Observation of Power Superbroadening of Spectral Line Profiles on IBM Quantum

TL;DR

The paper addresses controlling spectral linewidth in driven two-state systems by engineering the drive envelope to exceed conventional power broadening, building on prior observations of power narrowing for Lorentzian pulses. It introduces two envelope families—orientation-changing quadratic and power-law pulses—that achieve power superbroadening while preserving the same pulse area $\mathcal{A}=\pi$, and supports the approach with adiabatic/superadiabatic analysis and IBM Quantum hardware demonstrations. Key findings show up to about a $3.3\times$ increase in linewidth for the quadratic family (e.g., $\beta=1$) and pronounced Ramsey-like interference patterns with power-law pulses up to $P=3$, explained by the SA framework in terms of mid-pulse curvature and zeros. The work provides practical, hardware-amenable pulse-shaping strategies to amplify off-resonant transitions and enhance quantum control and spectroscopy tasks in noisy or detuned regimes.

Abstract

Power broadening refers to the widening of the spectral line profile in a two-state quantum transition as the strength of the driving field increases. This phenomenon commonly arises in continuous-wave driving when the radiation field's intensity exceeds the transition's saturation intensity and it has been extensively studied in spectroscopy. For pulsed-field excitation, the spectral response of the quantum system may differ significantly: while a rectangular-shaped pulse leads to a linear power broadening, pulses with smooth shapes show significantly reduced power broadening, for instance, logarithmic for the Gaussian shape and none for the hyperbolic-secant shape. Recently [Phys. Rev. Lett. 132, 020802 (2024)], in a dramatic paradigm shift, we have demonstrated experimentally that for Lorentzian-shaped pulses, the opposite effect - power narrowing - takes place: the width of the spectral profile decreases when the driving pulse amplitude increases, with a narrowing factor of as much as 10 observed. While in high-resolution spectroscopy the push is for eliminating or even inverting the power broadening, there are applications where it is used to an advantage for it facilitates off-resonance excitation. Here, we present a number of shaped pulses that exhibit power broadening much greater than that of the rectangular pulse of the same pulse area. They are grouped in two families of pulse shapes. In particular, in regard to the width of the second Rabi oscillation maximum, the quadratic pulse family shows an increase by a factor of 3.3 whereas the even-exponent pulse family exhibits an increase by a factor of more than 3.5.

Figures (3)

• Figure 1: [Color online] Super-nonadiabatic coupling (dot-dashed curves) and superadiabatic energy splitting (dashed curves) for three drive envelopes (solid curves), shown left-to-right: (i) quadratic pulse with $\beta = –1$ (see Eq. \ref{['eq-fcquadratic']}), (ii) quadratic pulse with $\beta = +1$ (see Eq. \ref{['eq-fcquadratic']}), and (iii) power-law pulse with $P = 3$ (see Eq. \ref{['eq-evenexp']}). All traces share the same time axis and peak Rabi amplitude, allowing a direct comparison of how the sign of $\beta$ and the power-law exponent $P$ modify the nonadiabatic region near the pulse center.
• Figure 2: [Color online] Top: Quadratic pulse envelopes $\Omega(t)$ for $\beta\in\{-1,0,0.25,0.5,0.75,1\}$ at fixed duration. Bottom: Final excited-state population $P_2(T)$ versus detuning $\Delta/2\pi$ (x-axis) and Rabi amplitude $\Omega_0/2\pi$ (y-axis, $\propto \sqrt{\text{power}}$). The operational linewidth is defined as the full excitation width in $\Delta$ of the second Rabi maximum. Increasing $\beta$ enhances nonadiabatic coupling near the pulse midpoint (see Fig. \ref{['fig:superadb']}), yielding pronounced power superbroadening relative to the rectangular case ($\beta=0$).
• Figure 3: [Color online] Top: Power-law pulse envelopes $\Omega(t)$ with a mid-pulse pit of tunable width for $P=0,1,2,3$ (rectangular pulse at $P=0$). Bottom: Excitation landscapes. For $P>0$ the two horns act as Ramsey-like $\pi/2$ drives separated by a dark interval, yielding near-vertical interference fringes off-resonance. The pronounced increase of the operational linewidth is an indicator of power superbroadening for growing area.