Classical Analogues of Two-Photon Quantum Interference

Chirped-pulse interferometry (CPI) captures the metrological advantages of quantum Hong-Ou-Mandel (HOM) interferometry in a completely classical system. Modified HOM interferometers are the basis for a number of seminal quantum-interference effects. Here, the corresponding modifications to CPI allow for the first observation of classical analogues to the HOM peak and quantum beating. They also allow a new classical technique for generating phase super-resolution exhibiting a coherence length dramatically longer than that of the laser light, analogous to increased two-photon coherence lengths in entangled states.

Figure 1

Two-photon interferometers and their time-reversed analogues. The three top figures show a schematic of the quantum interferometers used to observe (a) the HOM peak, (b) quantum beating (note the inclusion of two filters with different bandpasses), and (c) two-photon phase super-resolution. All of the interferometers rely on light created from spontaneous parametric down conversion (SPDC) in a nonlinear crystal. The interferograms correspond to the number of coincidence counts registered at a pair of photon counting detectors as a function of the path delay, $\Delta \tau$. The middle row of figures depict the time-reversed version of each quantum interferometer based on the recently described chirped-pulse interferometry [19]. These time-reversed interferometers were implemented as shown in the bottom row of the figures. Chirped (C) and antichirped (A) laser pulses with matched chirp rates are combined at the inputs of the interferometers. The light passes along the two arms of the interferometer, is recombined at a polarizing beam splitter (PBS), and is focused on a nonlinear crystal. High-pass filters (HP) remove the fundamental from the resulting sum-frequency generation (SFG). A narrow band of frequencies is filtered, via gratings and a slit, and detected via an amplified Si photodiode.

Figure 2

Phase-insensitive constructive interference in CPI. The system was set up as depicted in Fig. 1a (bottom) as the time-reversed version of the two-photon interferometer in Fig. 1a (top). In (b) the configuration was the same as in (a) except that we blocked $2.0\pm 0.3\mathrm{nm}$ near the center wavelength of the chirped pulses in the stretcher. Both plots show the measured photodiode signal as a function of delay. The data in (a) show a phase-insensitive interference peak with visibility $76\pm 2\%$ and FWHM $42\pm 2\mu \mathrm{m}$. The data in (b) show a peak with similar visibility and width, but with two new features where the signal drops at $+/-50\pm 4\mu \mathrm{m}$ by $20\pm 1\%$ of the plateau signal level.

Figure 3

“Quantum” beating in CPI. Filtering different spectral components of the chirped and antichirped input plays the same role in CPI as filtering different spectral components in the HOM interferometer shown in Fig. 1b (top). Measured interference patterns (a) and (c), and the corresponding spectra of the chirped (red or gray) and antichirped (blue or dark gray) beams (b) and (d), respectively, are shown. The measured fringe spacing is (a) $115\pm 15\mu \mathrm{m}$ and (c) $40\pm 2\mu \mathrm{m}$. This is in good agreement with theory where the fringe spacing is determined by the frequency difference between the chirped and antichirped spectra.

Figure 4

White-light interference pattern and phase super-resolution in CPI. (a) and (b) show the white-light interference pattern generated by the chirped pulse. (c) and (d) show the SFG signal detected in the modified CPI depicted in Fig. 1c (lower). By comparing (b) and (d) one can clearly see the reduction of the fringe wavelength in CPI; this is phase super-resolution. In addition, by comparing the signals in (a) and (c), we see that the CPI coherence length is roughly 80 times longer than the white-light coherence length.