Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0612049 · Physical Review B

Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment

Xiao-Zhong Yuan, Hsi‐Sheng Goan, Ka-Di Zhu

Published Jan 19, 2007• 100 citations
arXivHTMLPDF

Abstract

The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg $XY$ spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using an operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming-like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment, and the interaction between the constituents of the spin environment. We also investigate the effect of detuning, which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two-spin qubits.

DOI
10.1103/physrevb.75.045331

Related papers

Non-Markovian Reduced Dynamics and Entanglement Evolution of Central Spin Models in Quantum Spin Environments

Hsi‐Sheng Goan

We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.

OSA Workshop on Entanglement and Quantum Decoherence•Jan 1, 2008•0 citations

Non-Markovian dynamics and entanglement evolution of a qubit in a spin environment

J. Rodríguez Garzón, Rafael Gutiérrez

The dynamics of a central spin-1/2 in presence of a local magnetic field and a bath of N spin-1/2 particles is studied in the thermodynamic limit. The interaction between the spins is Heisenberg XY type and the bath is considered to be a perfect thermal reservoir. In this case, the evolution of the populations of the reduced density matrix is obtained for different temperatures. A Born approximation is made but not a Markov approximation resulting a non-Markovian dynamics. The measure of the entanglement between the spin and the bath is obtained by means of the von Neumann entropy. For low temperatures, results show that there are oscillations of populations and of the von Neumann entropy as measure of entanglement, indicating that the central spin becomes disentangled of the spins of the bath with characteristic time periods in which it is possible to extract or recuperate information. In the regime of high temperatures, the evolution shows a final maximum entangled state with entropy S = ln 2 as it is expected for a two level system. I

•Aug 4, 2013•0 citations

Quantum dynamics of double-qubits in a spin star lattice with an XY interaction

Jun Jing, Zhi-Guo Lü

The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. The bath, which consists of $N$ (in the thermodynamic limit $N\to\infty$) mutually coupled spins-1/2, is in a thermal state at the beginning. By the Holstein-Primakoff transformation, the model can be treated effectively as two spin qubits embedded in a single mode cavity. The time-evolution of the purity, z-component summation and the concurrence of the central spins can be determined by a Laguerre polynomial scheme. It is found that (i) at a low temperature, the uncoupled subsystem in a product state can be entangled due to the interaction with bath, which is tested by the Peres-Horodecki separability; however, at a high temperature, the bath produces a stronger destroy effect on the purity and entanglement of the subsystem; (ii) when the coupling strength between the two central spins is large, they are protected strongly against the bath; (iii) when the interaction between the subsystem and the bath is strong, the collapse of the two spin qubits from their initial entangled state is fast.

arXiv:quant-ph/0612115•Dec 14, 2006•0 citations

Dynamics of two center spins in a Quantum Heisenberg XY system

Jun Jing, Zhi-Guo Lü

The dynamics of two coupled spins of 1/2 coupled to spin-bath of a quantum Heisenberg XY type \\cite{Breuer, Yuan} is studied. The center pair of spins served as an quantum open subsystem were initially prepared in a Bell state or a product state and the bath consisted of $N$ ($N\\to\\infty$ as the thermodynamic limit) spins-1/2 is in a thermal state at different temperatures from the beginning. Transformed by the Holstein-Primakoff operator, the model will be treated effectively as two spin qubits embedded in a single mode cavity. Then the von-Neumann entropy, z-component summation and the concurrence of the center spins can be determined by a novel polynomial scheme for the time-evolution of quantum systems. It is found that (i) with increasing temperature, the bath plays a more strong destroy effect on the coherence or entanglement of the subsystem; (ii) the larger the coupling strength between the subsystem spins, the less the variation of the initial state; (iii) the stronger the interaction between the subsystem and the bath, the faster the variation of the initial state.

