Optical coherent feedback control of a mechanical oscillator

Coherent feedback is a quantum control technique that governs the behavior of a target
system by employing closed-loop actuation based on a coherent interaction with a
second quantum system, acting as a controller. This approach eliminates the need for
any invasive measurements that are typically required in feedback control. Especially
in optomechanics, where a light field coherently interacts with the mechanical degree of
freedom of an oscillator, coherent feedback is expected to expand the range of control
possibilities, promote the generation of non-classical states and allow for a reduction of
noise. Despite the numerous theoretical proposals emphasizing the potential advantages
of employing coherent feedback for optomechanical quantum control, experiments validating
these proposals are still scarce.
In this thesis I present the implementation of a coherent feedback platform for a cavity
optomechanical system. We demonstrate that a coherent feedback protocol involving
an optical light beam interacting twice with a mechanical oscillator, thus forming an optical
feedback loop with tunable parameters, opens up new avenues for controlling the
mechanical state.
Our optomechanical setup consists in a nanomechanical membrane placed in a Fabry-
Pérot optical cavity. The membrane, a thin sheet of silicon nitride embedded in a phononic
shield, couples to the cavity light through radiation pressure. The cavity has one incoupling
port that allows a coherent light field to drive a cavity mode. The light that
has interacted with the membrane and escapes the cavity is then collected, delayed and
phase shifted using an optical fiber and an auxiliary local oscillator beam. The polarization
of the light beam is subsequently rotated before the beam is sent back to the cavity,
allowing for a second interaction of the light with the mechanical oscillator in an orthogonal
cavity mode. During the second interaction, the light beam, already containing
the mechanical signal from the first interaction, implements an effective interaction of
the mechanical oscillator with itself. The feedback parameters, given by the delay and
phase in the feedback loop, strongly modify the nature of this self-interactions, making
it possible to implement a damping or an amplifying force.
As a result, tuning the optical phase and delay between the two interactions enables
us to control the motional state of the mechanical oscillator via its resonance frequency
and damping rate. We show theoretically that this coherent feedback loop enables
ground-state cooling even in the unresolved sideband regime, where the optical
cavity linewidth is much larger than the mechanical frequency and which cannot be
achieved by standard cooling techniques. Experimentally, we tune the feedback parameters
and show modifications of the mechanical susceptibility that are enabled by the coherent
feedback scheme. We demonstrate cooling of the mechanical mode to a state with
¯ nm = 4.89 ± 0.14 phonons (480 µK) in a 20K environment. This result is below the theoretical
limit of conventional dynamical backaction cooling in the unresolved sideband
regime. Our feedback scheme is highly versatile, offering unprecedented opportunities
for quantum control in a variety of optomechanical systems.
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