arXiv:1207.0395

Dynamics of relaxation, decoherence and entropy of a qubit in anisotropic photonic crystals

Jing-Nuo Wu, Chen, Hung-Kuang, Wen–Feng Hsieh, Szu-Cheng Cheng

Published Jul 2, 2012• 0 citations

Abstract

We study the quantum dynamics of relaxation, decoherence and entropy of a qubit embedded in an anisotropic photonic crystal (PhC) through fractional calculus. These quantum measurements are investigated by analytically solving the fractional Langevin equation. The qubit with frequency lying inside the photonic band gap (PBG) exhibits the preserving behavior of energy, coherence and information amount through the steady values of excited-state probability, polarization oscillation and von Neumann entropy. This preservation does not exist in the Markovian system with qubit frequency lying outside the PBG region. These accurate results are based on the appropriate mathematical method of fractional calculus and reasonable inference of physical phenomena.

DOI: 10.48550/arxiv.1207.0395

Related papers

Effect of photonic band gap on entanglement dynamics of qubits

Jing-Nuo Wu, Wen–Feng Hsieh, Szu-Cheng Cheng

We study how the environment of photonic band gap (PBG) materials affects entanglement dynamics of qubits. Entanglement between the single qubit and the PBG environment is investigated through the von Neumann entropy while that for two initially entangled qubits in this PBG reservoir is through concurrence. Dynamics of these measurements are solved in use of the fractional calculus which has been shown appropriate for the systems with non-Markovian dynamics. Entropy dynamics of the single qubit system reveals that the coupling with the PBG reservoir prevents decoherence of the qubit through the steady entropy with non-zero value. The effect of PBG reservoir on the concurrence of the two-qubit system leads to the long-time entanglement preservation. The concurrence dynamics shows that unphysical entanglement trapping does not exist in the system with the qubit frequency lying outside the PBG region. Long-time memory effect of the PBG reservoir occurs only for the qubit frequency in the PBG region. Entanglement mechanisms resulting from this long-time memory effect are discussed.

arXiv:1207.0464Jul 2, 20120 citations

Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal

Jing-Nuo Wu, Wen–Feng Hsieh, Hsin-Chien Huang +1 more

An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.

Advances in Condensed Matter PhysicsJan 1, 20130 citations

Fractional Dynamics of the Spontaneous Emission of an Atom in Photonic Crystals

Szu-Cheng Cheng, Ming‐Rung Tsai, Wen–Feng Hsieh

We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by the fractional calculus. And the results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of allowed band edge which is encountered in the previous study [J. Opt. B: Quantum Semiclass. Opt. {\bf 5}, R43 (2003)]. The correctness of this result is validated by the ``cut-off smoothing'' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show the method of fractional calculus has logically concise property.

arXiv:0805.4375Journal of the Korean Physical SocietyAug 14, 20080 citations

Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach

Szu-Cheng Cheng, Jing-Nuo Wu, Ming‐Rung Tsai +1 more

We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.

Journal of Physics Condensed MatterDec 1, 200815 citations

Dynamics of Quantum Coherence and Hilbert-Schmidt Speed of V-Type Three-level Atom in Anisotropic Photonic Crystal

Mousavi, S.Nafise, Naeimi, Ghasem, Saeidian, Shahpoor +1 more

In this paper, the time evolution of quantum coherence and Hilbert-Schmidt speed, as a criterion to measure the memory of the quantum system, of a V-type three-level atom embedded in an anisotropic photonic crystal are investigated. The effect of the different relative positions of the upper levels from the forbidden gap and the initial relative phase values on the mentioned quantum features are studied. We show that the photonic band gap crystal, as a structured environment, significantly influences the preservation and enhancement of these quantum features. The photonic gap band materials have non-Markovian properties and offer a new approach as a basic solution in overcoming the decoherence problem and subsequently in problems related to quantum information.

Iranian Journal of Physics ResearchSep 1, 20240 citations

Fidelity of structured amplitude-damping channels

Jing Wang, Jiang Li, Han Zhang +2 more

We study the properties of the fidelity of one-qubit operations in amplitude damping channels and reveal their properties as a function of coupling to the photonic crystal environment. We show that there is a direct connection between the information fidelity and the detuning of the atomic frequency from the photonic band gap (PBG). When the atomic transition frequency is far inside the band gap, the time evolution of the fidelity maintains asymptotically a steady-state value and can be controlled by the controllable PBG environment. We finally study the entanglement fidelity of the two-qubit system in this quantum channel. The theoretical results could be applied to the implementation of linear-optical and solid-state quantum information processing in nanostructured materials.

Physica ScriptaMar 22, 20111 citation