Atomic Coherent States and Sphere Maps
نویسنده
چکیده
Robert Gilmore Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA (Dated: November 11, 2011) An atomic coherent state will evolve to an atomic coherent state under a classical driving field. Under a time-periodic driving field the phase space for the dynamics is S ×S, so that chaotic motion is possible. We explore the types of motion that can occur for periodically driven atomic coherent states by investigating the properties of the first return map S → S. The sphere map that we introduce is a generalization of the Kolmogorov-Arnold circle map that is based on the Gauss sphere map. We find mixtures of mode-locking, quasiperiodicity, forward and reverse period-doubling cascades, and chaos.
منابع مشابه
Gazeau- Klouder Coherent states on a sphere
In this paper, we construct the Gazeau-Klauder coherent states of a two- dimensional harmonic oscillator on a sphere based on two equivalent approaches. First, we consider the oscillator on the sphere as a deformed (non-degenerate) one-dimensional oscillator. Second, the oscillator on the sphere is considered as the usual (degenerate) two--dimensional oscillator. Then, by investigating the quan...
متن کاملبرهمنهی حالتهای همدوس غیرخطی روی سطح کره
In this paper, by using the nonlinear coherent states on a sphere, we introduce superposition of the aforementioned coherent states. Then, we consider quantum optical properties of these new superposed states and compare these properties with the corresponding properties of the nonlinear coherent states on the sphere. Specifically, we investigate their characteristics function, photon-number d...
متن کاملCoherent Transport of Single Photon in a Quantum Super-cavity with Mirrors Composed of Λ-Type Three-level Atomic Ensembles
In this paper, we study the coherent transport of single photon in a coupled resonator waveguide (CRW) where two threelevel Λ-type atomic ensembles are embedded in two separate cavities. We show that it is possible to control the photon transmission and reflection coefficients by using classical control fields. In particular, we find that the total photon transmission and reflection are achieva...
متن کاملQuantum baker map on the sphere
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps. In the simplest case of the model the system does not possess a time reversal symmetry and the quantum map is represented by real, orthogonal matrices of eve...
متن کاملMean Dynamical Entropy of Quantum Maps on the Sphere Diverges in the Semiclassical Limit
We analyze quantum dynamical entropy based on the notion of coherent states. The mean value of this quantity for quantum maps on the sphere is computed as an average over the uniform measure on the space of unitary matrices of size N . Mean dynamical entropy is positive for N $ 3, which supplies a direct link between random matrices of the circular unitary ensemble and the chaotic dynamics of t...
متن کامل