We present a method for dealing with quantum systems coupled to a structured reservoir with any density of modes and with more than one excitation. We apply the method to a two-level atom coupled to the edge of a photonic band gap and a defect mode. Results pertaining to this system, provide the solution to the problem of two photons in the reservoir and possible generalization is discussed.
We present a formalism that enables the study of the non-Markovian dynamics of a three-level ladder system in a single structured reservoir. The three-level system is strongly coupled to a bath of reservoir modes and two quantum excitations of the reservoir are expected. We show that the dynamics only depends on reservoir structure functions, which are products of the mode density with the coupling constant squared. This result may enable pseudomode theory to treat multiple excitations of a structured reservoir. The treatment uses Laplace transforms and an elimination of variables to obtain a …
We study the exact entanglement dynamics of two qubits in a common structured reservoir. We demonstrate that, for certain classes of entangled states, entanglement sudden death occurs, while for certain initially factorized states, entanglement sudden birth takes place. The backaction of the non-Markovian reservoir is responsible for revivals of entanglement after sudden death has occurred, and also for periods of disentanglement following entanglement sudden birth.
The non-Markovian master equations are derived to study quantum discord dynamics of two qubits coupled to a common reservoir and two independent reservoirs, respectively. We compare the dynamics under different parameters, such as reservoir spectra and resonant parameters, at high temperature and at zero temperature. The results indicate that the dynamics at these two extreme temperatures share similar characters, as well as differences.
We address the evolution of entanglement in bimodal continuous variable quantum systems interacting with two independent structured reservoirs. We derive an analytic expression for the entanglement of formation without performing the Markov and the secular approximations and study in details the entanglement dynamics for various types of structured reservoirs and for different reservoir temperatures, assuming the two modes initially excited in a twin-beam state. Our analytic solution allows us to identify three dynamical regimes characterized by different behaviors of the entanglement: the ent…
We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jump method [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clear physical picture of how the structured reservoir affects the system dynamics, indicating the role of the pseudomodes as an effective description of the environmental memory.
We study a single two-level atom interacting with a reservoir of modes defined by a reservoir structure function with a frequency gap. Using the pseudomodes technique, we derive the main features of a trapping state formed in the weak coupling regime. Utilising different entanglement measures we show that strong correlations and entanglement between the atom and the modes are in existence when this state is formed. Furthermore, an unexpected feature for the reservoir is revealed. In the long time limit and for weak coupling the reservoir spectrum is not constant in time.
We propose the entropic measurement-induced nonlocality (MIN) as the maximal increment of von Neumann entropy induced by the locally non-disturbing measurement, and study behaviors of it both in the independent and common structured reservoirs. We present schemes for preserving the MIN, and show that for certain initial states the MIN, including the quantum correlations, can even be enhanced by the common reservoir. Additionally, we also show that the different measures of MIN may give different qualitative characterizations of nonlocal properties, i.e., it is rather measure dependent than sta…
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated…
Seeking flexible methods to control quantum teleportation in open systems is an important task of quantum communication. In this paper, we study how the super-Ohmic, Ohmic and sub-Ohmic reservoirs affect teleportation of a general one-qubit state. The results revealed that the structures of the reservoirs play a decisive role on quality of teleportation. Particularly, the fidelity of teleportation may be improved by the strong backaction of the non-Markovian memory effects of the reservoir. The physical mechanism responsible for this improvement are determined.
