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Journal of Optics B Quantum and Semiclassical Optics

Mesoscopic multistability with atomic coherence effects

Saad S. M. Hassan, Yasser Amoun Sharaby

Published Nov 22, 2005• 7 citations
Publisher

Abstract

The steady state behaviour describing the interaction of a mesoscopic system of coherently injected two-level Rydberg atoms with a coherently driven single-mode cavity is investigated in both resonant and non-resonant regimes. Multiple-switching effects between the output field states are predicted with the atomic coherent excitation (θ) and relative coherent phase parameter (Φ r ) of the atomic coherent state . The relation between the transmitted field ( x ) and the atomic cooperation parameter ( C ) shows multistable behaviour for some values of the polar and azimuthal angles (θ,ϕ). The transverse field feature in the form of a Gaussian beam profile tends to degrade the multistable structure in the ( C – x ) and the input–output field ( x – Y ) relations. Micromaser action is analysed for the system with atomic coherence within and without the plane wave approximation.

DOI
10.1088/1464-4266/7/12/034

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The steady state behaviour describing the interaction of a mesoscopic system of coherently injected two-level Rydberg atoms with a coherently driven single-mode cavity is investigated in both resonant and non-resonant regimes. Multiple-switching effects between the output field states are predicted with the atomic coherent excitation (θ) and relative coherent phase parameter (Φ r ) of the atomic coherent state . The relation between the transmitted field ( x ) and the atomic cooperation parameter ( C ) shows multistable behaviour for some values of the polar and azimuthal angles (θ,ϕ). The transverse field feature in the form of a Gaussian beam profile tends to degrade the multistable structure in the ( C – x ) and the input–output field ( x – Y ) relations. Micromaser action is analysed for the system with atomic coherence within and without the plane wave approximation.
The interaction of a mesoscopic system of coherently injected two-level Rydberg atoms with a coherently driven single cavity mode is treated outside the rotating wave approximation (RWA). The additional first harmonic component of the output field (outside RWA) exhibits closed hysteresis loops and multiple-switching processes, compared with the hysteresis cycles for the nonoscillatory (fundamental) component within the RWA. This is achieved via two controls: (i) varying the coherent population excitation and relative phase parameters (θ, ϕ) of the coherently injected atoms, and, (ii) varying simultaneously atom and cavity detuning parameters.
We consider a mesoscopic maser, in which a beam of excited two-level Rydberg atoms interacts with a single radiation mode during propagation through a resonant cavity. The number of atoms in the cavity ranges from a few tens to a few hundreds. Steady-state and nonlinear dynamics are investigated both with and without a coherent driving field. At steady state, atomic cooperation can induce multistability and temporal instabilities. A novel type of bistability is predicted for the amplitude of the coherently driven cavity field as a function of atomic density. The system dynamics exhibits a variety of regimes, including chaos. We have explored them by varying the experimentally accessible parameters: atomic density, cavity linewidth and driving field amplitude.
We describe a system of N two-level Rydberg atoms which travel through a resonant cavity and interact with a single mode of the resonator. N is assumed to be on the order of a few tens or hundreds of atoms. In particular, we analyze the case where the atoms are injected to the lower state (absorber) and the system is driven by an external coherent radiation field exactly resonant with the atoms and with the cavity. In the case of a monoenergetic atomic beam, the picture that arises is substantially different from that of standard optical bistability. The switching behavior is not governed by saturation, but by the Rabi cycles of the atoms in the cavity. The hysteresis cycle of the population of the upper level is butterfly shaped. When the bistability parameter exceeds an appropriate second threshold, the system displays multistability rather than simple bistability, and under proper conditions it develops domains of instability in positive-slope regions of the steady-state curve. We analyze the effects of a velocity distribution (thermal or Gaussian) in the atomic beam, and of inhomogeneous broadening caused by stray electric fields. Finally, we discuss the feasibility of an experimental observation of the effects predicted by our analysis.
The interaction of a mesoscopic system of two-level Rydberg atoms with a coherently driven single cavity mode is treated outside the rotating wave approximation (RWA). This yields a system of non-autonomous Maxwell–Bloch equations that can be solved using Fourier decomposition of both field and atomic variables up to first harmonics and to O ( Q −1 ), where Q is the cavity quality factor. For the absorber and amplifier regimes, the first harmonic component of the output field (outside the RWA) exhibits closed hysteresis loops compared with hysteresis cycles for the non-oscillatory (fundamental) component within the RWA. A cooperative switching diagram (output field versus cooperative atomic parameter) outside the RWA shows overlapping branches in the resonant case and closed loops in the non-resonant case.
Dispersive switching effect is examined for a mesoscopic system of coherently injected two-level Rydberg atoms into a driven single-mode superconducting cavity. The effect concerns the switching of the output field by simultaneously varying the atomic and cavity detuning parameters at fixed values of the coherent driving field. For certain atomic coherence parameters, symmetric and asymmetric switching diagrams are exhibited, which include one- and two-way process via multistep transitions between output field states.
A mesoscopic beam of two-level Rydberg atoms, prepared in the lower state, interacts with a coherently driven cavity mode. The dynamics is described by Maxwell-Bloch equations with atomic propagation. On resonance, the system was predicted to exhibit multistability, upper-branch instabilities, and self-pulsing. In the presence of atomic detuning its dynamical behavior is shown to include in addition period doubling, frequency locking, quasiperiodicity, and chaos, thus providing a remarkable example of nonlinear dynamics of a passive autonomous atomic system with propagation. \textcopyright{} 1996 The American Physical Society.