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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Dipole and quadrupole patterns in cold atoms via light induced interactions

I. Kresici, G. Labeyrie, Gian‐Luca Oppo, W. J. Firth, Gordon R. M. Robb, Paul F. Griffin, Aidan S. Arnold, Robin Kaiser, T. Ackemann

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Recent years have witnessed considerable interest in simulating the dynamics of complex many-body systems by well-controlled cold atom model systems. Among others, magnetic ordering phenomena draw a lot of attention. We demonstrated an unconventional approach to light mediated atomic interactions using laser light undergoing diffraction [1]. Diffractive propagation of periodically modulated light fields leads to an exchange between phase and amplitude modulated planes (Talbot effect) which can be used to couple atomic degrees of freedom. In a feedback scheme this can lead to the spontaneous formation of coupled lattices in the light field and the atomic degrees of freedom. After adiabatic elimination of the dynamics of the light field, one is left with light mediated atomic interactions. The coupling can occur via optomechanical nonlinearities [1] or via optical pumping [2]. In the latter case, the result is a spontaneous magnetic ordering in the atomic cloud, a spin or a magnetic dipole pattern [2]. We will provide further details on the latter as well as evidence for novel alignment patterns, corresponding to quadrupole states.

DOI
10.1109/cleoe-eqec.2017.8087450

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Recent years have witnessed considerable interest in simulating the dynamics of complex many-body systems by well-controlled cold atom model systems. Among others, magnetic ordering phenomena draw a lot of attention. We demonstrated an unconventional approach to light mediated atomic interactions using laser light undergoing diffraction [1]. Diffractive propagation of periodically modulated light fields leads to an exchange between phase and amplitude modulated planes (Talbot effect) which can be used to couple atomic degrees of freedom. In a feedback scheme this can lead to the spontaneous formation of coupled lattices in the light field and the atomic degrees of freedom. After adiabatic elimination of the dynamics of the light field, one is left with light mediated atomic interactions. The coupling can occur via optomechanical nonlinearities [1] or via optical pumping [2]. In the latter case, the result is a spontaneous magnetic ordering in the atomic cloud, a spin or a magnetic dipole pattern [2]. We will provide further details on the latter as well as evidence for novel alignment patterns, corresponding to quadrupole states.
Abstract Cold atom setups are now commonly employed in simulations of condensed matter phenomena. We present an approach to induce strong magnetic interactions between atoms on a self-organized lattice using diffraction of light. Diffractive propagation of structured light fields leads to an exchange between phase and amplitude modulated planes which can be used to couple atomic degrees of freedom via optical pumping nonlinearities. In the experiment a cold cloud of Rb atoms placed near a retro-reflecting mirror is driven by a detuned pump laser. We demonstrate spontaneous magnetic ordering in the Zeeman sublevels of the atomic ground state: anti-ferromagnetic structures on a square lattice and ferrimagnetic structures on a hexagonal lattice in zero and a weak longitudinal magnetic field, respectively. The ordered state is destroyed by a transverse magnetic field via coherent dynamics. A connection to the transverse (quantum) Ising model is drawn.
This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.
Self-organized phases in cold atoms as a result of light-mediated interactions can be induced by coupling to internal or external degrees of the atoms. There has been growing interest in the interaction of internal spin degrees of freedom with the optomechanical dynamics of the external center-of-mass motion. We present a model for the coupling between magnetic and optomechanical structuring in a $J=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=3/2$ system in a single-mirror feedback scheme, which is representative of a larger class of diffractively coupled systems such as longitudinally pumped cavities and counterpropagating-beam schemes. For negative detunings, a linear stability analysis demonstrates that optical pumping and optomechanical driving cooperate to create magnetic ordering. However, for long-period transmission gratings the magnetic driving will strongly dominate the optomechanical driving, unless one operates very close to the existence range of the magnetic instability. At small lattice periods, in particular at wavelength-scale periods, the optomechanical driving will dominate.
When applying a red-detuned retro-reflected laser beam to a large cloud of cold atoms, we observe the spontaneous formation of 2D structures in the transverse plane corresponding to high contrast spatial modulations of both light field and atomic spins. By applying a weak magnetic field, we explore the rich resulting phase space and identify specific phases associated with both dipolar and quadrupolar terms of the atomic magnetic moment. In particular we demonstrate spontaneous structures in optically induced ground state coherences representing magnetic quadrupoles.
Summary form only given. Spontaneous optical pattern formation occurs in a variety of nonlinear systems [1], including hot atomic vapors [2]. On the other hand, the spatial self-organization of atomic ensembles due to opto-mechanical coupling has received a lot of interest in recent years [3].We report on the observation of transverse self-organization of a cold atomic cloud (issued from a magnetooptical trap) under the action of a single pump laser beam. Two symmetries (translation and rotation) in the plane orthogonal to the beam propagation direction are spontaneously broken. We use a simple optical feedback scheme [4], where the transmitted pump beam is retro-reflected to the atoms by a high-reflectivity mirror located at a distance d behind the cloud. This feedback loop transforms phase fluctuations of the transmitted wave into intensity fluctuations, which then react on the atomic medium. If the feedback is positive, a transverse instability can develop leading to the spontaneous apparition of patterns in the transmitted pump intensity profile, as shown in the figure below (left).Using a weak probe beam sent a few tens of μs after the e,tinction of the pump, we demonstrate that the instability also results in a transverse spatial ordering of the atomic medium as shown in the right image. The cold atoms thus e,perience strong spatial bunching due to the dipole force associated to the inhomogeneous intensity distribution. We identified two different instability regimes. For short pump durations (- 1 μs), high pump intensity and cloud optical density, the instability relies on the Kerr effect (electronic nonlinearity). For longer pump durations (- 100 μs), the instability is driven by the opto-mechanical effect, resulting in lower intensity and optical density thresholds than for the electronic nonlinearity. These observations are well reproduced by a theoretical model including the coupled dynamics of the light field and the atomic e,ternal degrees of freedom.
Optomechanical pattern forming instabilities in a cloud of cold atoms lead to self-organized spatial structures of light and atoms. Here, we consider the optomechanical self-structuring of a cold atomic cloud in the presence of a phase structured input field, carrying orbital angular momentum. For a planar ring cavity setup, a model of coupled cavity field and atomic density equations describes a wide range of drifting modulation instabilities in the transverse plane. This leads to the formation of rotating self-organized rings of light-atom lattices. Using linear stability analysis and numerical simulations of the coupled atomic and optical dynamics, we demonstrate the presence of macroscopic atomic transport corresponding to the pattern rotation, induced by the structured pump phase profile.