We show the first quantum simulation involving genuine number (Fock) states with up to four photons. Already this resource-efficient basic demonstration reveals topological matter not known before, and that number-state interference can simulate nonlinear systems. It also elucidates perfect quantum wave packet transfer mechanism.
Abstract Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show a quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by interfering pairs of Fock states with up to five photons on an interferometer, and measuring the output states with photon-number-resolving detectors. Already this resource-efficient demonstration reveals topological matter, simulates non-linear systems and elucidates a perfect quantum transfer mechanism which can be used to transport Majorana fermions.
The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.
In this work I demonstrate the interference of three photons, a generalisation of the famous Hong Ou Mandel (HOM) interference. I show that three-photon interference is governed by four parameters and measure three-photon interference independent of two-photon interference. I demonstrate that even when the states of the photons are highly distinguishable they can still exhibit strong quantum interference, challenging our intuition formed by the double slit and HOM interference. This is followed by a demonstration of four-photon interference, where surprisingly we can still observe a "fringe" when the involved particles are pairwise orthogonal. To explain these effects, I present a new framework to describe multi-photon interference in terms of a graph-theoretical approach, which illustrates the origin of different orders of multi-photon interference. My work leads to a more general definition of what we regard as an interference fringe in multi-photon scattering. This study of multi-photon interference is followed by an interdisciplinary work between photonics and solid state physics in the newly developing field of topological photonics. I realise a simulation of the Jackiw-Rossi model as a localised topological mode in a photonic-crystal analogue of the 2D graphene lattice. I succeed in the experimental demonstration of a single such excitation and I am able to study the detailed mode structure for the first time. The mode is a result of a topological defect and is, as such, protected against errors that do not change the topology of the system.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.
The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wave packet prepared in a continuous-mode multiphoton state. A continuous-mode multiphoton state is a state of a traveling light wave packet that contains a definite number of photons and is characterized by a temporal (or, equivalently, spectral) profile. After the interaction with the system, the outgoing light can be monitored by means of homodyne detection or photodetection. Filters for both measurement schemes are derived in this paper. Unlike the vacuum or the coherent state case, the annihilation operator of the light field acting on a multiphoton state changes the state by annihilating a photon, and this makes the traditional filtering techniques inapplicable. To circumvent this difficulty, we adopt a non-Markovian embedding technique proposed in [J. E. Gough, M. R. James, and H. I. Nurdin, Quantum Inf. Process., 12 (2013), pp. 1469--1499] for the study of the single-photon filtering problem. However, the multiphoton nature of the problem addressed in this paper makes the study much more mathematically involved. Moreover, as demonstrated by an example---a two-level system driven by a continuous-mode two-photon state---multiphoton filters can reveal interesting strong nonlinear optical phenomena absent in both the single-photon state case and the continuous-mode Fock state case.
We investigate a generic tripartite quantum system featuring a single qubit interacting concurrently with two quantized harmonic oscillators via nonlinear multiphoton Jaynes-Cummings (MPJC) interactions. Assuming the qubit is initially prepared in a superposition state and the two oscillators are in arbitrary Fock states, we analytically trace the temporal evolution of this tripartite pure initial state. We identify four broad cases, each further divided into two subcases, and derive exact analytical solutions for most cases. Notably, we obtain perfect transfer of excitations between the oscillators by carefully selecting system parameters. In addition, we extensively examine the manner in which the nonclassicalities of various initial oscillator Fock states, quantified by the volume of negative regions in the associated Wigner functions, evolve under the MPJC Hamiltonian, considering diverse system parameters including environmental effects. Besides producing substantial enhancements in the initial value for higher-photon-number states, our analysis reveals that driven solely by the initial qubit energy, with both oscillators initialized in the vacuum state, the nonlinear MPJC interaction yields a significant amount of nontrivial Wigner negativity in the oscillators. The additional nonlinearity introduced by the multiphoton process plays a pivotal role in surpassing the initial nonclassicalities of the photon-number states.