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

Physical Review A

Berry phase and quantum entanglement in a nonreciprocal composite system

Xin Wang, H. D. Liu, X. X. Yi

Published Jun 18, 2024• 5 citations
Publisher

Abstract

In this work, we study the geometric phases and quantum entanglement of a composite system consisting of two interacting spin-1/2 particles in the presence of an external magnetic field. The conditions for real and complex eigenvalues are derived and discussed. Based on the non-Hermitian Berry phase, we propose the geometric phase of projective quantum states, discuss their relationship, and analyze their geometric properties. We expound on how the geometric phase of projective quantum states is contingent upon the coupling strength and the nonreciprocity between two subsystems, illustrating the connection between the geometric phase of the composite system and the geometric phases of its subsystems. By studying the quantum entanglement of the subsystems, the role of the correlation between the subsystem and the nonreciprocity is discussed. The results show that the quantum entanglement is influenced and determined by the nonreciprocity of the coupling. These schemes can provide a way to manipulate the nonreciprocal correlation between the subsystems to control the non-Hermiticity, geometric phase, and entanglement of the subsystems.

DOI
10.1103/physreva.109.062220

Related papers

Berry's geometric phase for two spin-1/2 particles in an entangled quantum system

Qing‐Hu Zhong

The entanglement dependence of Berry's geometric phase is studied in the case of two spin-1/2 particles with a spin-spin interaction.Berry's phases for two spin-1/2 entanglement particles in the presence of spin-spin interaction and noninteraction are calculated,respectively.The expression of calculating geometric phase,when entanglement vanishes,is obtained.Moreover,the geometric phase is discussed when only one of the two particles is affected by the external magnetic field.It is shown that its geometric phase is not equal to that of single particle which is acted by the external magnetic field,and the result is related toαthat affect the strength of entanglement. A general entanglement-dependence geometric phase is formulated.

Chinese Journal of Quantum Electronics•Jan 1, 2010•0 citations

Berry phases for interacting spins in composite environments

Da-Bao Yang, Fulin Zhang, Jing-Ling Chen

Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.

arXiv:1202.3849•Feb 17, 2012•0 citations

Geometric phase and Berry's phase for the entangled system of pure state with two particles

Zheng Hai-xia

Above the work of E.Sjoqvist,the geometric phase and the entanglement of the system composed of a pair of noninteracting spin-1/ 2 particles pressing in an external time-independent magnetic field are considered using a new method.The relation between them is gained newly:only if the entanglement is zero will the geometric phase of the composite systems reduce to a sum of one-particle geometric phase.Further more,the Berry's phase and the entanglement of the system composed of a pair of noninteracting spin-1/2 particles pressing in a rotating magnetic field are studied.The same conclusion is gained.

Journal of Northeast Normal University•Jan 1, 2007•0 citations

Uhlmann phase in composite systems with entanglement

Jorge Villavicencio, E. Cota, F. Rojas +2 more

We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-$\frac{1}{2}$ particles with a magnetic field acting on one of them. Within a uniform noisy quantum channel setup, an exact analytical expression for this geometric phase in each subsystem is derived. We find an explicit connection to the concurrence of the density matrix of such a channel, which allows us to characterize the features of the Uhlmann phase in terms of the degree of entanglement in the system. In the space of field direction and coupling parameter, it exhibits a phase singularity revealing a topological transition between orders characterized by different winding numbers. The transition occurs for fields lying in the equator of the sphere of directions and at critical values of the coupling which can be controlled by tuning the depolarization strength. Notably, under these conditions the concurrence of the composite system is bounded to the range $[0,1/2]$. We also compare the calculated Uhlmann phase to an interferometric phase, which has been formulated as an alternative for density matrices. The latter does not present a phase vortex, although they coincide in the weak entanglement regime for vanishing depolarization (pure states). Otherwise, they behave clearly different in the strong-entanglement regime.

arXiv:2106.15879•Physical Review A•Oct 6, 2021•7 citations

BERRY PHASES OF A COMPOSITE SYSTEM IN EXTERNAL FIELDS

Hui Zhao, Xuean Zhao, You‐Quan Li

We apply the perturbation theory to investigate the behavior of the Berry phase of a composite system. The composite system consists of two weakly-coupled spin-½ particles, in which each particle is driven by a varying magnetic field. The result shows that the Berry phase for one subsystem is controlled by the state of the other subsystem. The method can also be used to deal with the effect of a spin environment on a single-particle system if the particle is weakly coupled to the spin environment.

