Sympathetic cooling and self-oscillations in a hybrid atom-membrane system

Hybrid systems combining mechanical oscillators and ultracold atoms provide novel
opportunities for cooling, detection and quantum control of mechanical motion with
applications in precision sensing, quantum-level signal transduction and for fundamental
tests of quantum mechanics.
In this thesis I present experiments performed with a hybrid atom-membrane
system, in which the vibrations of a Si_3N_4 membrane in an optical cavity are coupled
to the motion of laser-cooled atoms in an optical lattice. The interactions are
mediated by the lattice light over a macroscopic distance and enhanced by the cavity.
Via the coupling to the cold atoms, the fundamental vibrational mode of the
membrane at 2π x 276 kHz is cooled sympathetically from room temperature to
0.4(2) K, even though the mass of the mechanical oscillator exceeds that of the
atomic ensemble by a factor of 4 x 10^10. In other systems, sympathetic cooling
of molecules with cold atoms or ions has been limited to mass ratios of up to 90.
Previous theoretical work has shown that our coupling mechanism is able to cool the
membrane vibration into the ground state and to perform coherent state transfers
between atomic and membrane motion.
Under certain experimental conditions, the atom-membrane system shows self-oscillations,
which arise from an effective delay in the backaction of the atoms onto
the light. This retardation drives the system into limit-cycle oscillations if the coupling
is large. I study the dependence of this instability on several system parameters
and find that a larger atom number and a smaller atom-light detuning make the system
less stable. Further, the stability of the coupled system in presence of a delay is
investigated theoretically and a modified expression for the sympathetic cooling rate
is derived. This model allows to fit the measured atom number dependence with a
delay of τ = 88(1) ns. Moreover, direct measurements of the atomic backaction onto
the lattice light are presented. These show phase lags exceeding 180° in parameter
regimes where the instability is observed, proving that the retardation arises within
the atomic ensemble. Finally, I present the results of numerical simulations, which
show that collective atomic effects within the atomic ensemble in an asymmetric
lattice are able to induce the observed phase lag in the atomic backaction.