In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialised at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology.
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.
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.
We study the entanglement generated in the steady state of two interacting qubits coupled to thermal reservoirs. We show that the amount of steady-state entanglement can be enhanced by the presence of a third thermal reservoir which is common to both qubits. Specifically, we find that entanglement can be enhanced as long as the temperature of the common reservoir is below the thermalisation temperature of the qubits, whenever a single temperature can be assigned to the steady state of the qubits in the absence of the common reservoir. Moreover, the amount of entanglement generated with the com…
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 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.
We propose experimental methods to engineer reservoirs at arbitrary temperature which are feasible with current technology. Our results generalize to mixed states the possibility of quantum state engineering through controlled decoherence. Finite temperature engineered reservoirs can lead to the experimental observation of thermal entanglement --the appearance and increase of entanglement with temperature-- to the study of the dependence of finite time disentanglement and revival with temperature, quantum thermodynamical effects, among many other applications, enlarging the comprehension of te…
We analyze the entanglement evolution of two cavity photons being affected by the dissipation of two individual reservoirs. Under an arbitrary local unitary operation on the initial state, it is shown that there is only one parameter which changes the entanglement dynamics. For the bipartite subsystems, we show that the entanglement of the cavity photons is correlated with that of the reservoirs, although the local operation can delay the time at which the photon entanglement disappears and advance the time at which the reservoir entanglement appears. Furthermore, via a new defined four-qubit …
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased by the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reserv…
We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that this sudden change in dynamics of this specific state is extremely sensitive to white nois…
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.
In this work, a genuine mechanism of entanglement protection of a two-qubit system interacting with a dissipative common reservoir is investigated. Based on the generating of bound state for the system-reservoir, we show that stronger bound state in the energy spectrum can be created by adding other non-interacting qubits into the reservoir. In the next step, it is found that obtaining higher degrees of boundedness in the energy spectrum leads to better protection of two-qubit entanglement against the dissipative noises. Also, it is figured out that the formation of bound state not only exclus…
Entanglement plays a crucial role in quantum information protocols, thus the dynamical behavior of entangled states is of a great importance. In this paper we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized in the cavity-QED technology utilizing atoms as fying qubits. To quantify entanglement we use the concurrence. We derive the conditions, which assure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of sudden death entanglement (ESD) in a bipartite system subjected to squeezed v…
We construct a hybrid cavity magnomechanical system to transfer the bipartite entanglements and achieve the strong microwave photon-phonon entanglement based on the reservoir engineering approach. The magnon mode is coupled to the microwave cavity mode via magnetic dipole interaction, and to the phonon mode via magnetostrictive force (optomechanical-like). It is shown that the initial magnon-phonon entanglement can be transferred to the photon-phonon subspace in the case of these two interactions cooperating. In reservoir-engineering parameter regime, the initial entanglement is directionally …
In this work, a mechanism for long time protection of entanglement of a two-qutrit V-type atomic system each of which interacts independently with a dissipative reservoir is investigated. It is shown that the protection process is related exclusively on the formation of bound states in the system-reservoir energy spectrum. It is demonstrated that the degree of boundedness for the system-reservoir bound states is well-controlled by entering other V-type qutrits into the reservoirs, and also through the manipulation of the spontaneously generated interference related to decay channels of the V-t…
We study the output entanglement in a three-mode optomechanical system via reservoir engineering by shifting the center frequency of filter function away from resonant frequency. We find the bandwidth of the filter function can suppress the entanglement in the vicinity of resonant frequency of the system, while the entanglement will become prosperous if the center frequency departs from the resonant frequency. We obtain the approximate analytical expressions of the output entanglement, and from which we give the optimal center frequency at which the entanglement takes the maximum. Furthermore,…
We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we al…
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…
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…
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a genera…
The generation of quantum entanglement of macroscopic or mesoscopic bodies in mechanical motion is generally bounded by the thermal fluctuation exerted by their environments. Here we propose a scheme to establish stationary entanglement between two mechanically oscillating mirrors of a cavity. It is revealed that, by applying a broadband squeezed laser acting as a squeezed-vacuum reservoir to the cavity, a stable entanglement between the mechanical mirrors can be generated. Using the adiabatic elimination and master equation methods, we analytically find that the generated entanglement is esse…
Manipulation of sudden death of entanglement (ESD) of two qubits interacting with statistically uncorrelated thermal reservoirs is investigated. It is shown that for initially prepared X-states of the two qubits a simple (necessary and sufficient) criterion for ESD can be derived with the help of the Peres-Horodecki criterion. This criterion implies that, in contrast to the zero-temperature case, at finite temperature of at least one of the reservoirs all initially prepared two-qubit X-states exhibit ESD. General conditions are derived under which ESD can be hastened, delayed, or averted.