Modern Physics Letters B•Aug 10, 2006•0 citations

Berry Phase of Composite System Induced by Time-Dependent Interaction

Lin Yang

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field.Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.

理论物理通讯：英文版•Jan 1, 2010•0 citations
In this work, we study the geometric phases and quantum entanglement of a composite system consisting of two interacting spin-1/2 particles in the presence of an external magnetic field. The conditions for real and complex eigenvalues are derived and discussed. Based on the non-Hermitian Berry phase, we propose the geometric phase of projective quantum states, discuss their relationship, and analyze their geometric properties. We expound on how the geometric phase of projective quantum states is contingent upon the coupling strength and the nonreciprocity between two subsystems, illustrating the connection between the geometric phase of the composite system and the geometric phases of its subsystems. By studying the quantum entanglement of the subsystems, the role of the correlation between the subsystem and the nonreciprocity is discussed. The results show that the quantum entanglement is influenced and determined by the nonreciprocity of the coupling. These schemes can provide a way to manipulate the nonreciprocal correlation between the subsystems to control the non-Hermiticity, geometric phase, and entanglement of the subsystems.
The entanglement dependence of Berry's geometric phase is studied in the case of two spin-1/2 particles with a spin-spin interaction.Berry's phases for two spin-1/2 entanglement particles in the presence of spin-spin interaction and noninteraction are calculated,respectively.The expression of calculating geometric phase,when entanglement vanishes,is obtained.Moreover,the geometric phase is discussed when only one of the two particles is affected by the external magnetic field.It is shown that its geometric phase is not equal to that of single particle which is acted by the external magnetic field,and the result is related toαthat affect the strength of entanglement. A general entanglement-dependence geometric phase is formulated.
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.
Above the work of E.Sjoqvist,the geometric phase and the entanglement of the system composed of a pair of noninteracting spin-1/ 2 particles pressing in an external time-independent magnetic field are considered using a new method.The relation between them is gained newly:only if the entanglement is zero will the geometric phase of the composite systems reduce to a sum of one-particle geometric phase.Further more,the Berry's phase and the entanglement of the system composed of a pair of noninteracting spin-1/2 particles pressing in a rotating magnetic field are studied.The same conclusion is gained.
We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-12\frac{1}{2}21​ particles with a magnetic field acting on one of them. Within a uniform noisy quantum channel setup, an exact analytical expression for this geometric phase in each subsystem is derived. We find an explicit connection to the concurrence of the density matrix of such a channel, which allows us to characterize the features of the Uhlmann phase in terms of the degree of entanglement in the system. In the space of field direction and coupling parameter, it exhibits a phase singularity revealing a topological transition between orders characterized by different winding numbers. The transition occurs for fields lying in the equator of the sphere of directions and at critical values of the coupling which can be controlled by tuning the depolarization strength. Notably, under these conditions the concurrence of the composite system is bounded to the range [0,1/2][0,1/2][0,1/2]. We also compare the calculated Uhlmann phase to an interferometric phase, which has been formulated as an alternative for density matrices. The latter does not present a phase vortex, although they coincide in the weak entanglement regime for vanishing depolarization (pure states). Otherwise, they behave clearly different in the strong-entanglement regime.
We apply the perturbation theory to investigate the behavior of the Berry phase of a composite system. The composite system consists of two weakly-coupled spin-½ particles, in which each particle is driven by a varying magnetic field. The result shows that the Berry phase for one subsystem is controlled by the state of the other subsystem. The method can also be used to deal with the effect of a spin environment on a single-particle system if the particle is weakly coupled to the spin environment.
The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field.Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.