The mapping of photonic states to collective excitations of atomic ensembles is a powerful tool which finds a useful application in the realization of quantum memories and quantum repeaters. In this work we show that cold atoms in optical lattices can be used to perform an entangling unitary operation on the transferred atomic excitations. After the release of the quantum atomic state, our protocol results in a deterministic two qubit gate for photons. The proposed scheme is feasible with current experimental techniques and robust against the dominant sources of noise.
Information processing with light is ubiquitous, from communication, metrology and imaging to computing. When we consider light as a quantum mechanical object, new ways of information processing become possible. In this review I give an overview how quantum information processing can be implemented with single photons, and what hurdles still need to be overcome to implement the various applications in practice. I will place special emphasis on the quantum mechanical properties of light that make it different from classical light, and how these properties relate to quantum information processin…
We show that Bragg diffraction may be modeled by classical light propagation in photonic lattices having a square power law for the refraction index coefficient. The dynamics is shown to be fully integrable and therefore described in closed form. We examine the trajectories of classical light propagating in such structures.
All-optical photonic devices are crucial for many important photonic technology and applications, ranging from optical communication to quantum information processing. Conventional design of all-optical devices is based on photon propagation and interference in real space, which may reply on large numbers of optical elements and are challenging for precise control. Here we propose a new route for engineering all-optical devices using photon internal degrees of freedom, which form photonic crystals in such synthetic dimensions for photon propagation and interference. We demonstrate this new des…
Characterising the input-output photon-number distribution of an unknown optical quantum channel is an important task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work-in-progress. In this work, we propose a general method to rigorously bound the input-output photon number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors/homodyne detectors. To demonstr…
Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field…
By virtue of a silicon high-Q photonic crystal nanocavity, we propose and examine theoretically interactions between a stationary electron spin qubit of a semiconductor nanocrystal and a flying photon qubit. Firstly, we introduce, derive and demonstrate for the first time the explicit conditions towards realization of a spin-photon two-qubit phase gate, and propose these interactions as a generalized quantum interface for quantum information processing. Secondly, we examine novel single-spin-induced reflections as direct evidence of intrinsic bare and dressed modes in our coupled nanocrystal-c…
Integrated optics is an engineering solution proposed for exquisite control of photonic quantum information. Here we use silicon photonics and the linear combination of quantum operators scheme to realise a fully programmable two-qubit quantum processor. The device is fabricated with readily available CMOS based processing and comprises four nonlinear photon-sources, four filters, eighty-two beam splitters and fifty-eight individually addressable phase shifters. To demonstrate performance, we programmed the device to implement ninety-eight various two-qubit unitary operations (with average qua…
Rotation-induced splitting of the otherwise degenerate photonic bands is predicted for a two-dimensional photonic crystal made of evanescently coupled microcavities. The symmetry-broken energy splitting is similar to the Zeeman splitting of atomic levels or electron's (hole's) magnetic moment sublevels in an external magnetic field. The orbital motion of photons in periodic photonic lattice of microcavities is shown to enhance significantly such Coriolis-Zeeman splitting as compared to a solitary microcavity [D.L. Boiko, Optics Express 2, 397 (1998)]. The equation of motion suggests that nonst…
The analytic specifications of photonic lattices with fractional revival (FR) and perfect state transfer (PST) are reviewed. The approach to their design which is based on orthogonal polynomials is highlighted. A compendium of analytic models with PST is offered. New results on their FR properties are included. The nearest-neighbour approximation is adopted in most of the review; one analytic example with next-to-nearest neighbour interactions is also presented.
Optical lattice loaded with cold atoms can exhibit a tunable photonic band gap for a weak probe field under the conditions of electromagnetically induced transparency. This system possesses a number of advantageous properties, including reduced relaxation of Raman coherence and the associated probe absorption, and simultaneous enhancement of the index modulation and the resulting reflectivity of the medium. This flexible system has a potential to serve as a testbed of various designs for the linear and nonlinear photonic band gap materials at a very low light level and can be employed for real…
We show that the two-photon transition rates of quantum dots coupled to nanocavities are enhanced by up to 8 orders of magnitude relative to quantum dots in bulk host. We then propose how to take advantage of this enhancement to implement coherent quantum dot excitation by two-photon absorption, entangled photon pair generation by two-photon spontaneous emission, and single-photon generation at telecommunication wavelengths by two-photon stimulated and spontaneous emission.
