On-Chip Generation and Collectively Coherent Control of the Superposition of the Whole Family of Dicke States

Integrated quantum photonics has recently emerged as a powerful platform for generating, manipulating, and detecting entangled photons. Multipartite entangled states lie at the heart of the quantum physics and are the key enabling resources for scalable quantum information processing. Dicke state is an important class of genuinely entangled state, which has been systematically studied in the light-matter interactions, quantum state engineering, and quantum metrology. Here, by using a silicon photonic chip, we report the generation and collectively coherent control of the entire family of four-photon Dicke states, i.e., with arbitrary excitations. We generate four entangled photons from two microresonators and coherently control them in a linear-optic quantum circuit, in which the nonlinear and linear processing are achieved in a chip-scale device. The generated photons are in telecom band, which lays the groundwork for large-scale photonic quantum technologies for multiparty networking and metrology.

Figure 1

Concept of multiphoton entanglement creation and control. (a) Tunable entangled photon pair generation. A qubit-pair module, consisting of two photon-pair sources (S1 and S2), is coherently pumped. The generated photons are then controlled and combined with beam splitters. The generated quantum state is an entangled two-qubit state after interference on the network, as shown in Eq. (2). This state is then analyzed by universal qubit analyzers (Us) for implementing arbitrary local projective measurements. (b) Tunable entangled four-photon generation. The sources generate two pairs of photons simultaneously. The detections in four detectors result in the generation of the superposition of the whole family of four-photon Dicke states, as shown in Eq. (3). For both the two-photon state and the four-photon state, the phase shift $\varphi$ can control all photons coherently and adjust the weights of the respective states.

Figure 2

Device description and experimental setup. (a) Photograph of the silicon photonic chip. Important on-chip elements are labeled: two DMZI-ring photon-pair sources (S1 and S2), multimode interference devices (MMIs), universal qubit analyzers (Us), and the phase shifter for coherent control ($\varphi$). (b) Experimental setup for generating and characterizing the whole family of Dicke states. Two photon pairs are created. Each pair is in a superposition between two coherently pumped DMZI-ring sources (S1 and S2), and routed by a linear optical network of MMIs to four Us, which are composed of 8 MMIs and 8 phase shifters (PSs). All photons are then coupled out from the chip, filtered, and detected by 8 grating couplers, filters, and superconducting nanowire single-photon detectors (not shown). All on-chip PSs are controlled with current sources. (c) Two different pump photons (1557.0 nm and 1544.9 nm) generate two identical photons (1550.9 nm) via nondegenerate SFWM process. (d) Dual-color pulse pumping setup to generate degenerate photon pair. A picosecond pump pulse is compressed to increase the bandwidth to over 20 nm, then selected by a wave shaper and amplified by an erbium-doped fiber amplifier (EDFA). After synchronized by WDMs and a tunable optical delay line, two color pulses are coupled into the chip. (e) Twofold coincidence counts between detectors A0 and B1 (corresponding to the projection onto $|{\mathrm{\Psi }}^{+}⟩$, $\mathrm{visibility}=95.67\%\pm 0.26\%$, purple) and A0 and B0 (corresponding to the projection onto $|{\mathrm{\Phi }}^{-}⟩$, $\mathrm{visibility}=93.42\%\pm 0.32\%$, green) show the high-quality coherent control of two-photon states, $|{\mathrm{\Psi }}_2(\varphi )⟩$. (f) All 28 possible two-photon interference visibilities show the high quality and high homogeneity of our work. The average measured visibilities are $95.87\%\pm 0.07\%$ for $|{\mathrm{\Psi }}^{+}⟩$ (purple) and $93.76\%\pm 0.09\%$ for $|{\mathrm{\Phi }}^{-}⟩$ (green). Uncertainties are derived from Poissonian statistics and error propagation.

Figure 3

Real part of the density matrix for different states. (a) The symmetric Dicke state $|D_4^2⟩$ by setting $\varphi =0$. (b) The superposition of four-photon GHZ state $|GH{Z}_4⟩$ and symmetric Dicke state $|D_4^2⟩$ by setting $\varphi =\pi /2$. The experimentally obtained quantum-state fidelities are $0.817\pm 0.003$ for $|\mathrm{\Psi }(0)⟩$ and $0.829\pm 0.003$ for $|\mathrm{\Psi }(\pi /2)⟩$, respectively. The ideal density matrix for $|\mathrm{\Psi }(0)⟩$ and $|\mathrm{\Psi }(\pi /2)⟩$ are shown in (c) and (d), respectively. Uncertainties are obtained from 100 Monte Carlo simulations with counting Poisson statistics.

Figure 4

Collectively coherent control of the four-photon state. (a),(b) The expected ideal and experimentally measured coincidence distributions for photons measured in the mutually unbiased basis of $\{|L⟩,|R⟩\}$. The distributions remain constant independently of the relative phase $\varphi$. (c),(d) The ideal and experimental cases for photons measured in the computational basis of $\{|0⟩,|1⟩\}$. The relative pump phase $\varphi$ rotates the whole family of Dicke state coherently.