We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.We study the entanglement evolution of two three-level atoms in a fermionic environment. Our results show that the entanglement evolution depends not only on the strength of the interaction between the system and environment， but also on the structure of states. For the cases of concern， we find that the stronger the interaction between the system and environment is， the faster the entanglement of the system decreases. The entanglement of pure quantum states vanishes completely when the time goes to infinity; while for the mixed state，the entanglement will be completely destroyed by decoherence in finite time. The decoherence-free subspace SDF has been identified by using linear entropy to measure decoherence. A density matrix that only can be expanded by the elements of SDF does not perceive the presence of the environment and the entanglement and its linear entropy remain unchangeable. Our analysis will shed some light on the effect of a fermionic environment on the entanglement of bosonic systems.

Acta Physica SinicaJan 1, 20085 citations

Coherent states of finite-level systems

Alexander Igorevich Breev, Dmitry M. Gitman

arXiv:2506.10668The European Physical Journal PlusSep 25, 20250 citations

Decoherence dynamics of qubits coupled to systems at quantum transitions

Ettore Vicari

We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a $d$ -dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case in which the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a $d$-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case in which the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.

arXiv:1807.03485Physical Review ANov 21, 201816 citations

Bohm-Aharonov Type Effects in Dissipative Atomic Systems

A. I. Solomon, Sonia G. Schirmer

A state in quantum mechanics is defined as a positive operator of norm 1. For finite systems, this may be thought of as a positive matrix of trace 1. This constraint of positivity imposes severe restrictions on the allowed evolution of such a state. From the mathematical viewpoint, we describe the two forms of standard dynamical equations - global (Kraus) and local (Lindblad) - and show how each of these gives rise to a semi-group description of the evolution. We then look at specific examples from atomic systems, involving 3-level systems for simplicity, and show how these mathematical constraints give rise to non-intuitive physical phenomena, reminiscent of Bohm-Aharonov effects. In particular, we show that for a multi-level atomic system it is generally impossible to isolate the levels, and this leads to observable effects on the population relaxation and decoherence.A state in quantum mechanics is defined as a positive operator of norm 1. For finite systems, this may be thought of as a positive matrix of trace 1. This constraint of positivity imposes severe restrictions on the allowed evolution of such a state. From the mathematical viewpoint, we describe the two forms of standard dynamical equations - global (Kraus) and local (Lindblad) - and show how each of these gives rise to a semi-group description of the evolution. We then look at specific examples from atomic systems, involving 3-level systems for simplicity, and show how these mathematical constraints give rise to non-intuitive physical phenomena, reminiscent of Bohm-Aharonov effects. In particular, we show that for a multi-level atomic system it is generally impossible to isolate the levels, and this leads to observable effects on the population relaxation and decoherence.

arXiv:quant-ph/0512198Dec 1, 20060 citations

On the Structure of Quantum Finite-Level Systems: Decoherence-Free Subsystems, Quantum Nondemolition Variables, and Back-Action-Evading Measurements

Jia Gu, Guofeng Zhang, Ian R. Petersen

The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective dephasing illustrates these structural properties of quantum finite-level systems.The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective dephasing illustrates these structural properties of quantum finite-level systems.

quant-pharXiv:2610.30616Oct 23, 20260 citations

d

-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case in which the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.