Second quantization of the Liouville equation produces a Heisenberg equation for ancillary operators that suffices for nonadiabatic generation of ultra-highly squeezed states in Hermitian and non-Hermitian quantum systems.
The ancillary canonical variables⃗ u(⃗ a,⃗ a∗,t ) and⃗ u∗ (⃗ a,⃗ a∗,t ) are explicitly time-dependent and they satisfy the relation {uj,u ∗ k}⃗ q,⃗ p= −i{uj,u ∗ k}⃗ u,⃗ u∗ = −iδjk
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From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states
Second quantization of the Liouville equation produces a Heisenberg equation for ancillary operators that suffices for nonadiabatic generation of ultra-highly squeezed states in Hermitian and non-Hermitian quantum systems.