Introduction to average Hamiltonian theory. I. Basics

Brinkmann, Andreas

doi:10.1002/cmr.a.21414

Cited by 42 publications

(27 citation statements)

References 35 publications

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“…We can still work in the interaction picture by replacing the unitary propagator e iH 0 t with e i ∫ t 0 dt H 0 (t ) (see e.g. [51]). The integral can be simplified by noting that H 0 (t) varies over the orbital period, which is much smaller than the typical timescale associated with Rabi oscillations, especially at the resonant frequencies [cf.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Ultralight boson cloud depletion in binary systems

et al. 2019

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Ultralight scalars can extract rotational energy from astrophysical black holes through superradiant instabilities, forming macroscopic boson clouds. This process is most efficient when the Compton wavelength of the boson is comparable to the size of the black hole horizon, i.e. when the "gravitational fine structure constant" α ≡ GµM/ c ∼ 1. If the black hole/cloud system is in a binary, tidal perturbations from the companion can produce resonant transitions between the energy levels of the cloud, depleting it by an amount that depends on the nature of the transition and on the parameters of the binary. Previous cloud depletion estimates considered binaries in circular orbit and made the approximation α 1. Here we use black hole perturbation theory to compute instability rates and decay widths for generic values of α, and we show that this leads to much larger cloud depletion estimates when α 0.1. We also study eccentric binary orbits. We show that in this case resonances can occur at all harmonics of the orbital frequency, significantly extending the range of frequencies where cloud depletion may be observable with gravitational wave interferometers.

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Section: Acknowledgmentsmentioning

confidence: 99%

Ultralight boson cloud depletion in binary systems

et al. 2019

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“…We now consider the REDOR schemes more quantitatively using average Hamiltonian theory (AHT). [17][18][19][20] The first-order average Hamiltonian (H…”

Section: Theorymentioning

confidence: 99%

Measuring strong one-bond dipolar couplings using REDOR in magic-angle spinning solid-state NMR

Jain

Mote

Hellwagner

et al. 2019

The Journal of Chemical Physics

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1 Rotational-Echo DOuble Resonance, REDOR, is an experimentally robust and a well-established dipolar-recoupling technique to measure dipolar couplings between isolated pairs of spin-1/2 heteronuclei in solid-state Nuclear Magnetic Resonance (NMR). REDOR can also be used to estimate motional order parameters when the bond distance is known, for example, in the case of directly-bound nuclei. However, the relatively fast dipolar dephasing for strongly coupled spin-1/2 pairs, such as 13 C-1 H, makes the stroboscopic measurement required in this experiment challenging, even at fast Magic-Angle-Spinning (MAS) frequencies. In such cases, modified REDOR-based methods like Shifted-REDOR (S-REDOR) are used to scale the dipolar coupling compared to REDOR. This is achieved by changing the position of one of the two recoupling π-pulses in a rotor period. This feature, however, comes at the cost of mixing multiple Fourier components of the dipolar coupling and can, additionally, require high Radio-Frequency (RF) amplitudes to realise small scaling factors. We introduce here a general pulse scheme which involves shifting both the π pulses in the REDOR scheme to achieve arbitrary scaling factors whilst retaining the robustness and simplicity of REDOR recoupling and avoiding the disadvantages of S-REDOR. The classical REDOR is a specific case of this scheme with a scaling factor of one. We demonstrate the results on isolated 13 C-15 N and 1 H-13 C spin pairs at 20 and 62.5 kHz MAS, respectively.

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“…which is zero if the inversion is perfectly realized for an offset δ (we have in this case M z (δ, T ) = −1), and 2 if the spin is not excited at all. TF (or Interaction Frame) [45,51,52] is defined by a propagator whose dynamics are governed by H 0 only. In other words, it corresponds to a rotation matrix R 0 ∈ SO(3) which fulfills Ṙ0 = H 0 R 0 .…”

Section: The Model Systemmentioning

confidence: 99%

“…Analytical studies of the control of an ensemble of two-level quantum systems is much more difficult and requires in general some approximations to simplify the dynamics. For this purpose, Average Hamiltonian Theory (AHT) [44,45] uses a Magnus expansion to express the propagator. This expansion becomes extremely complicated above the second order, which limits the efficiency of this approach.…”

Section: Introductionmentioning

confidence: 99%

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Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Van Damme,

Sugny,

Glaser

2021

Preprint

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We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

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Introduction to average Hamiltonian theory. I. Basics

Cited by 42 publications

References 35 publications

Ultralight boson cloud depletion in binary systems

Ultralight boson cloud depletion in binary systems

Measuring strong one-bond dipolar couplings using REDOR in magic-angle spinning solid-state NMR

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

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