Artificial Coherent States of Light by Multiphoton Interference in a Single-Photon Stream

Coherent optical states consist of a quantum superposition of different photon number (Fock) states, but because they do not form an orthogonal basis, no photon number states can be obtained from it by linear optics. Here we demonstrate the reverse, by manipulating a random continuous single-photon stream using quantum interference in an optical Sagnac loop, we create engineered quantum states of light with tunable photon statistics, including approximate weak coherent states. We demonstrate this experimentally using a true single-photon stream produced by a semiconductor quantum dot in an optical microcavity, and show that we can obtain light with $g^{(2)}(0)\to 1$ in agreement with our theory, which can only be explained by quantum interference of at least 3 photons. The produced artificial light states are, however, much more complex than coherent states, containing quantum entanglement of photons, making them a resource for multiphoton entanglement.

Figure 1

Experimental setup. (a) Photons from the single-photon source (SPS) are diagonally polarized by WP1 before sent to the loop setup consisting of a polarizing beam splitter and half-wave plate WP2 at 22.5°. Light from the loop setup is analyzed with the polarization-resolved HBT setup. Panel (b) shows the interferometric loop length stabilization.

Figure 2

Characterization of the single-photon source (a) and loop setup (b), experimental data has been accumulated over 3 h; solid lines show the model calculations. In (a) the three-level model is fitted to the experimental $g_{VV}^{(2)}(\tau )$ data to obtain the single-photon source and detector parameters used throughout the Letter. Panel (b) shows $VH$ correlations between photons directly from the source and from the loop, confirming the validity of our model.

Figure 3

Photon correlations $g_{HH}^{(2)}(\tau )$ (symbols) for misaligned loop (a, $V\approx 0.03$, distinguishable photons) and aligned loop (b, $V\approx 0.9$, indistinguishable photons) compared to the model predictions (blue curves). Raw coincidence counts corresponding to $g_{HH}^{(2)}(\tau )=1$ were 880 (a) and 9700 (b). The green curves show the model results for the case without spectral diffusion.

Figure 4

Comparison of the photon number distribution of a weak coherent state (bars) and thermal state (through blue line) with same mean photon number $\overline{n}\approx 0.2$, to the results from our theoretical model (squares for the case of indistinguishable photons, $M=1$, and circles for the case of distinguishable photons, $M=0$). A fixed round-trip loss of 0.1 is included in both cases. The artificial state matches best to the weak coherent light state.

Figure 5

Experimental $g_{HH}^{(2)}(0)$ (black squares), corrected for dark state dynamics, compared to our theoretical expectations (blue line,convolved with IRF) as a function of the photon indistinguishability or wave-function overlap, expressed by the visibility $V$.Light with coherent photon statistics is obtained for $V\to 1$. The green line shows the expected results for detectors with perfect timing resolution. Results include a fixed round-trip loss of 0.1.