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Journal of Modern Optics

Effect of quantum subsystem–subsystem coupling in hybrid systems

Xiaofen Huang, L.C. Wang, Xun Yi

Published Jul 2, 2008• 0 citations
Publisher

Abstract

In this paper, we study the effect of quantum subsystem–subsystem coupling on the magnetic-like field that the classical subsystem feels in a quantum–classical hybrid system. The hybrid system is composed of a classical magnetic particle and two coupled spins. We show that (i) when the spin–spin interaction is equal to the magnetic–spin interaction, the magnetic-like field changes sharply. This observation becomes more clear when the distance between the two subsystems is much longer than the magnetic particle's rotating radius. (ii) When the spin–spin interaction is larger than the coupling between the quantum classical systems, the effect that the quantum subsystem acts on in the classical part approaches zero. Some useful applications are also discussed.

DOI
10.1080/09500340801923844

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In this paper, we study the effect of quantum subsystem–subsystem coupling on the magnetic-like field that the classical subsystem feels in a quantum–classical hybrid system. The hybrid system is composed of a classical magnetic particle and two coupled spins. We show that (i) when the spin–spin interaction is equal to the magnetic–spin interaction, the magnetic-like field changes sharply. This observation becomes more clear when the distance between the two subsystems is much longer than the magnetic particle's rotating radius. (ii) When the spin–spin interaction is larger than the coupling between the quantum classical systems, the effect that the quantum subsystem acts on in the classical part approaches zero. Some useful applications are also discussed.
It is well known that the dynamics of a hybrid system, which consists of a quantum subsystem and a classical subsystem, can be studied by transforming the quantum subsystem into a classical one. Based on our previous work [Phys. Rev. A 102, 032213 (2020)], we present the formalism of the quantum-classical hybrid system containing a quantum subsystem with energy degeneracy. By simulating the non-Abelian dynamics and geometric phases for the quantum subsystem with classical non-Abelian dynamics and geometric angles, the effect of the non-Abelian gauge field and the geometric phase of the quantum (sub)system on the dynamics of the classical subsystem is revealed by a simple canonical transformation. Remarkably, the non-Abelian angle geometric vector potential is found not only to induce the Wilczek-Zee phase in the dynamics of the quantum subsystem but also to give rise to a Lorentz-like non-Abelian geometric force. To illustrate the dynamics of the hybrid system, we examine the interaction between a spin-half particle and a magnetic field coupled with a magnetic particle. The explicit expression of the non-Abelian magneticlike gauge field is presented, introducing a different form of non-Abelian geometric force in the realm of quantum-classical dynamics.
The vector potential and Berry-phase-induced force in a dissipative hybrid system are studied in this paper. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the dissipative quantum subsystem on the motion of its classical partner, whereas in the second case, we show how the dynamics of the quantum single spin are affected by the dissipation of the classical particle. Extension to general dissipative hybrid systems is discussed.
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.
It is believed that an isolated and far-from-equilibrium quantum many-body system should try to attain equilibrium via a mechanism whereby any given subsystem acts as an open quantum system that is coupled to an environment, which is the complementary part of the full system, and undergoes a complicated equilibration process such that all the subsystems in the long-time limit attain equilibrium states compatible with the global equilibrium state. This picture begs the question whether the dynamics of any given subsystem is Markovian (monotonic loss of information and memory) or non-Markovian. In this work, by numerically probing the dynamical behaviour of the quantum distances between temporally-separated\textit{temporally-separated}temporally-separated states of small subsystems, we reveal the telltale signatures of (non-)Markovianity of the dynamics of subsystems of an isolated quantum spin system brought in the far-from-equilibrium regime, exemplified with the mixed-field Ising spin chain quenched between parameter regimes deep inside its magnetically ordered and disordered regimes. Additionally, remarkably systematic behaviour is seen in a measure of classical distances between the quantum states of the considered subsystems. These features strongly depend on the direction of quenching in the parameter space, with paramagnetic-to-ferromagnetic quenches offering considerably stronger signatures of subsystem non-Markovianity, for which we offer heuristic arguments.
The Berry phase, which was discovered more than two decades ago, provides very deep insight into the geometric structure of quantum mechanics. Its classical counterpart, Hannay's angle, is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper we study the Berry phase and Hannay's angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By the term quantum-classical hybrid system, we mean a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay's angle are explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have a small effect on the Hannay's angle.