Hong-Ou-Mandel two-photon x-ray states

Abstract

We have observed Hong-Ou-Mandel interference of high-brightness synchrotron x-rays with a Mach-Zehnder interferometer, yielding two-photon states of potential interest for x-ray quantum optics.

Figures (5)

• Figure 1: Hong--Ou--Mandel (HOM) interference. Left: A 50-50 beam splitter with indistinguishable incident photons produces either two photons exiting from one output port or two photons exiting from the other. The output wavefunction $\lvert \psi \rangle_{\mathrm{out}}$ is a coherent superposition of these two configurations. Right: Idealized plot of the coincidence rate for one photon exiting each output port, $(1,1)$, as a function of beam-splitter displacement $\Delta x$, showing the HOM dip. Also shown is the corresponding peak in the rate of two photons exiting from the same port, $(2,0)$ and $(0,2)$.
• Figure 2: Schematic of beamline optics. (a) Synchrotron radiation enters from the left through the white-beam slits and is monochromated by a high heat-load monochromator. That exit beam enters the high energy-resolution monochromator to reduce the band width. After another set of slits, the beam enters the Mach-Zehnder interferometer; the final splitter is where HOM interference can occur. Exit beams are detected by dual APDs. (b) HOM beamsplitter rocking curves for both detectors versus angular shift; arrow denotes location where each incident beam is equally reflected and transmitted.
• Figure 3: Raw count-rate data. (a) Histogram of avalanche photodiode (APD) detector output from 13 MHz synchrotron x-ray pulses; mean count per pulse is approximately unity. (b) After conversion of the APD outputs to integer values, each synchrotron pulse is represented by a pair of integers, e.g., $(1,1)$, $(2,0)$, or $(0,2)$. (c) Measured rates of $(1,1)$ pairs and of $(2,0)$,$(0,2)$ pairs as a function of beam-splitter displacement $\Delta x$, revealing a Hong--Ou--Mandel dip in the $(1,1)$ rate and a corresponding peak in the two-photon rate. Each data point is the average of five scans of 2 s duration, converted to units of Hz. A baseline shift of $+0.1\times10^{6}$ Hz has been applied to the raw $(1,1)$ data to facilitate comparison. The marker indicates the range of overlap between the beam splitter and the intersecting $\sim 80\times80~\mu\mathrm{m}^{2}$ beams.
• Figure 4: HOM interference. The $(1,1)$ and the $(2,0)$$\&$$(0,2)$ rates are plotted versus beamsplitter position $\Delta x$, revealing the HOM dip and peak.
• Figure 5: Intersection of overlapping x-ray beams. A HOM dip is observed when the beamsplitter samples the large diamond, where beam width $L_v$ is set by the vertical slit and is smaller than the lateral coherence length; $\Delta x$ indicates the direction of beamsplitter displacement. The smaller diamond is the overlap of the longitudinal coherence length of two simultaneous x-rays. Interference occurs even when the beamsplitter is outside this diamond, where the photons never overlap temporally.