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Register a new userPossible Knot-type Time-dependent Quantum-mechanically Dynamical System
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Authors
Zotin K.-H. Chu
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We illustrate schematically a possible traversing along the path of trefoil-type and $8_{18}$ knots during a specific time period by considering a quantum-mechanic system which satisfies a specific kind of phase dynamics of quantum mechanics. This result is relevant to the composite particle which is present in the initial or final configuration.
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The cascaded decay in a four-level quantum emitter is a well established mechanism to generate polarization entangled photon pairs, the building blocks of many applications in quantum technologies. The four most prominent maximally entangled photon pair states are the Bell states. In a typical experiment based on an undriven emitter only one type of Bell state entanglement can be observed in a given polarization basis. Other types of Bell state entanglement in the same basis can be created by continuously driving the system by an external laser. In this work we propose a protocol for time-dependent entanglement switching in a four-level quantum emitter--cavity system that can be operated by changing the external driving strength. By selecting different two-photon resonances between the laser-dressed states, we can actively switch back and forth between the different types of Bell state entanglement in the same basis as well as between entangled and nonentangled photon pairs. This remarkable feature demonstrates the possibility to achieve a controlled, time-dependent manipulation of the entanglement type that could be used in many innovative applications.
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of the phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.
The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.
Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can be used to discriminate the amplitude or frequency of an external periodic perturbation or input. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation. end{abstract}
We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in a finite-temperature heat bath. A Born-Markovian quantum master equation is formally derived for the time-dependent system with discrete energy levels. This quantum master equation can be applied to situations with a broad range of driving speeds and bath temperatures and thus be used to study the finite-time quantum thermodynamics even when nonadiabatic transition and dissipation coexist. The dissipative Landau-Zener model is analyzed as an example. The population evolution and transition probability of the model reveal the importance of the competition between driving and dissipation beyond the adiabatic regime. Moreover, local maximums of irreversible entropy production occur at intermediate sweep velocity and finite temperature, which the low-dissipation model cannot describe.
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