Recently, it has been realized that nonlocal disentanglement may take a finite time as opposite to the asymptotic decay of local coherences. We find in this paper that a sudden irreversible death of entanglement takes place in a two atom optical Stern-Gerlach model. In particular, the one degree non dissipative environment here considered suddenly destroys the initial entanglement of any Bell's states $\ket{ϕ^{\pm}}$ superposition.
We describe a scheme for entangling mechanical resonators which is efficient also beyond the resolved sideband regime. It employs the radiation pressure force of the squeezed light produced by a degenerate optical parametric oscillator, which acts as a reservoir of quantum correlations (squeezed reservoir), and it is effective when the spectral bandwidth of the reservoir and the fields frequencies are appropriately selected. It allows for the steady state preparation of mechanical resonatrs in entangled EPR states and can be extended to the preparation of many entangled pairs of resonators whi…
The remote control of coherence is a crucial step for its application in quantum computation. We investigate the maximal steered coherence (MSC) and its conversion to entanglement in multiple bosonic reservoirs. It is shown that the MSC decays with time in the Markovian regime and behaves as damped oscillations in the non-Markovian regime. The MSC can also be connected directly to the strength of non-Markovianity, through which we show that it can be noticeably enhanced by taking full advantage of the non-Markovian effects. Besides, the MSC can be converted completely to entanglement via optim…
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in details the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density entanglemen…
We consider four two-level atoms interacting with independent non-Markovian reservoirs with detuning. We mainly investigate the effects of the detuning and the length of the reservoir correlation time on the decoherence dynamics of the multipartite entanglement. We find that the time evolution of the entanglement of atomic and reservoir subsystems is determined by a parameter, which is a function of the detuning and the reservoir correlation time. We also find that the decay and revival of the entanglement of the atomic and reservoir subsystems are closely related to the sign of the decay rate…
We study the dynamics of entanglement transfer in a system composed of two initially correlated three-level atoms, each located in a cavity interacting with its own reservoir. Instead of tracing out reservoir modes to describe the dynamics using the master equation approach, we consider explicitly the dynamics of the reservoirs. In this situation, we show that the entanglement is completely transferred from atoms to reservoirs. Although the cavities mediate this entanglement transfer, we show that under certain conditions, no entanglement is found in cavities throughout the dynamics. Consideri…
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 study the entanglement dynamics of two qubits, each of which is embedded into its local amplitude-damping reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components, which is much different to the result obtained under the Born-Markovian approximation by C. E. López {\it et al.} [Phys. Rev. Lett. \textbf{101}, 080503 (2008)], and particularly it also satisfies an identity. Our unified treatment includes the previous results as…
We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviors indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system …
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the init…
In composed quantum systems, the presence of local dissipative channels causes loss of coherence and entanglement at a rate that grows with the temperature of the reservoirs. However, here we show that if temperature is artificially added to the system, entanglement decay can be significantly slowed down or even suppressed conditioned on suitable local monitoring of the reservoirs. We propose a scheme to implement the joint reservoir monitoring applicable in different experimental setups like trapped ions, circuit and cavity QED or quantum dots coupled to nanowires and we analyze its general r…
We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, we observe that, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find that when the cavity entanglement suddenly disappear, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this {\it entanglement sudden birth} can manifest before, simultaneously, or even after {\it entanglement sudden death}. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.
We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.
