We study the paradigmatic model of a qubit interacting with a structured environment and driven by an external field by means of a microscopic and a phenomenological model. The validity of the so-called fixed-dissipator (FD) assumption, where the dissipation is taken as the one of the undriven qubit is discussed. In the limit of a flat spectrum, the FD model and the microscopic one remarkably practically coincide. For a structured reservoir, we show in the secular limit that steady states can be different from those determined from the FD model, opening the possibility for exploiting reservoir engineering. We explore it as a function of the control field parameters, of the characteristics of the spectral density and of the environment temperature. The observed widening of the family of target states by reservoir engineering suggests new possibilities in quantum control protocols.
We investigate the heat transport between two nonthermal reservoirs based on a microscopic collision model. We consider a bipartite system consisting of two identical subsystems, and each subsystem interacts with its own local reservoir, which consists of a large collection of initially uncorrelated ancillas. Then a heat transport is formed between two reservoirs by a sequence of pairwise collisions (inter-subsystem and subsystem-local reservoir). In this paper we consider two kinds of reservoir's initial states, the thermal state, and the state with coherence whose diagonal elements are the s…
Quantum resources, such as entanglement, steering, and Bell nonlocality, are evaluated for three coupled qubits in the steady-state configuration. We employ the phenomenological master equation and the microscopic master equation to probe such quantum resources, which provide very different results depending on the system configuration. In particular, steering and Bell nonlocality are null within the phenomenological model, while they reach considerable values within the microscopic model. These results show that the phenomenological approach is not able to capture all quantum resources of the…
In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.
In this work we propose an approach to deal with radiation field states which incorporates damping effects at zero temperature. By using some well known results on dissipation of a cavity field state, obtained by standard ab-initio methods, it was possible to infer through a phenomenological way the explicit form for the evolution of the state vector for the whole system: the cavity-field plus reservoir. This proposal turns out to be of extreme convenience to account for the influence of the reservoir over the cavity field. To illustrate the universal applicability of our approach we consider …
Liouvillian Response for Temporal Information in Quantum Reservoir Computing
School of Physics, Sun Yat-sen University（中山大学物理学院）；School of Electronics and Information Technology, Sun Yat-sen University（中山大学电子与信息工程学院）；State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University（中山大学光电信息材料与技术国家重点实验室）；Department of Physics, Hunan Normal University（湖南师范大学物理学院）
We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C. E. Lopez et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.
We analyze the effect of a dissipative bosonic environment on the Landau-Zener-Stuckelberg-Majorana (LZSM) level crossing model by using a microscopic approach to derive the relevant master equation. For an environment at zero temperature and weak dissipation our microscopic approach confirms the independence of the survival probability on the decay rate that has been predicted earlier by the simple phenomenological LZSM model. For strong decay the microscopic approach predicts a notable increase of the survival probability, which signals dynamical decoupling of the initial state. Unlike the p…
In this paper, we derive a microscopic master equation for a pair of XY-coupled two-level systems interacting with the same memoryless reservoir. In particular, we apply this master equation to the case of a pair of two-level atoms in free space where we can clearly contrast the predictions made with the microscopic master equation obtained here and the phenomenological approaches where the atom-atom coupling is included just \textit{a posteriori}, i.e, not taking into account in the derivation of the open system equation of motion. We show, for instance, that the phenomenological approach fai…
We present a derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3+1)-D microscopic model with local U(1) gauge symmetry. We show that inclusion of local chemical potential and driving velocity fields as a gauge field allows derivation of the hydrodynamic equations of motion for the driven macroscopic phase differences across simple aperture arrays. For a single aperture, the current-phase equation for driven flow contains sinusoidal, linear, and current-bias contributions. We compute the renormalizatio…
Based on a system-reservoir model and an appropriate choice of nonlinear coupling, we have explored the microscopic quantum generalization of classical Liénard systems. Making use of oscillator coherent states and canonical thermal distributions of the associated c-numbers, we have derived the quantum Langevin equation of the reduced system which admits of single or multiple limit cycles. It has been shown that detailed balance in the form of fluctuation-dissipation relation preserves the dynamical stability of the attractors even in case of vacuum excitation. The quantum versions of Rayleigh,…
From quantum mechanical first principles only, we rigorously study the time-evolution of a $N$-level atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at thermal equilibrium (reservoir). In particular, we establish the relation between the full dynamics of the compound system and the effective dynamics for the $N$-level atom, which is studied in detail in [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012]. Together with [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012] t…
We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by coupling each site to a local fermionic bath. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the time evolution of the reduced density matrix. In spite of a local coupling to the baths, the found Lindblad operators are non-local in space. We compare with the local approximation, where those non-local effects are neglected. Furthermore, we prop…
We study the effect of the environment on the process of the measurement of a state of a microscopic spin half system. The measuring apparatus is a heavy particle, whose center of mass coordinates can be considered at the end of the measurement as approximately classical, and thus can be used as a pointer. The state of the pointer, which is the result of its interaction with the spin, is transformed into a mixed state by the coupling of the pointer to the environment. The environment is considered to be a gas reservoir, whose particles interact with the pointer. This results in a Fokker-Planck…
In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies in the possibility of splitting the complex environment in a direct sum of sub-reservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different sub-reservoirs, characterize the average system decay dynamics. As an example, we study the anomal…
We use the microscopic derivation of the Jaynes-Cummings model master equation under field losses to study the dynamics of initial field states beyond the single-excitation manifold. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate in the model using entropy measures, like qubit-field purity and von Neumann entropy of the field, for initial Fock states. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the s…
Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows a detailed investigation and comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, we find that the structure of widely used phenomenological master equations with memory kernel may be incompatible with a …
A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the gene…
Finite-Size Effects in Quantum Metrology at Strong Coupling: Microscopic vs Phenomenological Approaches
Koç University（科奇大学）；Korea Research Institute of Standards and Science（韩国标准科学研究所）；University of Calgary（卡尔加里大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科技研究基金会基础科学研究院（TBAE））
We consider interacting one-dimensional, spinless Fermi gases, whose low-energy properties are described by Luttinger liquid theory. We perform a systematic, in-depth analysis of the relation between the macroscopic, phenomenological parameters of Luttinger liquid effective field theory, and the microscopic interactions of the Fermi gas. In particular, we begin by explaining how to model effective interactions in one dimension, which we then apply to the main forward scattering channel -- the interbranch collisions -- common to these systems. We renormalise the corresponding interbranch phenom…
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive "phenomenological" model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for bot…
The microscopic theory of the Casimir effect in the dielectric is studied in the framework when absorption is realized via a reservoir modeled by a set of oscillators with continuously distributed frquencies with the aim to see if the effects depend on the form of interaction with the reservoir. A simple case of the one-dimensional dielectric between two metallic plates is considered. Two possible models are investigated, the direct interaction of the electromagnetic field with the reservoir and indirect interaction via an intermediate oscillator imitating the atom. It is found that with the s…
