hybrid as an open quantum system, such that environment effects are accounted by the master equation in the Born–Markov approximation. Then, we apply the Peres’ positive partial transpose criterion to quantify the entanglement of the hybrid. We show that this entanglement is a direct signature of the mathbb {Z}_2 invariant of topological insulators.

Trion-phonon interaction in atomically thin semiconductors

Optical and transport properties of doped monolayer semiconductors are dominated by trions, which are three-particle compounds formed by two electrons and one hole or vice versa. In this work, we investigate the trion-phonon interaction on a microscopic footing and apply our model to the exemplary case of a molybdenum diselenide (MoSe2) monolayer. We determine the trion series of states and their internal quantum structure by solving the trion Schr\"odinger equation. Transforming the system into a trion basis and solving equations of motion, including the trion-phonon interaction within the second-order Born-Markov approximation, provides a microscopic access to the trion dynamics. In particular, we investigate trion propagation and compute the diffusion coefficient and mobility. In the low density limit, we find that trions propagate less efficiently than excitons and electrons due to their stronger coupling with phonons and their larger mass. For increasing densities, we predict a drastic enhancement of diffusion caused by the build-up of a large pressure by the degenerate trion gas, which is a direct consequence of the fermionic character of trions. Our work provides microscopic insights into the trion-phonon interaction and its impact on the diffusion behaviour in atomically thin semiconductors.

Non-Markovianity in photosynthetic reaction centers: a noise-induced quantum coherence perspective

The long-standing problem of nearly perfect photosynthetic yield in some types of bacteria and nearly all kinds of plants despite the interaction with a hot and noisy environment has witnessed quantum optical explanations in the last decade. Typically in these explanations, photosynthetic reaction centers are modeled as five-level quantum heat engines where the generation of Fano-type interference due to the coupling of discrete state transitions with a common Markovian reservoir is held responsible for the enhancement of the photosynthetic efficiency. In this work, we go beyond the Born-Markov approximation used in the earlier works and study the impact of non-Markovian environments with Lorentzian spectral densities on the dynamics of light-harvesting complexes. As the main result of this work we find that irrespective of our choice of parameters falling in the over-, under-, and critically damped regimes, the non-Markovian effects can increase noise-induced coherence as compared to the corresponding Markovian case under the transient time conditions.

Non-Markovian vibrational relaxation dynamics at surfaces.

Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as a model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation of a D-Si-Si bending mode at a D:Si(100)-(2 × 1) surface, induced by a "bath" of more than 2000 phonon modes [Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], to extend previous work along various directions. First, we use a Hierarchical Effective Mode (HEM) model [Fischer et al., J. Chem. Phys. 153, 064704 (2020)] to study relaxation of higher excited vibrational states than hitherto done by solving a high-dimensional system-bath time-dependent Schrödinger equation (TDSE). In the HEM approach, (many) real bath modes are replaced by (much less) effective bath modes. Accordingly, we are able to examine scaling laws for vibrational relaxation lifetimes for a realistic surface science problem. Second, we compare the performance of the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) approach with that of the recently developed coherent-state-based multi-Davydov-D2 Ansatz [Zhou et al., J. Chem. Phys. 143, 014113 (2015)]. Both approaches work well, with some computational advantages for the latter in the presented context. Third, we apply open-system density matrix theory in comparison with basically "exact" solutions of the multi-mode TDSEs. Specifically, we use an open-system Liouville-von Neumann (LvN) equation treating vibration-phonon coupling as Markovian dissipation in Lindblad form to quantify effects beyond the Born-Markov approximation.

Quantum regression beyond the Born-Markov approximation for generalized spin-boson models

The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multitime correlation functions, thus requiring full access to the total ``$\mathrm{system}+\mathrm{environment}$'' evolution, and providing a stronger requirement than completely positive (CP) divisibility. Here, we analyze CP divisibility and check the validity of quantum regression beyond the Born-Markov approximation (e.g., the weak-coupling limit) for a class of generalized spin-boson models giving rise to a multilevel amplitude-damping evolution; in all cases, it is possible to engineer the system-bath coupling in such a way that quantum regression is exactly satisfied.

Three qubits in less than three baths: Beyond two-body system-bath interactions in quantum refrigerators

We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.

