Tunable Subluminal Propagation of Narrow-band X-Ray Pulses

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Subluminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}\mathrm{Fe}$ Mössbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.

Figure 1

Concept of the experiment: A single line absorber (SLA), mounted on a Doppler drive, imprints an absorption band on the broadband SR pulse, effectively generating a spectrally narrow x-ray pulse (SNXP) plus an unscattered constant contribution. Next, the x ray is reflected off of a thin-film cavity containing near-resonant nuclei. The nuclei imprint a spectral dispersion onto the pulse, which results in a temporal delay. Detuning the SNXP frequency via Doppler shifts allows one to tune the pulse delay. The polarimeter around the cavity blocks the constant offset of nonresonant background photons such that neither mechanical chopper nor a high-resolution monochromator for the SR are required. The residual signal of the unscattered constant contribution, which interacted with the cavity and passed the polarimeter is filtered out by variable a posteriori time gating (red shaded area). The delay of the SNXP is most clearly visible in comparing the beating minima in the time domain. The lower panels depict the frequency- and time-resolved amplitude of the field, and the two curves in the bottom right panels show the pulse with and without the induced delay $\tau$. In the experiment, the SLA was placed behind the analyzer (see main text).

Figure 2

(a) Photon counts as a function of time and Doppler detuning of the single line analyzer. Black pixels mark zero counts in the experiment. White dashed lines indicate theoretical predictions for beating minima positions without pulse delay. Solid white curves show corresponding predictions including the pulse delay. The additional oscillatory structure superimposing the data is due to photons $R_{\mathrm{NI}}(t)$. The bleached area $t\le 50\mathrm{ns}$ contains mostly data from $R_{\mathrm{NI}}(t)$ and is excluded from the data analysis, whereas times $t>50\mathrm{ns}$ contain mostly the desired $R_{\mathrm{SNXP}}(t)$. (b) Sections through (a) at constant detuning ${\mathrm{\Delta }}_D$. Close to resonance ${\mathrm{\Delta }}_D\approx 0$, the temporal response is clearly shifted compared to the off-resonant case. For example, the minimum at $t\approx 60\mathrm{ns}$ is shifted to later times as indicated by the arrow. Solid lines are theoretical predictions for the pulse part $R_{\mathrm{SNXP}}$ only, which is expected to deviate from the experimental data at initial times due to the omission of $R_{\mathrm{NI}}(t)$.

Figure 3

Time delay for the SNXP as a function of the detuning ${\mathrm{\Delta }}_D$ between SNXP and the nuclear resonance. Red dots show the delay extracted from the experimental data. The blue solid curve shows the corresponding theoretical prediction. Error bars are described in the Supplemental Material [28].