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arXiv:1409.8551 · Physical Review A

Emergence of a metastable pointer-state basis in non-Markovian quantum dynamics

F. Lastra, C. E. López, Sebastián A. Reyes, Sascha Wallentowitz

Published Dec 1, 2014• 8 citations
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Abstract

We investigate the dynamics of classical and quantum correlations between two qubits. Each qubit is implemented by a pair of phosphorous impurities embedded in a silicon substrate. The main decoherence mechanism affecting these types of qubits is provided by the coupling of the phosphorous impurities to the acoustical vibrations of the silicon lattice. We find that depending on the temperature of the substrate and the initial state, three different dynamics can be found. These are characterized by the number of abrupt changes in both classical and quantum correlations. We also show that the correlations do not disappear. Moreover, before the classical correlations reach a constant value, they may experience successive abrupt changes associated with the apparition of a metastable pointer-states basis. Then a constant value for the classical correlations is reached when the preferred basis is established.

DOI
10.1103/physreva.90.062103

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We investigate the dynamics of classical and quantum correlations between two qubits. Each qubit is implemented by a pair of phosphorous impurities embedded in a silicon substrate. The main decoherence mechanism affecting these types of qubits is provided by the coupling of the phosphorous impurities to the acoustical vibrations of the silicon lattice. We find that depending on the temperature of the substrate and the initial state, three different dynamics can be found. These are characterized by the number of abrupt changes in both classical and quantum correlations. We also show that the correlations do not disappear. Moreover, before the classical correlations reach a constant value, they may experience successive abrupt changes associated with the apparition of a metastable pointer-states basis. Then a constant value for the classical correlations is reached when the preferred basis is established.
We study the dynamics of quantum and classical correlations in a two-qutrit system coupled to independent reservoirs. In particular, we address the differences in the dynamics of Markovian and non-Markovian regimes and show that for specific initial states, classical correlations exhibit abrupt changes along the dynamics. A particular sudden change occurs when the classical correlations freeze to a certain value at a given time, revealing the apparition of a pointer-state basis. After this given time, the decoherence only affects quantum correlations. Here we identify two regimes in the decoherence dynamics: a mixed regime when both classical and quantum correlations decay and a quantum regime when only quantum correlations decay. We show that the freezing of classical correlations can be stable or metastable depending on the system-reservoir parameters. In the long-time limit, we find analytical expressions for the pointer-state basis the system settles in and consequently for classical and quantum correlations.
Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary XXX-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.
We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a nonasymptotic emergence of the pointer basis, while the system apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.
Two initially correlated coherent states, each interacting with its own independent dissipative environment, exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence in the sense that depending on the average number of photons of each harmonic oscillator, decoherence can even be suppressed. Indeed, the quantum state is time independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer-state basis.
We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit XXX states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial XXX states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.
In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. \n \nIn the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. \n \nIn the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. \n \nThe dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.