  An enduring challenge in constructing mechanical oscillator-based hybrid
quantum systems is to ensure engineered coupling to an auxiliary degree of
freedom while maintaining good mechanical isolation from the environment, that
is, low quantum decoherence, consisting of thermal decoherence and dephasing.
Here, we overcome this challenge by introducing a superconducting circuit
optomechanical platform which exhibits a low quantum decoherence while having a
large optomechanical coupling, which allows us to prepare the quantum ground
and squeezed states of motion with high fidelity. We directly measure a thermal
decoherence rate of 20.5 Hz (corresponding to T_1 = 7.7 ms) as well as a pure
dephasing rate of 0.09 Hz, resulted in a 100-fold improvement of quantum-state
lifetime compared to the prior optomechanical systems. This enables us to reach
to 0.07 quanta motional ground state occupation (93% fidelity) and realize
mechanical squeezing of -2.7 dB below zero-point-fluctuation. Furthermore, we
observe the free evolution of mechanical squeezed state, preserving its
non-classical nature over milli-second timescales. Such ultra-low quantum
decoherence not only increases the fidelity of quantum control and measurement
of macroscopic mechanical systems, but may also benefit interfacing with
qubits, and places the system in a parameter regime suitable for tests of
quantum gravity. (Keywords: Quantum optomechanics, Superconducting circuit
electromechanics, Quantum squeezing, Quantum memory, Quantum coherence)
