Kavli Affiliate: Felix Fischer
| First 5 Authors: Sahel Ashhab, Sahel Ashhab, , ,
| Summary:
We show unexpected behaviour in simulations of generalized squeezing
performed with finite-dimensional truncations of the Fock space: even for
extremely large dimension of the state space, the results depend on whether the
truncation dimension is even or odd. This situation raises the question whether
the simulation results are physically meaningful. We demonstrate that, in fact,
the two truncation schemes correspond to two well-defined, distinct unitary
evolutions whose generators are defined on different subsets of the
infinite-dimensional Fock space. This is a consequence of the fact that the
generalized squeezing Hamiltonian is not self-adjoint on states with finite
excitations, but possesses multiple self-adjoint extensions. Furthermore, we
present results on the spectrum of the squeezing operators corresponding to
even and odd truncation size that elucidate the properties of the two different
self-adjoint extensions corresponding to the even and odd truncation scheme. To
make the squeezing operator applicable to a physical system, we must regularize
it by other terms that depend on the specifics of the experimental
implementation. We show that the addition of a Kerr interaction term in the
Hamiltonian leads to uniquely converging simulations, with no dependence on the
parity of the truncation size, and demonstrate that the Kerr term indeed
renders the Hamiltonian self-adjoint and thus physically interpretable.
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