Observation of Four-Photon Orbital Angular Momentum Entanglement

We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.

Figure 1

Experimental implementation. A frequency-doubled (sum frequency generation, SFG) mode-locked picosecond laser is short-pass filtered (SPF) and focused (L1) into the PPKTP crystal. The SPDC photons are spectrally filtered with a GaP plate and a bandpass filter (BPF), and distributed with beam splitters (BSs) to the four equal detection units. The crystal facet is imaged with a telescope (L2 and L3) onto the spatial light modulators (SLMs), which in turn is far-field imaged onto the core of the detection single mode fibers connected to single photon counters. The pinhole (PH) selects the 1st diffraction order of the SLM holograms. We explore the four-photon transverse-mode space by changing the holograms on the SLMs and recording fourfold coincidence events with a multichannel time tagging computer card.

Figure 2

Four-photon OAM state production. Pump-power dependent single-photon count rate (a),(b) and fourfold coincidence rate (c),(d), for various combinations of the detection transverse modes $\{G,H,V,L,R\}$. The single rates depend linearly on pump power, while the fourfold coincidence rates show quadratic dependency. The comparison between zero time delay (a),(c) and the case where photon 3 and 4 are delayed by 12.5 ns shows that most detected four-photon detection events are indeed due to four photons that were produced within a single pump pulse.

Figure 3

Four-photon OAM correlations. Four-photon joint detection probabilities in each of the three mutually unbiased bases: (a) Hermite Gauss $\{H,V\}$, (b) diagonal Hermite Gauss $\{D,A\}$, and (c) Laguerre Gauss $\{R,L\}$. Labels indicate the phase and amplitude structure of the detected spatial modes. Gray bars: experimental data; the error bars show statistical errors. Boxes: theory. The experimental integration time per data point was 24 min. The probabilities are normalized to unity within each basis.

Figure 4

The reconstructed OAM quantum state. Modulus of the reconstructed experimental (a) and theoretical (b) density matrix (vertical axis scale $[0,0.3]$). The discrepancy between experiment and theory is mainly caused by residual misalignment of the transverse-mode detectors.