Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHidden symmetry operators for asymmetric generalised quantum Rabi models
453
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The hidden $mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) has recently been revealed via a systematic construction of the underlying symmetry operator. Based on the AQRM result, we propose an ansatz for the general form of the symmetry operators for AQRM-related models. Applying this ansatz we obtain the symmetry operator for three models: the anisotropic AQRM, the asymmetric Rabi-Stark model (ARSM) and the anisotropic ARSM.
rate research
Read More
The asymmetric quantum Rabi model (AQRM) has a broken $mathbb{Z}_2$ symmetry, with generally a non-degenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the $mathbb{Z}_2$-symmetric quantum Rabi model are recovered, however, without any obvious parity-like symmetry. This unknown symmetry has thus been referred to as hidden symmetry in the literature. Here we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunnelling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunnelling.
In this paper, we derive the symmetry operators ($J$s) in the asymmetric two-photon quantum Rabi models in terms of Bogoliubov operator approaches. $ J^2$ can be expressed as a polynomial in terms of the Hamiltonian, which uncovers the $mathbb{Z}_{2}$ nature of the hidden symmetry in this two-photon model rigorously. The previous symmetry operators in the asymmetric one-photon quantum Rabi models are reproduced readily in terms of Bogoliubov operator approaches, and the obtained operators are expressed much more concisely. It is found that the polynomial degree of $J^2$ in the two-photon model is twice of that in the one-photon model.
In this paper, we propose a general scheme to obtain the symmetry operators in the asymmetric quantum Rabi model within Bogoliubov operator approaches. The previous symmetry operators for small integer biases can be extremely easily reproduced in our scheme. Moreover, we can easily obtain the symmetry operators for arbitrary large biases hierarchically, which is perhaps hardly treated with the standard approach based on the expansions on the original Fock space.
Starting with the Gaudin-like Bethe ansatz equations associated with the quasi-exactly solved (QES) exceptional points of the asymmetric quantum Rabi model (AQRM) a spectral equivalence is established with QES hyperbolic Schrodinger potentials on the line. This leads to particular QES Poschl-Teller potentials. The complete spectral equivalence is then established between the AQRM and generalised Poschl-Teller potentials. This result extends a previous mapping between the symmetric quantum Rabi model and a QES Poschl-Teller potential. The complete spectral equivalence between the two systems suggests that the physics of the generalised Poschl-Teller potentials may also be explored in experimental realisations of the quantum Rabi model.
We study machines that take N identical replicas of a pure qudit state as input and output a set of M_A clones of a given fidelity and another set of $M_B$ clones of another fidelity. The trade-off between these two fidelities is investigated, and numerous examples of optimal N -> M_A+M_B cloning machines are exhibited using a generic method. A generalisation to more than two sets of clones is also discussed. Finally, an optical implementation of some such machines is proposed. This paper is an extended version of [xxx.arxiv.org/abs/quant-ph/0411179].
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
