  Two-mode squeezed states, which are entangled states with bipartite quantum
correlations in continuous-variable systems, are crucial in quantum information
processing and metrology. Recently, continuous-variable quantum computing with
the vibrational modes of trapped atoms has emerged with significant progress,
featuring a high degree of control in hybridizing with spin qubits. Creating
two-mode squeezed states in such a platform could enable applications that are
only viable with photons. Here, we experimentally demonstrate two-mode squeezed
states by employing atoms in a two-dimensional optical lattice as quantum
registers. The states are generated by a controlled projection conditioned on
the relative phase of two independent squeezed states. The individual squeezing
is created by sudden jumps of the oscillators' frequencies, allowing generating
of the two-mode squeezed states at a rate within a fraction of the oscillation
frequency. We validate the states by entanglement steering criteria and Fock
state analysis. Our results can be applied in other mechanical oscillators for
quantum sensing and continuous-variable quantum information.
