Bloch-Siegert shift in a hybrid quantum register: Quantification and compensation

Zhang, Jingfu; Saha, Sagnik; Suter, Dieter

doi:10.1103/physreva.98.052354

Cited by 7 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Bloch-Siegert Hamiltonian, here denoted H BS (t ), is possibly the simplest model to exhibit nontrivial physical effects due to time dependencies in the driving radio-frequency fields. The detailed study of these effects is of paramount importance in the broad field of quantum computing, as they have a deleterious impact on qubit driving and stored quantum information [33]. The Hamiltonian reads as…”

Section: Introductionmentioning

confidence: 99%

Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR

Giscard

Bonhomme

2020

Phys. Rev. Research

View full text Add to dashboard Cite

Comprehending the dynamical behavior of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood as the usual methods including diagonalization of the Hamiltonian do not work in this setting. In fact, since the inception of Magnus' expansion [Commun. Pure Appl. Math. 7, 649 (1954)], no fundamentally novel mathematical approach capable of solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here on an entirely different nonperturbative approach, termed path sum, which is always guaranteed to converge, yields the exact analytical solution in a finite number of steps for finite systems, and is invariant under scale transformations of the quantum state space. Path sum can be combined with any state-space reduction technique and can exactly reconstruct the dynamics of a many-body quantum system from the separate, isolated, evolutions of any chosen collection of its subsystems. As examples of application, we solve analytically for the dynamics of all two-level systems as well as of a many-body Hamiltonian with a particular emphasis on nuclear magnetic resonance applications: Bloch-Siegert effect, coherent destruction of tunneling, and N-spin systems involving the dipolar Hamiltonian and spin diffusion.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR

Giscard

Bonhomme

2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…However, it is a basic fact that the Rabi-RWA method breaks down in the strong driving regime or off-resonant situation since the CR terms can not be neglected in comparison with the rotating one. Actually, many interesting phenomena are attributed to the contribution of CR terms, such as coherent destruction of tunneling (CDT) [35][36][37], Bloch-Siegert(BS) shift [38][39][40], quantum Zeno effect [41], etc. Therefore, various methods sprang up in order to improve the analytical results in some parameter regime and offer perspectives to discover the insight of these significant phenomena, such as the RWA in a rotating frame (RWA-RF) [42], Floquet theory [43,44], transfer-matrix approach [42,45], etc.…”

Section: Introductionmentioning

confidence: 99%

Plateau dynamics with quantized oscillations of a strongly driven qubit

Chen,

Lü,

Yan

et al. 2020

Preprint

View full text Add to dashboard Cite

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 counterrotating-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, and quantitative analyses are given to comprehensively describe the features of the plateau phenomenon. 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, and the general tendency of evolution coincides with the result of the original CHRW method because of a linear trend of the phase function; (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, which offers a novel dynamical pattern, namely, armchair plateau possessing a two-stair structure rather than the complete destruction. Besides, the characteristics of the plateau (position, frequency, the envelope and number of quantized oscillations) are revealed by our analytical formalism. Both of the dynamical patterns are of great interest to strongly driven physics in the ongoing research on driven TLS systems.

show abstract