•Dec 1, 2006•0 citations

Exact dynamics of a two-qubit system in a spin star environment

Yamen Hamdouni, M. Fannes, Francesco Petruccione

We derive the exact reduced dynamics of a central two-qubit system in a spin star configuration. The exact evolution of the reduced system density matrix is obtained and we compute the limit of an infinite number of environment spins. Initially pure states of the central system evolve into mixed ones and we determine the decoherence-free states of the model. The long-time behavior is studied, partial decoherence is shown to be a result of the coupling of the qubits to the environment, and entanglement evolution of the central system is investigated.

Physical Review B•Jun 19, 2006•82 citations

Decoherence and entanglement evolution of two qubits coupled through Heisenberg interactions to a spin bath in thermal equilibrium

Yamen Hamdouni

The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.

Journal of Physics A Mathematical and Theoretical•Sep 4, 2007•9 citations
The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XYXYXY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using an operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming-like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment, and the interaction between the constituents of the spin environment. We also investigate the effect of detuning, which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two-spin qubits.
We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.
The dynamics of a central spin-1/2 in presence of a local magnetic field and a bath of N spin-1/2 particles is studied in the thermodynamic limit. The interaction between the spins is Heisenberg XY type and the bath is considered to be a perfect thermal reservoir. In this case, the evolution of the populations of the reduced density matrix is obtained for different temperatures. A Born approximation is made but not a Markov approximation resulting a non-Markovian dynamics. The measure of the entanglement between the spin and the bath is obtained by means of the von Neumann entropy. For low temperatures, results show that there are oscillations of populations and of the von Neumann entropy as measure of entanglement, indicating that the central spin becomes disentangled of the spins of the bath with characteristic time periods in which it is possible to extract or recuperate information. In the regime of high temperatures, the evolution shows a final maximum entangled state with entropy S = ln 2 as it is expected for a two level system. I
The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. The bath, which consists of NNN (in the thermodynamic limit N→∞N\to\inftyN→∞) mutually coupled spins-1/2, is in a thermal state at the beginning. By the Holstein-Primakoff transformation, the model can be treated effectively as two spin qubits embedded in a single mode cavity. The time-evolution of the purity, z-component summation and the concurrence of the central spins can be determined by a Laguerre polynomial scheme. It is found that (i) at a low temperature, the uncoupled subsystem in a product state can be entangled due to the interaction with bath, which is tested by the Peres-Horodecki separability; however, at a high temperature, the bath produces a stronger destroy effect on the purity and entanglement of the subsystem; (ii) when the coupling strength between the two central spins is large, they are protected strongly against the bath; (iii) when the interaction between the subsystem and the bath is strong, the collapse of the two spin qubits from their initial entangled state is fast.
The dynamics of two coupled spins of 1/2 coupled to spin-bath of a quantum Heisenberg XY type \\cite{Breuer, Yuan} is studied. The center pair of spins served as an quantum open subsystem were initially prepared in a Bell state or a product state and the bath consisted of NNN (NtoinftyN\\to\\inftyNtoinfty as the thermodynamic limit) spins-1/2 is in a thermal state at different temperatures from the beginning. Transformed by the Holstein-Primakoff operator, the model will be treated effectively as two spin qubits embedded in a single mode cavity. Then the von-Neumann entropy, z-component summation and the concurrence of the center spins can be determined by a novel polynomial scheme for the time-evolution of quantum systems. It is found that (i) with increasing temperature, the bath plays a more strong destroy effect on the coherence or entanglement of the subsystem; (ii) the larger the coupling strength between the subsystem spins, the less the variation of the initial state; (iii) the stronger the interaction between the subsystem and the bath, the faster the variation of the initial state.
We derive the exact reduced dynamics of a central two-qubit system in a spin star configuration. The exact evolution of the reduced system density matrix is obtained and we compute the limit of an infinite number of environment spins. Initially pure states of the central system evolve into mixed ones and we determine the decoherence-free states of the model. The long-time behavior is studied, partial decoherence is shown to be a result of the coupling of the qubits to the environment, and entanglement evolution of the central system is investigated.
The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.