We propose the implementation of a light source, which can deterministically generate a rich variety of multi-mode quantum states. The desired states are encoded in the collective population of different ground hyperfine states of an atomic ensemble and converted to multi-mode photonic states by excitation to optically excited levels followed by cooperative spontaneous emission. Among our examples of applications, we demonstrate how two-photon entangled states can be prepared and implemented in a protocol for reference frame free quantum key distribution and how one-dimensional as well as high…
We report the study of non-classical light in a photonic lattice having parabolic coupling distribution, also known as Jx photonic lattice. We focus on two photon Fock state, two photon N00N state, and single mode squeezed state along with coherent state as input to the lattice. We investigate the possibility of perfect transfer of mean photon number as well as quantum state from one waveguide mode to other. We study photon-photon correlation for two photon N00N state. For single mode squeezed state we study in detail, the evolution of squeezing factor and entanglement between the waveguide mo…
We demonstrate two key components for optical quantum information processing: a bright source of heralded single photons; and a bright source of entangled photon pairs. A pair of pump photons produces a correlated pair of photons at widely spaced wavelengths (583 nm and 900 nm), via a $χ^{(3)}$ four-wave mixing process. We demonstrate a non-classical interference between heralded photons from independent sources with a visibility of 95%, and an entangled photon pair source, with a fidelity of 89% with a Bell state.
We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where self-energies or couplings are alternated. For didactic reasons, we split the analysis in classical propagation and quantum transport but all methods can be implemented, mutatis mutandis, in any given case. On the classical side, we use coupled mode theory and present an operator approach to Floquet-Bloch theory in order to study the propagation of a classical electroma…
Recirculating Quantum Photonic Networks for Fast Deterministic Quantum Information Processing
DTU Electro, Technical University of Denmark（丹麦技术大学电气工程系）；NanoPhoton - Center for Nanophotonics, Technical University of Denmark（丹麦技术大学纳米光子学中心）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气工程和计算机科学系）
Photonic processors are pivotal for both quantum and classical information processing tasks using light. In particular, linear optical quantum information processing requires both largescale and low-loss programmable photonic processors. In this paper, we report the demonstration of the largest universal quantum photonic processor to date: a low-loss, 12-mode fully tunable linear interferometer with all-to-all coupling based on stoichiometric silicon nitride waveguides.
We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic bandgap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit none, double or multiple photonic bandgaps depending on the ratio between the interparticle distance $\varrho$ inside the cell and the cell size $a$. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in f…
We investigate the properties of parity-time symmetric periodic photonic structures using Heesh-Shubnikov group theory. Classical group theory cannot be used to categorize the symmetry of the eigenmodes because the time-inversion operator is antiunitary. Fortunately, corepresentations of Heesh-Shubnikov groups have been developed to characterize the effect of antiunitary operators on eigenfunctions. Using the example structure of a one-dimensional photonic lattice, we identify the corepresentations of eigenmodes at both low and high symmetry points in the photonic band diagram. We find that th…
We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local PT symmetries. Such PT structure is introduced via a judicious arrangement of gain or loss across the honeycomb lattice, characterized by a gain/loss parameter γ. We found a new class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to Sqrt (γ).
We experimentally demonstrate the photonic realization of a dispersionless flat-band in a quasi-one-dimensional photonic lattice fabricated by ultrafast laser inscription. In the nearest neighbor tight binding approximation, the lattice supports two dispersive and a non-dispersive (flat) band. We experimentally excite superpositions of flat-band eigen modes at the input of the photonic lattice and show the diffractionless propagation of the input states due to their infinite effective mass. In the future, the use of photonic rhombic lattices, together with the successful implementation of a sy…
We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal polynomials. We present propagation examples of non-classical states of light: single photon, coherent state, path-entangled state and two-mode squeezed vacuum impinging into two-waveguide couplers and a photonic lattice producing coherent transport.
The single photon occupation of a localized field mode within an engineered network of defects in a photonic band-gap (PBG) material is proposed as a unit of quantum information (qubit). Qubit operations are mediated by optically-excited atoms interacting with these localized states of light as the atoms traverse the connected void network of the PBG structure. We describe conditions under which this system can have independent qubits with controllable interactions and very low decoherence, as required for quantum computation.
We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator where the mass and frequency depend on the propagation distance. In these photonic lattices refractive indices and second neighbor couplings define the mass and frequency of the analog quantum oscillator, while first neighbor couplings are a free parameter to adjust the model. The quantum model conserves the Ermakov-Lewis invariant, thus the photonic crystal also posses this symmetry.
We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the quantum optical analogy. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1,1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.
We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large and strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation
The quantum version of Google PageRank has recently been investigated by various groups and shown to be quadratically faster in time than the classical PageRank algorithm. In this paper we propose the implementation of Quantum PageRank by a stochastic quantum walk of correlated photons in a photonic waveguide lattice, where we allow the density matrix to evolve according to the Lindblad-Kossakowski master equation. This yields a stationary state, the diagonal of whose density matrix gives the page ranking.
