  It is shown theoretically that an optical bottle resonator with a nanoscale
radius variation can perform a multi-nanosecond long dispersionless delay of
light in a nanometer-order bandwidth with minimal losses. Experimentally, a 3
mm long resonator with a 2.8 nm deep semi-parabolic radius variation is
fabricated from a 19 micron radius silica fiber with a sub-angstrom precision.
In excellent agreement with theory, the resonator exhibits the
impedance-matched 2.58 ns (3 bytes) delay of 100 ps pulses with 0.44 dB/ns
intrinsic loss. This is a miniature slow light delay line with the record large
delay time, record small transmission loss, dispersion, and effective speed of
light.
