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arXiv:1605.05593 · Journal of Physics Conference Series

Interaction of a single mode field cavity with the 1D XY model: Energy spectrum

H Tonchev, Alexander A. Donkov, Hassan Chamati

Published Feb 9, 2016• 2 citations
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Abstract

In this work we use the fundamental in quantum optics Jaynes-Cummings model to study the response of spin 1/2chain to a single mode of a laser light falling on one of the spins, a focused interaction model between the light and the spin chain. For the spin-spin interaction along the chain we use the XY model. We report here the exact analytical results, obtained with the help of a computer algebra system, for the energy spectrum in this model for chains of up to 4 spins with nearest neighbors interactions, either for open or cyclic chain configurations. Varying the sign and magnitude of the spin exchange coupling relative to the light-spin interaction we have investigated both cases of ferromagnetic or antiferromagnetic spin chains.

DOI
10.1088/1742-6596/682/1/012032

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Energy spectra of a spin-12\frac{1}{2}21​ XY spin molecule interacting with a single mode field cavity
We report results from our continued investigations on a finite-size chain (molecule) of L spin- spins with XY spin exchange interaction coupled at an arbitrary spin site to a single mode of an electromagnetic field via the Jaynes-Cummings model. Here we study the energy spectra in the case of an arbitrary photon fill number n , as compared to the n = 1 limit in our previous work [J. Phys.: Conf. Ser. 682 (2016) 012032] and [J. Phys.: Conf. Ser. 764 (2016) 012017]. By building the appropriate combinations of basis product states involving the photon as well as the up down spins it is possible to simplify the systems that are necessary to diagonalize from n × 2 L to at most 2 L . This results are in tune with those reported in the recent paper by N. Wu [Phys. Rev. B 97 (2018) 014301], and may prove to be useful for the quantum computing aficionados.
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We study the energy spectrum of a dual spin chain with an XY interaction among nearest neighbors. This model is applicable in particular to the description of the magnetic properties of the compound Cu(NO3)2 · 2.5H2O. We obtain exact expressions for the energy and wave functions of the one- and two- magnon states. Analysis of the stationary states with a large number of excitations is carried out in terms of perturbation theory under the condition that the exchange interaction J1 between the members of a spin pair significantly exceeds the interaction between pairs, J2. For small ratios J2/J1 the curves of the thermodynamic functions obtained as functions of magnetic field indicate the presence of two critical fields at low temperatures (T≪J2), in agreement with the experimental data.
The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two-level system which can be tuned in resonance with the cavity. Here, we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where intercavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread over many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.