Defying Conventional Wisdom in Spectroscopy: Power Narrowing on IBM Quantum

Abstract

Power broadening $-$ the broadening of the spectral line profile of a two-state quantum transition as the amplitude of the driving field increases $-$ is a well-known and thoroughly examined phenomenon in spectroscopy. It typically occurs in continuous-wave driving when the intensity of the radiation field increases beyond the saturation intensity of the transition. In pulsed-field excitation, linear power broadening occurs for a pulse of rectangular temporal shape. Pulses with smooth shapes are known to exhibit much less power broadening, e.g. logarithmic for a Gaussian pulse shape. It has been predicted, but never experimentally verified, that pulse shapes which vanish in time as $\sim |t|^{-λ}$ should exhibit the opposite effect $-$ power narrowing $-$ in which the post-pulse transition line width decreases as the amplitude of the driving pulse increases. In this work, power narrowing is demonstrated experimentally for a class of powers-of-Lorentzian pulse shapes on the IBM Quantum processor ibmq_manila. Reduction of the line width by a factor of over 10 is observed when increasing the pulse area from $π$ to $7π$, in a complete reversal of the power broadening paradigm. Moreover, thorough theoretical and experimental study is conducted on the truncation of the pulse wings which introduces a (small) power-broadened term which prevents power narrowing from reaching extreme values $-$ a hitherto unknown cut-off broadening effect for which an explicit analytical formula is derived. In the absence of other power broadening mechanisms, Lorentzian pulses truncated at sufficiently small values can achieve as narrow line profiles as desired.

Figures (5)

• Figure 1: Left: A typical spectral profile of the post-pulse transition probability between two quantum states. The width of the spectral line profile is determined by the detuning range wherein the adiabatic condition is violated. Right: Qualitative behavior of the transition probability excitation landscape vs detuning and peak Rabi frequency (on a color map). The dashed lines depict the limits on the spectral line width induced by the power narrowing effect due to the Lorentzian pulse shape. The area between the dotted lines show the power broadened contribution due to the truncation of the pulse wings.
• Figure 2: Excitation landscapes (transition probability vs detuning $\Delta$ and peak Rabi frequency $\Omega_0$) of a Lorentzian pulse truncated at the cut-off points $\pm t_c$, at which the pulse amplitude value $\Omega_c = \Omega_0 f(t_c)$ is a fraction of its maximum value $\Omega_0$, indicated in each frame.
• Figure 3: Excitation landscapes (transition probability vs detuning $\Delta$ and peak Rabi frequency $\Omega_0$) of different pulse shapes $L^n(t)$, with the power $n$ listed in each plot.
• Figure 4: The transition probability vs detuning for 6 different pulse shapes $L^n(t)$. The data points are fitted with a function that is a sum of a hyperbolic secant and a Lorentzian.
• Figure 5: Off-resonant Rabi oscillations of 6 Lorentzian-based pulses. The 6 plots are vertical slices of the colour maps in Fig. \ref{['fig-narrowing-2d']} at $\Delta = 30$, $25$, $12.5$, $12.5$, $12.5$ and $12.5$ MHz for the $n=2$, $3/2$, $1$, $3/4$, $2/3$ and $3/5$ Lorentzian pulses respectively, labelled in the upper-right corner of each plot.