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

Atomic Interaction via Diffractive Light Coupling

T. Ackemann, Adrian Costa Boquete, Ivor Krešić, Giuseppe Baio, Gordon R. M. Robb, Gian‐Luca Oppo, Paul F. Griffin, G. Labeyrie, Robin Kaiser

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Transversely pumped cavities have been a workhorse for mediating global coupling between atoms and recent progress has been made towards multi-mode situations with more localized coupling [1]. However, in transversely pumped cavities, symmetries will be always constrained by the pump and cavity axes whereas in a system with a single distinguished axis the translational and rotational symmetries in the 2D transverse plane can be broken spontaneously. Recent work demonstrated that in a feedback system (Fig. 1a) using coupling to external degrees of freedom or internal spin degrees of freedom [2-4]. In this contribution, we are giving a generalized treatment of this coupling and show how the different light degrees of freedom on the Poincaré sphere can be utilized to address different atomic moments. We also investigate the transfer of this concept to longitudinally pumped cavities.

DOI
10.1109/cleoe-eqec.2019.8872783

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Transversely pumped cavities have been a workhorse for mediating global coupling between atoms and recent progress has been made towards multi-mode situations with more localized coupling [1]. However, in transversely pumped cavities, symmetries will be always constrained by the pump and cavity axes whereas in a system with a single distinguished axis the translational and rotational symmetries in the 2D transverse plane can be broken spontaneously. Recent work demonstrated that in a feedback system (Fig. 1a) using coupling to external degrees of freedom or internal spin degrees of freedom [2-4]. In this contribution, we are giving a generalized treatment of this coupling and show how the different light degrees of freedom on the Poincaré sphere can be utilized to address different atomic moments. We also investigate the transfer of this concept to longitudinally pumped cavities.
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.
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.
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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.
We report out-of-equilibrium stabilization of the collective spin of an atomic ensemble through autonomous feedback by a driven optical cavity. For a magnetic field applied at an angle to the cavity axis, dispersive coupling to the cavity provides sensitivity to a combination of the longitudinal and transverse spin. Coherent backaction by cavity light onto the atoms, conditioned by the cavity susceptibility, stabilizes the spin state at an arbitrary energy. The setpoint tracking and closed-loop gain spectrum of the feedback system are characterized and found to agree closely with analytic predictions.
We investigate the physics of a gas of ultracold atoms coupled to three single-mode optical cavities and transversely pumped with a laser. Recent work has demonstrated that, for two cavities, the Z2{\mathbb{Z}}_{2}Z2​ symmetries of each cavity can be combined into a global U(1) symmetry [J. L\'eonard et al., Nature (London) 543, 87 (2017)]. Here we show that when adding an extra cavity mode, the low-energy description of this system can additionally exhibit an SO(3) rotational symmetry which can be spontaneously broken. This leads to a superradiant phase transition in all the cavities simultaneously, and the appearance of Goldstone and amplitude modes in the excitation spectrum. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We also obtain the excitation spectrum for each phase and discuss the atomic self-organized structures that emerge in the different superradiant phases. We argue that coupling the atoms equally to nnn different modes will in general generate a global SO(n)\text{SO}(n)SO(n) symmetry if the mode frequencies can be tuned to the same value.