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Journal of Experimental and Theoretical Physics

Feasibility of a feedback control of atomic self-organization in an optical cavity

D. A. Ivanov, T. Yu. Ivanova

Published Aug 1, 2015• 6 citations
Publisher

Abstract

Many interesting nonlinear effects are based on the strong interaction of motional degrees of freedom of atoms with an optical cavity field. Among them is the spatial self-organization of atoms in a pattern where the atoms group in either odd or even sites of the cavity-induced optical potential. An experimental observation of this effect can be simplified by using, along with the original cavity-induced feedback, an additional electronic feedback based on the detection of light leaking the cavity and the control of the optical potential for the atoms. Following our previous study, we show that this approach is more efficient from the laser power perspective than the original scheme without the electronic feedback.

DOI
10.1134/s1063776115080051

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Many interesting nonlinear effects are based on the strong interaction of motional degrees of freedom of atoms with an optical cavity field. Among them is the spatial self-organization of atoms in a pattern where the atoms group in either odd or even sites of the cavity-induced optical potential. An experimental observation of this effect can be simplified by using, along with the original cavity-induced feedback, an additional electronic feedback based on the detection of light leaking the cavity and the control of the optical potential for the atoms. Following our previous study, we show that this approach is more efficient from the laser power perspective than the original scheme without the electronic feedback.
We considered an application of a feedback loop to enhance the self-organization of atoms in a cavity. In contrast to the original setup, we assumed the light leaking from the cavity was photo-detected and the signal was used to appropriately adjust the atomic potential. It was shown that no additional feedback-induced quantum noise was introduced into the system. Numerical simulations performed in classical approximation showed that the application of feedback weakened the requirement for the atom-field coupling needed to observe the self-organization.
We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.
Self-structuring via symmetry breaking is a prominent collective phenomenon occurring in cold and ultracold atoms coupled to optical fields [1] . Experimental realizations by means of trapped dipolar gases and optical cavities have shed light onto supersolidity and crystallization in out-of-equilibrium atomic systems [2] , [3] . Recent work demonstrated the occurrence of structural phase transitions between hexagonally coordinated supersolid phases in dipolar condensates [4] . In this work, we address 2D structural transitions occurring in an ensemble of cold thermal atoms with effective optomechanical interactions mediated by a coherent beam retro-reflected by means of a feedback mirror. The feedback loop scheme is represented in Fig. 1(a) , where the dipole potential induces atomic density structures which, in turn, scatter photons into side-band modes enhancing the potential itself and leading to transverse light-atom self-structuring, sharing similarities with an effective-Kerr nonlinear medium [5] .
When atoms scatter photons from a transverse laser into a high-finesse optical cavity, they form crystalline structures which maximize the intracavity light field and trap the atoms in the ordered array. Stable organization occurs when the laser field amplitude exceeds a certain threshold. For planar single-mode cavities there exist two equivalent possible atomic patterns, which determine the phase of the intracavity light field. Under these premises, we show that the effect of an additional laser pumping the cavity makes one pattern more favorable than the other and that it can dynamically force the system into a predetermined configuration. This is an instance of pattern formation and seeding in a nonlinear quantum-optical system.
An experiment is described where slow laser-cooled atoms are injected into a high-finesse optical cavity. Single atoms are trapped in the cavity light field and observed by measuring the light intensity transmitted through the cavity. Feedback-based methods are realized to extend the time the atom stays in the cavity. The influence of atoms on the cavity transmission and the light force on atoms in a cavity are also analyzed theoretically. This allows to study the motion of an atom in the cavity and to interpret the experimental transmission signals. The current limitations for the storage time are identified and a strategy to overcome them is suggested. Apart from that, a method is proposed which allows a two-dimensional position measurement of atoms in the cavity.
We demonstrate feedback on the motion of a single neutral atom trapped in the light field of a high-finesse cavity. Information on the atomic motion is obtained from the transmittance of the cavity. This is used to implement a feedback loop in analog electronics that influences the atom's motion by controlling the optical dipole force exerted by the same light that is used to observe the atom. In spite of intrinsic limitations, the time the atom stays within the cavity could be extended by almost 30% beyond that of a comparable constant-intensity dipole trap.