We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin- $\frac{1}{2}$ particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin $S$ constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large- $S$ limit. We find an insightful expression for the propagator of the whole system, where we identify an effective ``back-action'' term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-$\frac{1}{2}$ particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin $S$ constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-$S$ limit. We find an insightful expression for the propagator of the whole system, where we identify an effective ``back-action'' term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.

arXiv:1609.05389Physical Review ADec 30, 20165 citations

Spinning Quantum System in an External Magnetic Field

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

Springer eBooksJan 1, 20030 citations

Spontaneous magnetism after a "remote" quench: a proposal to test Copenhagen interpretation

Jianda Wu, Wenxin Ding

A change of quantum states for a quantum particle may lead to a change of physical field it exerts to the environment. We discuss such Gedankenexperiment for measuring the magnetic dipole fields associated with the electronic spins. When entangled, electrons are no longer free Dirac electrons but become an excited state in a quantum-electrodynamics sense. A measurement of magnetism associated with entanglement-collapse of electrons becomes a test for Copenhagen interpretation in the reign of quantum-electrodynamics. This proposal is equally applicable to other particles and their associated fields and interactions, such as neutrons and the electroweak force.A change of quantum states for a quantum particle may lead to a change of physical field it exerts to the environment. We discuss such Gedankenexperiment for measuring the magnetic dipole fields associated with the electronic spins. When entangled, electrons are no longer free Dirac electrons but become an excited state in a quantum-electrodynamics sense. A measurement of magnetism associated with entanglement-collapse of electrons becomes a test for Copenhagen interpretation in the reign of quantum-electrodynamics. This proposal is equally applicable to other particles and their associated fields and interactions, such as neutrons and the electroweak force.

arXiv:2209.11665Sep 23, 20220 citations

\frac{1}{2}

particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin

S

constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-

S

limit. We find an insightful expression for the propagator of the whole system, where we identify an effective ``back-action'' term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.