We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states…
The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In González-Tudela \emph{et al} we show how exotic quantum dynamics emerge when QEs are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic interactions and novel super and subradiant behaviour. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the ban…
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…
We analyze the spontaneous emission of a two-level atom interacting with a special class of structured reservoirs of field modes with band gap edge coinciding with the atomic transition frequency. The exact time evolution of the population of the excited level is evaluated analytically through series of Fox-$H$ functions. Over estimated long time scales, inverse power law relaxations emerge, with powers decreasing continuously to 2 according to the choice of the special reservoir. No trapping of the population of the excited level emerges. The same results are recovered in presence of $N-1$ at…
The decay dynamics of the classical electromagnetic field in a leaky optical resonator supporting a single mode coupled to a structured continuum of modes (reservoir) is theoretically investigated, and the issue of threshold condition for lasing in presence of an inverted medium is comprehensively addressed. Specific analytical results are given for a single-mode microcavity resonantly coupled to a coupled resonator optical waveguide (CROW), which supports a band of continuous modes acting as decay channels. For weak coupling, the usual exponential Weisskopf-Wigner (Markovian) decay of the fie…
We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which can not be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band we predict an exponential relaxation at a rate different from that predicted by the Fermi's Golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directi…
Correlation Enhanced Autonomous Quantum Battery Charging via Structured Reservoirs
Abdelmalek Essaadi University（阿卜杜勒马利克·埃萨迪大学）；Mohammed VI Polytechnic University (UM6P)（穆罕默德六世polytechnic大学）；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Koç University（库奇大学）；TÜBİTAK Research Institute for Fundamental Sciences（土耳其科学与技术研究基金会基础科学研究所）
The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of inc…
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multi-photon pulses can yield a significantly higher steady-st…
We consider N driven two-level atoms interacting with a structured reservoir. By dressing the collective operators within a semiclassical approach, we derive a master equation and a mean-field single particle effective Hamiltonian. This Hamiltonian describes the optical bistability phenomenon occurring in the relation between an input electromagnetic field and the effective output generated by the N atoms. The dissipative part of the master equation and the effective single-particle Hamiltonian contain new terms due the reservoir structure of modes. In plotting the output field amplitude and p…
We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir under specific system symmetries. In the regime of multiple atoms coupled to a single reservoir with identical couplings, we identify remarkable effects, notably that the initial configuration of the atomic excited state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady state amplitudes of the excited states become independent of the choice of the reservoir. The framework introduced is applied to a structured photonic reser…
The spontaneous emission rate of a quantum dot coupled to a structured photonic reservoir is determined by the frequency dependence of its local density of photon states. Through phonon-dressing, a breakdown of Fermi's golden rule can occur for certain photonic structures whose photon decay time become comparable to the longitudinal acoustic phonon decay times. We present a polaron master equation model to calculate the photoluminescence intensity from a coherently excited quantum dot coupled to a structured photonic reservoir. We consider examples of a semiconductor microcavity and a coupled …
We investigate the long-lived quantum coherence of two-level spontaneous emission models within structured environments. The population of the system under the asymptotic non-Markovian dynamics is linked to the spectral density of the reservoir through a general functional relation between them. We figure out explicitly the preservation of quantum coherence, via notions of entanglement and quantum discord, in connection with the spectral parameters of Ohmic class reservoirs and then show how to achieve them optimally. We expect these results to contribute towards reservoir engineering with the…
Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and stru…
We introduce Hermite polynomial excitation squeezed vacuum (SV) H_{n}(O)S(r)|0> with O=u a+v a^{+}. We investigate analytically the nonclassical properties according to Mandel's Q parameter, second correlation function, squeezing effect and the negativity of Wigner function (WF). It is found that all these nonclassicalities can be enhanced by H_{n}(O)operation and adjustable parameters u and v. In particular, the optimal negative volume delta_{opt}of WF can be achieved by modulating u and v for n>=2,while delta is kept unchanged for n=1. Furthermore, the decoherence effect of phase-sensitive e…
We present a non-Markovian quantum trajectory method for treating atoms radiating into a reservoir with a non-flat density of states. The results of an example numerical simulation of the case where the free space modes of the reservoir are altered by the presence of a cavity are presented and compared with those of an extended system approach.
A structured electromagnetic reservoir can result in novel dynamics of quantum emitters. In particular, the reservoir can be tailored to have a memory of past interactions with emitters, in contrast to memory-less Markovian dynamics of typical open systems. In this Article, we investigate the non-Markovian dynamics of a superconducting qubit strongly coupled to a superconducting slow-light waveguide reservoir. Tuning the qubit into the spectral vicinity of the passband of this waveguide, we find non-exponential energy relaxation as well as substantial changes to the qubit emission rate. Furthe…
In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after t…
We study the effects of spontaneous emission on the entanglement dynamics of two qubits interacting with a common Lorentzian structured reservoir. We assume that the qubits are initially prepared in a Bell-like state. We focus on the strong coupling regime and study the entanglement dynamics for different regions of the spontaneous emission decay parameter. This investigation allows us to explore the cross-over between common and independent reservoirs in entanglement dynamics.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a coupled cavity waveguide, which are of current experimental interest. For the case of optical cavities, we dir…
We study a single two-level atom interacting with a reservoir of modes defined by its reservoir structure function. Within this framework we are able to define a density of entanglement involving a continuum of reservoir modes. The density of entanglement is derived for a system with a single excitation by taking a limit of the global entanglement. Utilizing the density of entanglement we quantify the entanglement between the atom and the modes, and also between the reservoir modes themselves.