We propose an effective approach for generating highly pure and strong cavity-mechanical entanglement (or optical-microwave entanglement) in a hybrid modulated three-mode optomechanical system. By applying two-tone driving to the cavity and modulating the coupling strength between two mechanical oscillators (or between a mechanical oscillator and a transmission line resonator), we obtain an effective Hamiltonian where an intermediate mechanical mode acting as an engineered reservoir cools the Bogoliubov modes of two target system modes via beam-splitter-like interactions. In this way, the two …
We present a short overview of quantum entanglement generation and preservation in a steady state. In addition to the focus on quantum entanglement stabilization, we briefly discuss the same objective for steady-state quantum coherence. The overview classifies the approaches into two main categories: hybrid drive and dissipation methods and purely dissipative schemes. Furthermore, purely dissipative schemes are discussed under two subclasses of equilibrium and nonequilibrium environments. The significance of the dissipative route to sustained quantum entanglement and challenges against it are …
We present a scheme to implement a steady lightwave-photon-and-magnon entanglement in a hybrid photon-magnon system by adiabatically eliminating the auxiliary microwave cavity and effectively laser cooling a delocalized Bogoliubov mode. The system consists of magnons, lightwave and microwave photons, and phonons. The magnons are embodied by a collective motion of a large number of spins in a macroscopic ferrimagnet. To achieve an entangling interaction between magnons and lightwave photons, we drive optical cavity and magnon at the red and blue sideband associated with the mechanical resonator…
Spin collective phenomena including superradiance are even today being intensively investigated with experimental tests performed based on state-of-the-art quantum technologies. Such attempts are not only for the simple experimental verification of predictions from the last century but also as a motivation to explore new applications of spin collective phenomena and the coherent control of the coupling between spin ensembles and reservoirs. In this paper, we investigate the open quantum dynamics of two spin ensembles (double spin domains) coupled to a common bosonic reservoir. We analyze in de…
Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. For giving a more physically intuitiv…
We study the entanglement of two impurity qubits immersed in a Bose-Einstein condensate (BEC) reservoir. This open quantum system is particularly interesting because the reservoir and system parameters are easily controllable and the reduced dynamics is highly non-Markovian. We show how the model allows for interpolation between a common dephasing scenario and an independent dephasing scenario by simply modifying the wavelength of the superlattice superposed to the BEC, and how this influences the dynamical properties of the impurities. We demonstrate the existence of very rich entanglement dy…
Ion chains are promising platforms for studying and simulating quantum reservoirs. One interesting feature is that their vibrational modes can mediate entanglement between two objects which are coupled through the vibrational modes of the chain. In this work we analyse entanglement between the transverse vibrations of two heavy impurity defects embedded in an ion chain, which is generated by the coupling with the chain vibrations. We verify general scaling properties of the defects dynamics and demonstrate that entanglement between the defects can be a stationary feature of these dynamics. We …
We demonstrate a new approach to the generation of custom entangled many-body states through reservoir engineering, using the symmetry properties of bosonic lattice systems coupled to a local squeezed reservoir. We outline an algorithm where, beginning with a desired set of squeezing correlations, one uses the symmetry to constrain the Hamiltonian and find a lattice configuration which stabilizes a pure steady state realizing these correlations. We demonstrate how to use this process to stabilize two unique pure states with non-local correlations that could be useful for quantum information ap…
We propose a scheme employing quantum-reservoir engineering to controllably entangle the internal states of two atoms trapped in a high finesse optical cavity. Using laser and cavity fields to drive two separate Raman transitions between metastable atomic ground states, a system is realized corresponding to a pair of two-state atoms coupled collectively to a squeezed reservoir. Phase-sensitive reservoir correlations lead to entanglement between the atoms, and, via local unitary transformations and adjustment of the degree and purity of squeezing, one can prepare entangled mixed states with any…
The sensitivity of entanglement to the thermal and squeezed reservoirs' parameters is investigated regarding entanglement decay and what is called sudden-death of entanglement, ESD, for a system of two qubit pairs. The dynamics of information is investigated by means of the information disturbance and exchange information. We show that for squeezed reservoir, we can keep both of the entanglement and information survival for a long time. The sudden death of information is seen in the case of thermal reservoir.
Following a recent proposal [C. Muschik et. al., Phys. Rev. A 83, 052312 (2011)], engineered dissipative processes have been used for the generation of stable entanglement between two macroscopic atomic ensembles at room temperature [H. Krauter et. al., Phys. Rev. Lett. 107, 080503 (2011)]. This experiment included the preparation of entangled states which are continuously available during a time interval of one hour. Here, we present additional material, further-reaching data and an extension of the theory developed in [C. Muschik et. al., Phys. Rev. A 83, 052312 (2011)]. In particular, we sh…
We analyze a system consisting of two spatially separated quantum objects, here modeled as two pseudo-spins, coupled with a mesoscopic environment modeled as a bosonic bath. We show that by engineering either the dispersion of the spin boson coupling or the environment dimensionality or both one can in principle tailor the spatial dependence of the induced entanglement on the spatial separation between the two spins. In particular we consider one, two and three dimensional reservoirs and we find that while for a two or three dimensional reservoir the induced entanglement shows an inverse power…
We show how strong steady-state entanglement can be achieved in a three-mode optomechanical system (or other parametrically-coupled bosonic system) by using one of the modes as a cold reservoir to effectively laser-cool a delocalized Bogoliubov mode. This approach allows one to surpass the bound on the maximum stationary intracavity entanglement possible with a coherent two-mode squeezing interaction. Unlike typical dissipative entanglement schemes, the entangling dynamics here are most effective in a regime where the effects of the engineered reservoir cannot be described by a Markovian Lindb…
Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two-qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a dete…
We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency $ω_{d}$ we show entanglement exists between environmental modes whose frequencies satisfy the condition $ω_{i} + ω_{j}= ω_{d}$. We…