A method for realizing asymmetric (one-way) transmission of discretized light in modulated, linear and purely passive optical lattices is suggested, which exploits the idea of unidirectional coherent perfect absorption. The system consists of a linear photonic lattice of coupled resonators or waveguides, side coupled to a chain of lossy elements, in which light can avoid the occupation of the dissipative sites when propagating in one way, but not in the opposite one. Non-reciprocity requires modulation of the resonator/waveguide parameters, realizing a dissipative optical Aharonov-Bohm diode w…
We extend the idea of quantum phase transitions of light in the photonic Bose-Hubbard model with interactions to two atomic species by a self-consistent mean field theory. The excitation of two-level atoms interacting with coherent photon fields is analyzed with a finite temperature dependence of the order parameters. Four ground states of the system are found, including an isolated Mott-insulator phase and three different superfluid phases. Like two weakly coupled superconductors, our proposed dual-species lattice system shows a photonic analogue of Josephson effect. The dynamics of the propo…
The polarisation of light is a powerful and widely used degree of freedom to encode information, both in classical and quantum applications. In particular, quantum information technologies based on photons are being revolutionised by the use of integrated photonic circuits. It is therefore very important to be able to manipulate the polarisation of photons in such circuits. We experimentally demonstrate the fabrication by femtosecond laser micromachining of components such as polarisation insensitive or polarising directional couplers, operating at 1550 nm wavelength, where the two opposite be…
Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactio…
In this article we use the method of shortcuts to adiabaticity to design a photonic lattice (array of waveguides) which can drive the input light to a controlled location at the output. The output position in the array is determined by functions of the propagation distance along the waveguides, which modulate the lattice characteristics (index of refraction, first and second neighbor couplings). The proposed coupler is expected to posses the robustness properties of the design method, coming from its adiabatic nature, and also to have a smaller footprint than purely adiabatic couplers. The pre…
Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as "time," accessing long timescales constitutes a severe experimental challenge. Here, we overcome this limitation by placing the photonic lattice in a cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon detector array, offers quasi-real time-resolve…
In this Letter, we propose a new approach to process high-dimensional quantum information encoded in a photon frequency domain. In contrast to previous approaches based on nonlinear optical processes, no active control of photon energy is required. Arbitrary unitary transformation and projection measurement can be realized with passive photonic circuits and time-resolving detection. A systematic circuit design for a quantum frequency comb with arbitrary size has been given. The criteria to verify quantum frequency correlation has been derived. By considering the practical condition of detector…
The development of large-scale optical quantum information processing circuits ground on the stability and reconfigurability enabled by integrated photonics. We demonstrate a reconfigurable 8x8 integrated linear optical network based on silicon nitride waveguides for quantum information processing. Our processor implements a novel optical architecture enabling any arbitrary linear transformation and constitutes the largest programmable circuit reported so far on this platform. We validate a variety of photonic quantum information processing primitives, in the form of Hong-Ou-Mandel interferenc…
We present a photonic integrated circuit architecture for a quantum programmable gate array (QPGA) capable of preparing arbitrary quantum states and operators. The architecture consists of a lattice of phase-modulated Mach-Zehnder interferometers, which perform rotations on path-encoded photonic qubits, and embedded quantum emitters, which use a two-photon scattering process to implement a deterministic controlled-$σ_z$ operation between adjacent qubits. By appropriately setting phase shifts within the lattice, the device can be programmed to implement any quantum circuit without hardware modi…
Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves th…
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on …
Photonic lattices are usually considered to be limited by their lack of methods to include interactions. We address this issue by introducing mean-field interactions through optical components which are external to the photonic lattice. The proposed technique to realise mean-field interacting photonic lattices relies on a Suzuki-Trotter decomposition of the unitary evolution for the full Hamiltonian. The technique realises the dynamics in an analogous way to that of a step-wise numerical implementation of quantum dynamics, in the spirit of digital quantum simulation. It is a very versatile tec…
We study the interaction of a Bose-Einstein condensate, which is confined in an optical lattice, with a largely detuned light field propagating through the condensate. If the condensate is in its ground state it acts as a periodic dielectric and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice-atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calcu…
We report measurements of Hanbury Brown and Twiss correlation of coherent light transmitted through disordered one-dimensional photonic lattices. Although such a lattice exhibits transverse Anderson localization when a single input site is excited, uniform excitation precludes its observation. By examining the Hanbury Brown--Twiss correlation for a uniformly excited disordered lattice, we observe intensity anticorrelations associated with photon antibunching--a signature of non-Gaussian statistics. Although the measured average intensity distribution is uniform, transverse Anderson localizatio…
We observe Wannier-Stark localization in curved photonic lattices, realized using arrays of evanescently coupled optical waveguides. By correctly tuning the strength of inter-site coupling in the lattice, we observe that Wannier-Stark states become increasingly localized, and eventually fully localized to one site, as the curvature of the lattice is increased. We then demonstrate that tunneling can be successfully restored in the lattice by applying a sinusoidal modulation to the lattice position, an effect that is a direct analogue of photon-assisted tunneling. This precise tuning of the tunn…
