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Advances in Natural Sciences Nanoscience and Nanotechnology

The quantum dynamics of two qubits inside two distant microcavities connected via a single-mode optical fiber

Văn Hiếu Nguyễn, Bich Ha Nguyen, Hai Trieu Duong

Published Mar 1, 2010• 9 citations
Publisher

Abstract

Abstract For application to studying the transmission of quantum information, also called quantum communication, between two identical qubits placed inside two identical single-mode microcavities connected via a single-mode optical fiber, the time evolution of this system is investigated. In the Markovian approximation, the von Neumann equation for its reduced density matrix contains a completely positive linear operator called the Liouvillian operator describing the decoherence of this system due to its interaction with the environment. By using the Linblad formula for the Liouvillian operator, a system of rate equations can be derived. In the special case of resonance between the energy difference of two states in each qubit and the energy of the fiber mode, the rate equations for the system excited up to the first level are solved in first order approximation with respect to the decoherence constants. It is shown that when there is no decoherence, the perfect quantum state transmission between two qubits can take place if the physical parameters of the system satisfy definite conditions. A possible extension to studying the system excited to high energy states is also discussed.

DOI
10.1088/2043-6254/1/1/015001

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Acta Physica Sinica•Jan 1, 2016•0 citations
Abstract For application to studying the transmission of quantum information, also called quantum communication, between two identical qubits placed inside two identical single-mode microcavities connected via a single-mode optical fiber, the time evolution of this system is investigated. In the Markovian approximation, the von Neumann equation for its reduced density matrix contains a completely positive linear operator called the Liouvillian operator describing the decoherence of this system due to its interaction with the environment. By using the Linblad formula for the Liouvillian operator, a system of rate equations can be derived. In the special case of resonance between the energy difference of two states in each qubit and the energy of the fiber mode, the rate equations for the system excited up to the first level are solved in first order approximation with respect to the decoherence constants. It is shown that when there is no decoherence, the perfect quantum state transmission between two qubits can take place if the physical parameters of the system satisfy definite conditions. A possible extension to studying the system excited to high energy states is also discussed.
The aim of this topical review is a systematic and concise presentation of the results of a series of theoretical works on the quantum dynamics of two-spin-qubit systems towards the elaboration of a physical mechanism of the quantum information transfer between two spin-qubits. For this purpose the main attention is paid to exactly solvable models of two-spin-qubit systems, since the analytical expressions of the elements of their reduced density matrices explicitly exhibit the mutual dependence of the quantum information encoded into the spin-qubits. The treatment of their decoherence due to the interaction with the environment is performed in the Markovian approximation. Rate equations for axially symmetric systems of two coupled spin-qubits non-interacting, as well as interacting, with the environment are exactly solved. It is shown how the solutions of rate equations demonstrate the physical mechanism of the quantum information exchange between the spin-qubits. This mechanism holds also in all two-spin-qubit systems whose rate equations can be solved only by means of numerical calculations. Exact solutions of rate equations for two uncoupled spin-qubits interacting with two separate environments reveal an interesting physical phenomenon in the time evolution of the qubit-qubit entanglement generated by their interaction with the environments: the entanglement sudden death and revival. A two-spin-qubit system with an asymptotically decoherence free subspace was also explicitly constructed. The presented calculations and reasonings can be extended for application to the study of spin-qubit chains or networks.
Abstract The general theory of the time-resolved luminescence of the coupled system consisting of a single-mode microcavity and a two-level quantum dot containing one electron placed inside this microcavity is presented. It is based on the study of the time evolution of the density matrix of a larger system consisting of one electron in the two-level quantum dot, single-mode photons in the microcavity and external photons in a spatial region in which the emitted photons are detected. The decoherence of the system is taken into account in the Markov approximation. The explicit analytical form of the time dependence of the intensity of the emitted photon beam is established. It depends not only on the physical parameters of the system but also contains the matrix elements determining the initial condition of the luminescence process.
