  We re-examine a scheme generalized by [R. Finkelstein et al, Phys. Rev. X 11,
011008 (2021)], whose original purpose was to remove the effects of static
Doppler broadening from an ensemble of non-interacting two-level systems
(qubits). This scheme involves the simultaneous application of red and blue
detuned drives between a qubit level and an auxiliary level, and by carefully
choosing the drive amplitudes and detunings, the drive-induced energy shifts
can exactly compensate the inhomogeneous static Doppler-induced frequency
shifts - effectively removing the inhomogeneous Doppler broadening. We
demonstrate that this scheme is far more powerful and can also protect a single
(or even an ensemble), qubit's energy levels from noise which depends on both
time and space: the same scheme can greatly reduce the effects of dephasing
noise induced by a time-fluctuating environment. As examples we study
protection against two types of non-Markovian environments that appear in many
physical systems: Gaussian noise and non-Gaussian noise - Random Telegraph
Noise. Through numerical simulations we demonstrate the enhancement of the spin
coherence time $T_2^*$, of a qubit in a fluctuating environment by three orders
of magnitude as well as the refocusing of its initially drifting frequency.
This same scheme, using only two drives, can operate on an collection of
qubits, providing temporal and spatial stabilization simultaneously and in
parallel yielding a collection of high quality near-identical qubits which can
be useful for many quantum technologies such as quantum computing and sensing,
with the potential to achieve fault tolerant quantum computation much sooner.
