Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles

Universal S-matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

Predicting colorectal cancer risk from adenoma detection via a two-type branching process model

Despite advances in the modeling and understanding of colorectal cancer development, the dynamics of the progression from benign adenomatous polyp to colorectal carcinoma are still not fully resolved. To take advantage of adenoma size and prevalence data in the National Endoscopic Database of the Clinical Outcomes Research Initiative (CORI) as well as colorectal cancer incidence and size data from the Surveillance Epidemiology and End Results (SEER) database, we construct a two-type branching process model with compartments representing adenoma and carcinoma cells. To perform parameter inference we present a new large-size approximation to the size distribution of the cancer compartment and validate our approach on simulated data. By fitting the model to the CORI and SEER data, we learn biologically relevant parameters, including the transition rate from adenoma to cancer. The inferred parameters allow us to predict the individualized risk of the presence of cancer cells for each screened patient. We provide a web application which allows the user to calculate these individual probabilities at https://ccrc-eth.shinyapps.io/CCRC/. For example, we find a 1 in 100 chance of cancer given the presence of an adenoma between 10 and 20mm size in an average risk patient at age 50. We show that our two-type branching process model recapitulates the early growth dynamics of colon adenomas and cancers and can recover epidemiological trends such as adenoma prevalence and cancer incidence while remaining mathematically and computationally tractable.

Colorectal cancer is a major public health burden. The development of colorectal cancer starts with the mutational initiation of non-cancerous growths in the form of benign adenomatous polyps. These adenomas grow over time with the potential to develop into carcinomas. Many mathematical and simulation-based models have been used to gain insight into this process. We aimed to understand rates of adenoma growth and transition into carcinomas, to enable better planning of colorectal cancer screening strategies. To this end, we expand the two-type branching process model, and fit it on data describing the frequency of sizes of adenomas and carcinomas. The results provide new, data-based, estimates of the rates of development for colorectal cancer.

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators

Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems. They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time τ_{E} in the quantum correlated regime. Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic N-particle systems. We first show how the growth of OTOCs up to τ_{E}=(1/λ)logN is related to the Lyapunov exponent λ of the corresponding chaotic mean-field dynamics in the semiclassical large-N limit. Beyond τ_{E}, where simple mean-field approaches break down, we identify the underlying quantum mechanism responsible for the saturation. To this end we express OTOCs by coherent sums over contributions from different mean-field solutions and compute the dominant many-body interference term amongst them. Our method further applies to the complementary semiclassical limit ℏ→0 for fixed N, including quantum-chaotic single- and few-particle systems.

Signatures of Indistinguishability in Bosonic Many-Body Dynamics

The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, are not only determined by interactions among the particles, but also by their mutual indistinguishability manifested in many-particle interference. We introduce a measure of indistinguishability for Fock states of bosons whose mutual distinguishability is controlled by an internal degree of freedom. We demonstrate how this measure emerges both in the noninteracting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle observables in the noninteracting limit. A nonvanishing interaction leads to a hierarchy of interaction-induced interference processes, such that even the expectation value of single-particle observables is influenced by the degree of indistinguishability.

Asymptotic Gaussian law for noninteracting indistinguishable particles in random networks

For N indistinguishable bosons or fermions impinged on a M-port Haar-random unitary network the average probability to count n ₁, … n _r particles in a small number r ≪ N of binned-together output ports takes a Gaussian form as N ≫ 1. The discovered Gaussian asymptotic law is the well-known asymptotic law for distinguishable particles, governed by a multinomial distribution, modified by the quantum statistics with stronger effect for greater particle density N/M. Furthermore, it is shown that the same Gaussian law is the asymptotic form of the probability to count particles at the output bins of a fixed multiport with the averaging performed over all possible configurations of the particles in the input ports. In the limit N → ∞, the average counting probability for indistinguishable bosons, fermions, and distinguishable particles differs only at a non-vanishing particle density N/M and only for a singular binning K/M → 1, where K output ports belong to a single bin.

Nonclassicality Criteria in Multiport Interferometry

Interference lies at the heart of the behavior of classical and quantum light. It is thus crucial to understand the boundaries between which interference patterns can be explained by a classical electromagnetic description of light and which, on the other hand, can only be understood with a proper quantum mechanical approach. While the case of two-mode interference has received a lot of attention, the multimode case has not yet been fully explored. Here we study a general scenario of intensity interferometry: we derive a bound on the average correlations between pairs of output intensities for the classical wavelike model of light, and we show how it can be violated in a quantum framework. As a consequence, this violation acts as a nonclassicality witness, able to detect the presence of sources with sub-Poissonian photon-number statistics. We also develop a criterion that can certify the impossibility of dividing a given interferometer into two independent subblocks.