This paper deals with non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in high Q cavities or photonic band gap materials. In cases such as the former, we show that the pseudo mode theory for single quantum reservoir excitations can be obtained by applying the Fano diagonalisation method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling…
We describe how a structured photonic medium controls the spontaneous emission rate from an excited quantum dot in the presence of electron-phonon coupling. We analyze this problem using a polaron transformed master equation and we consider specific examples of a photonic crystal cavity and a coupled cavity waveguide. We find that when the relaxation times of the photon and phonon baths are comparable, phonons influence spontaneous emission in a non-trivial way. We demonstrate why and how the broadband frequency dependence of the local photon density of states determines the photon emission ra…
We study the dissipative dynamics of neutral atoms in anisotropic harmonic potentials, immersed in a reservoir species that is not trapped by the harmonic potential. Considering initial motional excitation of the atoms along one direction, we explore the resulting spontaneous emission of reservoir excitations, across a range of trap parameters from strong to weak radial confinement. In different limits these processes are useful as a basis for analogies to laser cooling, or as a means to introduce controlled dissipation to many-body dynamics. For realistic experimental parameters, we analyse t…
We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e. the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature and the interaction time. Upon …
The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In…
By using the effective non-Markovian measure [H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a nega…
We investigate the collective interaction of a multi-atom three-level ladder system with an environmental incoherent reservoir. The exact solution of the master equation that describes such a system of atoms emitting distinguishable or indistinguishable photons on interaction with an incoherent reservoir is obtained. The quantum decay interference effects have no influences over steady-state distribution of population among the energy levels. However, the photon statistics of the collectively emitted photons are different in this case. In particular, the normalized second-order photon correlat…
The breaking of reciprocity is a topic of great interest in fundamental physics and optical information processing applications. We demonstrate non-reciprocal light transport in a quantum system of hot atoms by engineering the dissipative atomic reservoir. Our scheme is based on the phase-sensitive light transport in a multi-channel photon-atom interaction configuration, where the phase of collective atomic excitations is tunable through external driving fields. Remarkably, we observe inter-channel quantum correlations which originate from interactions with the judiciously engineered reservoir…
Evaluating quantum circuits in the reservoir computing paradigm
Indian Institute of Technology (Banaras Hindu University)（印度技术学院（贝拿勒斯印度教大学））；Jay Chaudhry Software Innovation Centre（杰·乔杜里软件创新中心）；Department of Computer Science and Engineering, Indian Institute of Technology (Banaras Hindu University)（印度技术学院（贝拿勒斯印度教大学）计算机科学与工程系）；Indian Institute of Technology Tirupati（蒂鲁帕蒂印度技术学院）
Bound state and time evolution for single excitation in one dimensional XXZ spin chain within non-Markovian reservoir are studied exactly. As for bound state, a common feature is the localization of single excitation, which means the spontaneous emission of excitation into reservoir is prohibited. Exceptionally the pseudo-bound state can always be found, for which the single excitation has a finite probability emitted into reservoir. We argue that under limit $N\rightarrow \infty$ the pseudo-bound bound state characterizes an equilibrium between the localization in spin chain and spontaneous e…
We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions $\mathcal{E}$ through an exchange of particles in preferred states. We describe the asymptotic state of $\mathcal{S}$ in terms the initial state of $\mathcal{E}$, with especially simple formulae in the limit of small coupling strength. We also study the particle fluxes into the different parts of the reservoir.
We investigate temperature reservoir effects in a lossy Kerr nonlinear resonator considering selective excitation of ooscillatory mode driven by a sequence of Gaussian pulses. In this way, we analyze time-dependent populations of photon-number states and quantum statistics on the base of second-order photon correlation function in one-photon and two-photon transitions. The effects coming from thermal reservoirs are interesting for performing more realistic approach to generate Fock states and for study phenomena connecting quantum engineering and temperature. We also study the role of pulse-sh…
We present a numerical method for studying the real time dynamics of a small interacting quantum system coupled to an infinite fermionic reservoir. By building an orthonormal basis in the operator space, we turn the Heisenberg equation of motion into a system of linear differential equations, which is then solved iteratively by constructing excitation operators. The application of our method depends on a layer structure in the operator space, which help us to turn an infinite linear system into a series of small systems. We apply the method to investigate the decoherence dynamics of quantum im…
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservo…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. C…
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubits system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
We study a driven two-state system interacting with a structured environment. We introduce the non-Markovian master equation ruling the system dynamics, and we derive its analytic solution for general reservoir spectra. We compare the non-Markovian dynamics of the Bloch vector for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic timescale…
We study two two-level systems (TLSs) interacting with a reservoir of guided modes confined in a rectangular waveguide. For the energy separation of the identical TLSs far away from the cutoff frequencies of transverse modes, the delay-differential equations are obtained with single excitation initial in the TLSs. The effects of the inter-TLS distance on the time evolution of the concurrence of the TLSs are examined.
Quantum reservoir computing is a neuro-inspired machine learning approach harnessing the rich dynamics of quantum systems to solve temporal tasks. It has gathered attention for its suitability for NISQ devices, for easy and fast trainability, and for potential quantum advantage. Although several types of systems have been proposed as quantum reservoirs, differences arising from particle statistics have not been established yet. In this work, we assess and compare the ability of bosons, fermions, and qubits to store information from past inputs by measuring linear and nonlinear memory capacity.…
