Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

Luo, Xiang-Qian; Yang, Baiyuan; Zhang, Xiaofei; Li, Lei; Yu, Xiaoguang

doi:10.1103/physreva.95.052128

Cited by 16 publications

(13 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most famous solutions in the history may be Landau-Zener Transition [7,8], Rabi problems [9] and hyperbolic secant pulse [10]. Also in the past ten years, some different analytical schemes was proposed, like shortcuts scheme or single-shot shaped pulse [11][12][13][14][15][16][17] and others [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Solution in Detuned Two Level Systems

He¹,

Wu²,

Xue³

2022

Preprint

View full text Add to dashboard Cite

Finding the evolution of two level Hamiltonian is of great importance in quantum computation and quantum precision manipulation due to the requirement of quantum experiment control. However, the Schrödinger equation of an arbitrary time-dependent two level Hamiltonian is hardly solvable due to its non-commutativity Hamiltonian in different times. In this article, we expand and demonstrate an exact solution of Schrödinger equation respect to general two level systems with a few limitations. This analytical solution has lots of manipulative parameters and a few boundary restrictions, which could drive many applications. Furthermore, we show the adaptive capacity of our scheme, which demonstrated the widely use of our scheme, and make it suitable for most of experiment Hamiltonian directly.

show abstract

Section: Introductionmentioning

confidence: 99%

An Analytical Solution in Detuned Two Level Systems

He¹,

Wu²,

Xue³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The single-particle model also can be derived from a many-particle two-level system, [39][40][41][42] by using the Feshbach-resonance technique to make zero interparticle interaction. Analytically solvable driven two-level quantum systems without SOC have continuously attracted considerable attention in diverse areas of physics, [43][44][45][46][47][48][49][50][51][52] since exact analytical solutions are invaluable in the contexts of qubit control [49] and can render the control strategies more transparent. [53] The presence of SOC increases the difficult for searching the solvability of the systems and leads the corresponding exact solutions to remain extremely rare.…”

Section: Introductionmentioning

confidence: 99%

Transparently manipulating spin–orbit qubit via exact degenerate ground states*

Kuo¹,

Zhu²,

Chen³

et al. 2020

Chinese Phys. B

View full text Add to dashboard Cite

By investigating a harmonically confined and periodically driven particle system with spin–orbit coupling (SOC) and a specific controlled parameter, we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten (or cat) states. In the undriven case, application of a modulation resonance results in the exact stationary states. We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states. The expected energy consisting of quantum and continuous parts is derived, and the energy deviations caused by the exchange operations are much less than the quantum gap. The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin–orbit qubits via the robust spin-motion entangled degenerate ground states.

show abstract

“…[30] Recently, the analytical results for the parity-time-symmetric two-level system under synchronous combined modulations was studied. [31] To the best of our knowledge, an exact analytic solution for the 𝒫𝒯 -symmetric Rabi model is still lacking up to now. In this article, we will focus on how to obtain the analytic solutions for 𝒫𝒯 -symmetric Rabi models.…”

Section: Introductionmentioning

confidence: 99%

Analytic solutions for generalized PT -symmetric Rabi models*

et al. 2019

View full text Add to dashboard Cite

We theoretically investigate the exact solutions for generalized parity–time( P T )-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the P T -symmetric two-level systems.

show abstract

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

Cited by 16 publications

References 43 publications

An Analytical Solution in Detuned Two Level Systems

An Analytical Solution in Detuned Two Level Systems

Transparently manipulating spin–orbit qubit via exact degenerate ground states*

Analytic solutions for generalized PT -symmetric Rabi models*

Contact Info

Product

Resources

About