  Propagated acoustic waves, which generate radiation pressure, exert a
non-contact force on a remote object. By suitably designing the wave field,
remote tweezers are produced that stably levitate particles in the air without
any mechanical contact forces. Recent works have revealed that holographic
traps can levitate particles even with a single-sided wave source. However, the
levitatable objects in the previous studies were limited to particles smaller
than the wavelength, or flat parts placed near a rigid wall. Here, we achieve a
stable levitation of a macroscopic rigid body by a holographic design of
acoustic field without any dynamic control. The levitator models the acoustic
radiation force and torque applied to a rigid body by discretising the body's
surface, as well as the acoustic wave sources, and optimizes the acoustic field
on the body surface to achieve the Lyapunov stability so that the field can
properly respond to the fluctuation of the body position and rotation. In an
experiment, a 40 kHz (8.5 mm wavelength) ultrasonic phased array levitated a
polystyrene sphere and a regular octahedron with a size of ~50 mm located 200
mm away from acoustic elements in the air. This method not only expands the
variety of levitatable objects but also contributes to microscopic contexts,
such as in-vivo micromachines, since shorter-wavelength ultrasound than the
size of target objects can be used to achieve higher controllability and
stability.
