Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to
PT-Symmetric Qubits
- URL: http://arxiv.org/abs/2206.09162v2
- Date: Wed, 2 Nov 2022 08:45:36 GMT
- Title: Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to
PT-Symmetric Qubits
- Authors: L. Tetling, M.V. Fistul, and Ilya M. Eremin
- Abstract summary: We develop the linear response theory formulation suitable for application to various pHH systems.
We apply our results to two textitPT-symmetric non-Hermitian quantum systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Motivated by the recent advances in modelling the pseudo-Hermitian
Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum
dynamics subject to a small time-dependent perturbation. In particular, We
develop the linear response theory formulation suitable for application to
various pHH systems and compare it to the ones available in the literature. We
derive analytical expressions for the generalized temporal quantum-mechanical
correlation function $C(t)$ and the time-dependent dynamic susceptibility
$\chi(t) \propto \text{Im} ~C(t)$. We apply our results to two
\textit{PT}-symmetric non-Hermitian quantum systems: a single qubit and two
unbiased/biased qubits coupled by the exchange interaction. For both systems we
obtain the eigenvalues and eigenfunctions of the Hamiltonian, identify
\textit{PT}-symmetry unbroken and broken quantum phases and quantum phase
transitions between them. The temporal oscillations of the dynamic
susceptibility of the qubits polarization ($z$-projection of the total spin),
$\chi(t)$, relate to {\it ac} induced transitions between different eigenstates
and we analyze the dependencies of the oscillations frequency and the amplitude
on the gain/loss parameter $\gamma$ and the interaction strength $g$. Studying
the time dependence of $\chi(t)$ we observe different types of oscillations,
i.e. undamped, heavily damped and amplified ones, related to the transitions
between eigenstates with broken (unbroken) $PT$-symmetry. These predictions can
be verified in the microwave transmission experiments allowing controlled
simulation of the pHH systems.
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