arXiv subjects

Ting Yu

Publications and source records attributed to Ting Yu.

At least 181 records · Page 10Linked to original sources

arXiv2007

Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D \textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to $N$, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations and dissipation of mesoscopic objects towards the construction of a theoretical framework for macroscopic quantum phenomena.

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arXiv2007

Pairwise Concurrence Dynamics: A Four-Qubit Model

We examine entanglement dynamics via concurrence among four two-state systems labeled $A, ~a, ~B, ~b$. The four systems are arranged on an addressable "lattice" in such a way that $A$ and $a$ at one location labeled $Aa$ can interact with each other via excitation exchange, and the same for $B$ and $b$ at location $Bb$. The $Aa$ location is prepared entangled with the $Bb$ location, but their mutual complete isolation prevents interaction in the interval between actions of an external addressing agent. There are six pairwise concurrences on the lattice, and we follow their evolution in the interval between external actions. We show how entanglement evolves and may exhibit the non-analytic effect termed entanglement sudden death (ESD), with periodic recovery. These loss and gain processes may be interpreted as entanglement transfer between the subsystems.

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arXiv2007

Quantum Brownian Motion of a Macroscopic Object in a General Environment

For the purpose of understanding the quantum behavior such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of $N$ interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of multi-partite macroscopic states such as quantum superposition of mirrors in a high Q cavity. To address a key conceptual issue for macroscopic quantum phenomena we examine the conditions for an assumption often implicitly made in these studies to be valid, namely, that the quantum behavior of a macroscopic object in an environment can be accurately represented by only treating the dynamics of its center-of-mass variable. We also mention how these results can be used to calculate the uncertainty principle governing a macroscopic object at finite temperature.

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arXiv2007

Many-Body Separability of Warm Qubits

We analyze the separability of the joint state of a collection of two-level systems at finite temperature T. The fact that only separable states are found in the neighborhood of their thermal equilibrium state guarantees that decoherence will destroy any initially arranged entanglement in a finite time.

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arXiv2007

Negative Entanglement Measure, and What It Implies

In this paper, we extract from concurrence its variable part, denoted $Λ$, and use $Λ$ as a time-dependent measure of "distance", either postive or negative, from the separability boundary. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment.

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arXiv2007

Evolution from Entanglement to Decoherence of Bipartite Mixed "X" States

We examine a class of bipartite mixed states which we call X states and report several analytic results related to the occurrence of so-called entanglement sudden death (ESD) under time evolution in the presence of common types of environmental noise. Avoidance of sudden death by application of purely local operations is shown to be feasible in some cases.

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arXiv2006

Entanglement Decay Versus Energy Change: A Model

We present a simple quantum open system to show quantitatively how entanglement decoherence is related to the energy transfer between the system of interest and its environment. Particularly, in the case of the exact entanglement decoherence of two qubits, we find an upper bound for the energy transfer between the two-qubit system and its environments.

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arXiv2006

Quantum Open System Theory: Bipartite Aspects

We demonstrate in straightforward calculations that even under ideally weak noise the relaxation of bipartite open quantum systems contains elements not previously encountered in quantum noise physics. While additivity of decay rates is known to be generic for decoherence of a single system, we demonstrate that it breaks down for bipartite coherence of even the simplest composite systems.

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arXiv2006

Sudden Death of Entanglement of Two Jaynes-Cummings Atoms

We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.

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arXiv2006

Sudden Death of Entanglement: Classical Noise Effects

When a composite quantum state interacts with its surroundings, both quantum coherence of individual particles and quantum entanglement will decay. We have shown that under vacuum noise, i.e., during spontaneous emission, two-qubit entanglement may terminate abruptly in a finite time [T. Yu and J. H. Eberly, \prl {93}, 140404 (2004)], a phenomenon termed entanglement sudden death (ESD). An open issue is the behavior of mixed-state entanglement under the influence of classical noise. In this paper we investigate entanglement sudden death as it arises from the influence of classical phase noise on two qubits that are initially entangled but have no further mutual interaction.

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arXiv2004

Finite-Time Disentanglement via Spontaneous Emission

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite time, and in a specific example we find the time to be given by $\ln \Big(\frac{2 +\sqrt 2}{2}\Big)$ times the usual spontaneous lifetime.

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arXiv2004

Non-Markovian Quantum Trajectories Versus Master Equations: Finite Temperature Heat Bath

The interrelationship between the non-Markovian stochastic Schrödinger equations and the corresponding non-Markovian master equations is investigated in the finite temperature regimes. We show that the general finite temperature non-Markovian trajectories can be used to derive the corresponding non-Markovian master equations. A simple, yet important solvable example is the well-known damped harmonic oscillator model in which a harmonic oscillator is coupled to a finite temperature reservoir in the rotating wave approximation. The exact convolutionless master equation for the damped harmonic oscillator is obtained by averaging the quantum trajectories relying upon no assumption of coupling strength or time scale. The master equation derived in this way automatically preserves the positivity, Hermiticity and unity.

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arXiv2004

Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited

Stochastic Schr{ö}dinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schr{ö}dinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most-employed exactly soluble models of open system dynamics. We show explicitly how to establish the direct connection between the exact convolutionless master equation of QBM and the corresponding convolutionless exact stochastic Schrödinger equation.

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arXiv2003

Qubit Disentanglement and Decoherence via Dephasing

We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and non-local measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter than the time for local dephasing of the individual qubits.

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arXiv2002

Generalized quantum measurement

We overcome one of Bell's objections to `quantum measurement' by generalizing the definition to include systems outside the laboratory. According to this definition a {\sl generalized quantum measurement} takes place when the value of a classical variable is influenced significantly by an earlier state of a quantum system. A generalized quantum measurement can then take place in equilibrium systems, provided the classical motion is chaotic. This paper deals with this classical aspect of quantum measurement, assuming that the Heisenberg cut between the quantum dynamics and the classical dynamics is made at a very small scale. For simplicity, a gas with collisions is modelled by an `Arnold gas'.

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arXiv1999

Quantum trajectories for Brownian motion

We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarkable feature of our approach is its localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system considered here, the localization being stronger the smaller $\hbar$.

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arXiv1999

Post-Markov master equation for the dynamics of open quantum systems

A systematic first-order correction to the standard Markov master equation for open quantum systems interacting with a bosonic bath is presented. It extends the Markov Lindblad master equation to the more general case of non-Markovian evolution. The meaning and applications of our `post'-Markov master equation are illustrated with several examples, including a damped two-level atom, the spin-boson model and the quantum Brownian motion model. Limitations of the Markov approximation, the problem of positivity violation and initial slips are also discussed.

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arXiv1999

Non-Markovian quantum state diffusion: Perturbation approach

We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review {\bf A 58}, 1699, (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general non-Markovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

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