In this research work, I have derived analytical models for decoherence of quantum states of light and developed techniques based on Dynamical Decoupling (DD) to preserve the quantum state of polarization qubit and Orbital Angular Momentum (OAM) qudit in single-mode, multi-mode and specialized optical fibers. In subsequent work, I have derived the analytical model for decoherence of an entangled state in an optical fiber to show that such a decoherence causes loss of entanglement. I also showed that such states can be preserved with DD. In Chapter 1, I have introduced the subject of a quantum computer and its relation to quantum communication. I give a brief overview of fundamental concepts and tools required to understand the subject matter. In Chapter 2, I discuss optical fibers from the perspective of the electromagnetic wave in a waveguide and explain the modes in an optical fiber. Later, I explain about the sources of noise or refractive index fluctuation in an optical fiber and show how to numerically reproduce a model of an optical fiber. In Chapter 3, I introduce the topic of quantum decoherence and discuss in detail an open-loop control technique called Dynamical Decoupling, that is applied to the system to minimize decoherence. I discuss ideal and nonideal pulse sequences used for suppressing decoherence. In Chapter 4, I derive the analytical model for decoherence of a polarization qubit in a single-mode, multi-mode fiber, and decoherence OAM qudit in specialized multi-mode fiber. In Chapter 5, I introduce the topic of entanglement for the bipartite system and multi-partite system, and a measure called concurrence to quantify the entanglement. I then derive the analytic model for decoherence of a pure entangled state and show that decoherence causes loss of entanglement for the case of a pure and mixed Werner-like state. \break In Chapter 6, I discuss the method of numerical simulation and show by numerical simulation that polarization qubit, OAM qudit and entanglement of polarization qudit can be preserved with dynamical decoupling in an optical fiber. In Chapter 7, I have summarized the results and discuss the scope of future work. In the appendix, I have included additional research work not directly related to the current topic of decoherence in an optical fiber. To summarize my research, I have derived a model for decoherence and then numerically showed that a polarization qubit can be preserved in a single mode and multi-mode optical fiber. I
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.
Abstract The theory of coherent oscillations of the matrix elements of the density matrix of the two-state system as a quantum bit is presented. Different calculation methods are elaborated in the case of a free quantum bit. Then the most appropriate methods are applied to the study of the density matrices of the quantum bits interacting with a classical pumping radiation field as well as with the quantum electromagnetic field in a single-mode microcavity. The theory of decoherence of a quantum bit in Markovian approximation is presented. The decoherence of a quantum bit interacting with monoenergetic photons in a microcavity is also discussed. The content of the present work can be considered as an introduction to the study of the quantum dynamics of quantum bits.
Entanglement and nonlocality, two most striking features of quantum mechanics, are fundamental resources for quantum information processing. They play an important role in quantum information processing. Therefore, studying the dynamics of quantum nonlocality and entanglement is of importance for both fundamental research and practical applications. In this paper we consider the case that three identical two-level atoms are trapped respectively in the three separated equidistance single-mode cavities, which are placed at the vertices of an equilateral triangle and are coupled by three fibers. Each atom resonantly interacts with cavity via a one-photon hopping. The evolution of the state vector of the system is given by solving the schrodinger equation when the total excitation number of the system equals one. The dynamics of nonlocality in the system is investigated via Mermin-Ardehali-Belinksii-Klyshko (MABK) inequality. By the numerical calculations, the MABK inequality is studied when the initial state vector of three atoms is W state or the initial state vector of three cavities is also W state. The influence of cavity-fiber coupling constant on the MABK inequality is discussed. The evolution curves of the MABK parameters Ba and Bc are plotted. The curves show that Ba and Bc both display periodic oscillations, and their oscillation frequencies all increase with the increase of cavity-fiber coupling constant. Ba and Bc are both larger than 1 when the scaling time gt takes a certain value. The results show that the quantum state of three atoms or that of three cavities displays nonlocality. On the other hand, the nonlocality of three-atom quantum state is strengthened with the increase of cavity-fiber coupling constant.