Plateau dynamics with quantized oscillations of a strongly driven qubit
- URL: http://arxiv.org/abs/2010.11785v1
- Date: Thu, 22 Oct 2020 15:00:54 GMT
- Title: Plateau dynamics with quantized oscillations of a strongly driven qubit
- Authors: Yejia Chen, Zhiguo L\"u, Yiying Yan, Hang Zheng
- Abstract summary: We show that the collective effects of all even harmonics contribute to the generation of zigzag plateau with quantized oscillation.
We also show that the dynamics of the coherent destruction of tunneling under strong driving is exactly exhibited by including the odd-harmonic effect.
- Score: 1.6058099298620423
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present an interesting dynamical temporal localization of a strongly
driven two-level system (TLS), a plateau with quantized oscillation, by an
analytical and transparent method, the counter-rotating-hybridized
rotating-wave (CHRW) method. This approach, which is based on unitary
transformations with a single parameter, treats the rotating and
counter-rotating terms on equal footing. In the unitarily transformed
representation, we find that it is the multiple-harmonic terms shown in the
transformed Hamiltonian that make a crucial contribution to the generation of
the exotic plateau phenomenon. By comparing the results of the numerically
exact calculation and several other methods, we show that the CHRW results
obtained by analytical formalism involving the collective effects of multiple
harmonics are in good agreement with the numerical results, which illustrates
not only the general tendency of the dynamical evolution of strongly driven
TLS, but also the interesting phenomena of plateaus. The developed CHRW method
reveals two kinds of plateau patterns: zigzag plateau and armchair plateau. The
plateau phenomenon has a periodical pattern whose frequency is double the
driving frequency, and possesses quantized oscillations the number of which has
a certain, precise value. Besides, fast oscillation is produced on every
plateau which is determined by the relevant driving parameters of the TLS. Our
main results are as follows: (i) in the large-amplitude oscillatory case, it
turns out that the collective effects of all even harmonics contribute to the
generation of zigzag plateau with quantized oscillation; (ii) in the
small-amplitude oscillatory case, the dynamics of the coherent destruction of
tunneling under strong driving is exactly exhibited by including the
odd-harmonic effect, namely, armchair plateau possessing a two-stair structure
rather than the complete destruction.
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