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arXiv:2108.12064 · Physical Review A

Coupling of magnetic and optomechanical structuring in cold atoms

T. Ackemann, G. Labeyrie, Adrian Costa Boquete, Giuseppe Baio, J. G. M. Walker, Robin Kaiser, Gian‐Luca Oppo, Gordon R. M. Robb

Published Jun 8, 2022• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.105.063508

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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.
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.
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.
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.
We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam.
Clouds of cold neutral atoms driven by a coherent light beam in a ring cavity exhibit self-structured states transversely with respect to the beam axis due to optomechanical forces and the backaction of the atomic structures on the beam. Below the instability threshold for extended hexagonal structures, localized solitonlike excitations can be stable. These constitute peaks or holes of atom density, depending on the linear susceptibility of the cloud. Complex rotating and spiraling motion of coupled atom-light solitons, and, hence, atomic transport, can be achieved via phase gradients in the input field profile. We also discuss the stability of rotating soliton chains in view of soliton-soliton interactions. The investigations are performed in a cavity scheme but expected to apply to other longitudinally pumped schemes with diffractive coupling.