Conditions for two-photon interference with coherent pulses

We study the conditions for two-photon classical interference with coherent pulses. We find that the temporal overlap between optical pulses is not required for interference. However, coherence within the same inputs is found to be essential for the interference.

Figure 1

The schematic of Hong-Ou-Mandel interference with four weak coherent pulses.

Figure 2

Feynman diagrams for $\Delta l=0$. In general, all cases (a)–(d) are distinguishable, so they do not interfere. However, when pulses in the same inputs (between $a_i$ and $a_j$, for example) are coherent, (a) and (b) become indistinguishable, so they interfere. For single-photon pulses, one can effectively suppress (c) and (d) while maintaining the coherence, so one can measure a $V=1$ HOM dip with temporally nonoverlapping pulses. For classical optical pulses such as coherent states, however, one cannot remove cases (c) and (d) without disturbing the coherence, so the maximum visibility is limited to 0.5.

Figure 3

Experimental setup. BS: beam splitter; AOM: acousto-optic modulator; FPC: fiber polarization controller; FBS: fiber beamsplitter; D1 and D2: single photon detectors. The AOMs are used for the phase randomization between two arms.

Figure 4

Single and coincidence counts for various conditions. Single and coincidence counts are proportional to $\langle I_C\rangle$ ($\langle I_D\rangle$) and $\langle I_C{I}_D\rangle$, respectively. Error bars are the experimentally obtained standard deviations. The single counts when RF signals to AOM1 and AOM2 are (a) synchronized and (b) independent. The inset of (a) shows the envelope of the single-photon interference. (c)–(f) Coincidence counts between D1 and D2. (c) ${\tau }_d=0$. (d) ${\tau }_d=212\mathrm{n}\mathrm{s}$. (e),(f) ${\tau }_d=0$ and ${\tau }_d=212\mathrm{n}\mathrm{s}$ with an additional noise input to the FM input of the RF driver to AOM1. Estimated visibilities are also shown. (c) and (e) correspond to a HOM interference with classical pulses so a standard HOM dip is observed. (d) and (f) correspond to the two-photon interference between temporally nonoverlapping optical pulses.