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Linear optics underpins tests of fundamental quantum mechanics and computer science, as well as quantum technologies. Here we experimentally demonstrate the longstanding goal of a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of that circuit. Our six-mode universal system consists of a cascade of 15 Mach-Zehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons and their measurement with a 12 single-photon detector system. We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards. We implemented 100 Haar random unitaries with average fidelity 0.999 $pm$ 0.001. Our system is capable of switching between these and any other linear optical protocol in seconds. These results point the way to applications across fundamental science and quantum technologies.
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We present modular and optimal architectures for implementing arbitrary discrete unitary transformations on light. These architectures are based on systematically combining smaller M-mode linear optical interferometers together to implement a larger N-mode transformation. Thus this work enables the implementation of large linear optical transformations using smaller modules that act on the spatial or the internal degrees of freedom of light such as polarization, time or orbital angular momentum. The architectures lead to a rectangular gate structure, which is optimal in the sense that realizing arbitrary transformations on these architectures needs a minimal number of optical elements and minimal circuit depth. Moreover, the rectangular structure ensures that each the different optical modes incur balanced optical losses, so the architectures promise substantially enhanced process fidelities as compared to existing schemes.
We introduce a constructive algorithm for universal linear electromagnetic transformations between the $N$ input and $N$ output modes of a dielectric slab. The approach uses out-of-plane phase modulation programmed down to $N^2$ degrees of freedom. The total area of these modulators equals that of the entire slab: our scheme satisfies the minimum area constraint for programmable linear optical transformations. We also present error correction schemes that enable high-fidelity unitary transformations at large $N$. This ``programmable multimode interferometer (ProMMI) thus translates the algorithmic simplicity of Mach-Zehnder meshes into a holographically programmed slab, yielding DoF-limited compactness and error tolerance while eliminating the dominant sidewall-related optical losses and directional-coupler-related patterning challenges.
We show how to implement several continuous-variable coherent protocols with linear optics. Noise can accumulate when implementing each coherent protocol with realistic optical devices. Our analysis bounds the level of noise accumulation. We highlight the connection between a coherent channel and a nonlocal quantum nondemolition interaction and give two new protocols that implement a coherent channel. One protocol is superior to a previous method for a nonlocal quantum nondemolition interaction because it requires fewer communication resources. We then show how continuous-variable coherent superdense coding implements two nonlocal quantum nondemolition interactions with a quantum channel and bipartite entanglement. We finally show how to implement continuous-variable coherent teleportation experimentally and provide a way to verify the correctness of its operation.
The study of non-equilibrium physics from the perspective of the quantum limits of thermodynamics and fluctuation relations can be experimentally addressed with linear optical systems. We discuss recent experimental investigations in this scenario and present new proposed schemes and the potential advances they could bring to the field.
We show theoretically that two atomic dipoles in a resonator constitute a non-linear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics could be observed as a result of self-organization of laser-cooled atoms in resonators.
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