René Heilmann

Experimental boson sampling

The boson-sampling problem is experimentally solved by implementing Aaronson and Arkhipovs model of computation with photons in integrated optical circuits. These results set a benchmark for a type of quantum computer that can potentially outperform a conventional computer by using only a few photons and linear optical elements.

Laser written circuits for quantum photonics

The femtosecond laser direct-writing (FLDW) of waveguide circuits in glasses has seen interest from a number of fields over the previous 20 years. It has evolved from a curiosity to a viable platform for the rapid prototyping of small scale circuits. The field of quantum information science has exploited this capability and in the process advanced the fabrication technique. In this review the technological aspects of the laser inscription method relevant to quantum information science will be discussed. A range of demonstrations which have been enabled by laser written circuits will be outlined; these include novel circuits, simulations, photon sources and detection. This places the FLDW technique among the few integrated optical platforms to have produced individually every component required for scalable quantum computation.

Generalized Multiphoton Quantum Interference

Non-classical interference of photons lies at the heart of optical quantum information processing. This effect is exploited in universal quantum gates as well as in purpose-built quantum computers that solve the BosonSampling problem. Although non-classical interference is often associated with perfectly indistinguishable photons this only represents the degenerate case, hard to achieve under realistic experimental conditions. Here we exploit tunable distinguishability to reveal the full spectrum of multi-photon non-classical interference. This we investigate in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis which decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers.

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices

Within all physical disciplines, it is accepted that wave transport is predetermined by the existence of disorder. In this vein, it is known that ballistic transport is possible only when a structure is ordered, and that disorder is crucial for diffusion or (Anderson-)localization to occur. As this commonly accepted picture is based on the very foundations of quantum mechanics where Hermiticity of the Hamiltonian is naturally assumed, the question arises whether these concepts of transport hold true within the more general context of non-Hermitian systems. Here we demonstrate theoretically and experimentally that in ordered time-independent -symmetric systems, which are symmetric under space-time reflection, wave transport can undergo a sudden change from ballistic to diffusive after a specific point in time. This transition as well as the diffusive transport in general is impossible in Hermitian systems in the absence of disorder. In contrast, we find that this transition depends only on the degree of dissipation.

Arbitrary photonic wave plate operations on chip: Realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits

Chip-based photonic quantum computing is an emerging technology that promises much speedup over conventional computers at small integration volumes. Particular interest is thereby given to polarisation-encoded photonic qubits, and many protocols have been developed for this encoding. However, arbitrary wave plate operation on chip are not available so far, preventing from the implementation of integrated universal quantum computing algorithms. In our work we close this gap and present Hadamard, Pauli-X, and rotation gates of high fidelity for photonic polarisation qubits on chip by employing a reorientation of the optical axis of birefringent waveguides. The optical axis of the birefringent waveguide is rotated due to the impact of an artificial stress field created by an additional modification close to the waveguide. By adjusting this length of the defect along the waveguide, the retardation between ordinary and extraordinary field components is precisely tunable including half-wave plate and quarter-wave plate operations. Our approach demonstrates the full range control of orientation and strength of the induced birefringence and thus allows arbitrary wave plate operations without affecting the degree of polarisation or introducing additional losses to the waveguides. The implemented gates are tested with classical and quantum light.

Enhancing coherent transport in a photonic network using controllable decoherence

Transport phenomena on a quantum scale appear in a variety of systems, ranging from photosynthetic complexes to engineered quantum devices. It has been predicted that the efficiency of coherent transport can be enhanced through dynamic interaction between the system and a noisy environment. We report an experimental simulation of environment-assisted coherent transport, using an engineered network of laser-written waveguides, with relative energies and inter-waveguide couplings tailored to yield the desired Hamiltonian. Controllable-strength decoherence is simulated by broadening the bandwidth of the input illumination, yielding a significant increase in transport efficiency relative to the narrowband case. We show integrated optics to be suitable for simulating specific target Hamiltonians as well as open quantum systems with controllable loss and decoherence.

Implementation of quantum and classical discrete fractional Fourier transforms

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Experimental observation of N00N state Bloch oscillations.

Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.

Direct measurement of second-order coupling in a waveguide lattice

We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes.

Ultraprecise phase manipulation in integrated photonic quantum circuits with generalized directional couplers

We present an innovative approach for ultra-precise phase manipulation in integrated photonic quantum circuits. To this end, we employ generalized directional couplers that utilize a detuning of the propagation constant in optical waveguides by the overlap of adjacent waveguide modes. We demonstrate our findings in experiments with classical as well as quantum light.