Topological signatures in a weakly dissipative Kitaev chain of finite length

We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external bath to more than one lattice site generates quantum interference effects, arising from the possibility of fermions to tunnel through multiple paths. In the presence of two baths at different temperatures and/or chemical potentials, the steady-state particle current can be expressed through the Landauer-B\"uttiker formula, as in a ballistic transport setup, with the addition of an anomaly factor associated with the presence of the $p$-wave pairing in the Kitaev Hamiltonian. Such a factor is affected by the ground-state properties of the chain, being related to the finite-size equivalent of its Pfaffian topological invariant.

Diagrammatic approach to scattering of multiphoton states in waveguide QED

We give an exposure to diagrammatic techniques in waveguide QED systems. A particular emphasis is placed on the systems with delayed coherent quantum feedback. Specifically, we show that the $N$-photon scattering matrices in single-qubit waveguide QED systems, within the rotating wave approximation, admit for a parametrization in terms of $N-1$-photon effective vertex functions and provide a detailed derivation of a closed hierarchy of generalized Bethe-Salpeter equations satisfied by these vertex functions. The advantage of this method is that the above mentioned integral equations hold independently of the number of radiation channels, their bandwidth, the dispersion of the modes they are supporting, and the structure of the radiation-qubit coupling interaction, thus enabling one to study multi-photon scattering problems beyond the Born-Markov approximation. Further, we generalize the diagrammatic techniques to the systems containing more than a single emitter by presenting an exact set of equations governing the generic two and three-photon scattering operators. The above described theoretical machinery is then showcased on the example of a three-photon scattering on a giant acoustic atom, recently studied experimentally [Nat. Phys. 15, 1123 (2019)].

The Damping and Diffusion of Atoms Moving in the Background Electromagnetic Environment

The interaction between an atom and the quantized electromagnetic field depends on the position of the atom. Then the atom experiences a force which is the minus gradient of this interaction. Through the Heisenberg equations of motion and the Born-Markov approximation, the mean and correlation of the force are obtained, showing that the center-of-mass motion of the atom is damped and diffused. This approach can be easily generalized to multi-level atoms, where the damping force and diffusion coefficients are just the weighted average of the contributions from all pairs of energy levels that have nonvanishing dipole elements. It is shown that these results are invariant under Galilean transformation, and in principle can be used to determine the velocity of the lab relative to the background radiation.

Exact N -point-function mapping between pairs of experiments with Markovian open quantum systems

We formulate an exact spacetime mapping between the $\mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A \textbf{94}, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $\mathcal{N}$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schr\"odinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $\mathcal{N}$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

Master equation for multilevel interference in a superradiant medium

We derive a master equation for a superradiant medium which includes multilevel interference betwen the individual scatterers. The derivation relies on the Born-Markov approximation and implements the coarse graining formalism. The master equation fulfils the Lindblad form and contains terms describing single-atom multilevel interference, multi-atom interference between identical transitions, and multi-atom interference between different electronic transitions with parallel dipoles. This formalism is then applied to determine the excitation spectrum of two emitters using the parameters of the Hydrogen transitions 2S$_{1/2}\,\to$4P$_{1/2}$ and 2S$_{1/2}\,\to$4P$_{3/2}$, where the gap between the parallel dipoles is of the order of GHz. The distortion of the signal due to the interplay of multilevel and multi-emitter interference is analysed as a function of their distance. These results suggest that interference between parallel dipolar transition can significantly affect the spectroscopic properties of optically dense media.

Quantum entanglement and the Born-Markov approximation for an open quantum system.

We revisit the Born-Markov approximation for an open quantum system by considering a microscopic model of the bath, namely, the Bose-Hubbard chain in the parameter region where it is chaotic in the sense of quantum chaos. It is shown that strong ergodic properties of the bath justify all approximations required for deriving the Markovian master equation from the first principles.

Dynamics of two qubits in common environment

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

Detection of quantum non-Markovianity close to the Born-Markov approximation

We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on system propagator properties, here memory effects are related to a convolution structure involving two system propagators and the environment correlation. This structure allows to detect memory effects even close to the validity of the Born-Markov approximation. An alternative operational-based definition of environment-to-system backflow of information follows from this result. We provide experimental support to our results by implementing the dynamics and measurements in a photonic experiment.