标题： 广义压缩的有限维逼近 显示英文标题

标题： Finite-dimensional approximations of generalized squeezing

摘要： 我们在使用Fock空间的有限维截断进行广义压缩的模拟中展示了意想不到的行为：即使状态空间的维度非常大，结果仍取决于截断维度是偶数还是奇数。 这种情况引发了模拟结果是否具有物理意义的问题。 我们证明实际上，这两种截断方案对应于两个定义明确且不同的幺正演化，其生成元在无限维Fock空间的不同子集上定义。 这是由于广义压缩哈密顿量在有限激发态上不是自伴的，而是具有多个自伴扩张。 此外，我们给出了对应于偶数和奇数截断大小的压缩算符的谱结果，阐明了对应于偶数和奇数截断方案的两种不同自伴扩张的性质。 为了使压缩算符适用于物理系统，我们必须通过依赖于实验实现具体细节的其他项对其进行正则化。 我们表明，在哈密顿量中添加一个Kerr相互作用项会导致唯一收敛的模拟，不再依赖于截断大小的奇偶性，并证明Kerr项确实使哈密顿量自伴，从而具有物理可解释性。 显示英文摘要

摘要： 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.