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arXiv:1410.0294 · Scientific Reports

Photonic lattice simulation of dissipation-induced correlations in bosonic systems

Amit Rai, Changhyoup Lee, Changsuk Noh, Dimitris G. Angelakis

Published Feb 24, 2015• 15 citations
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Abstract

We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also show that a generalised model containing nearest-neighbour dissipative interaction can be engineered and probed in the proposed set-up.

DOI
10.1038/srep08438

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We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also show that a generalised model containing nearest-neighbour dissipative interaction can be engineered and probed in the proposed set-up.
We propose a method for optical visualization of the Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive indices than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over the direction of propagation for both ordered and disordered cases, exploring the sensitivity of the averaged picture with respect to the beam injection position. For our finite systems, the resulting patterns are reminiscent the ones set in billiards, and therefore we introduce a definition of discrete quantum billiards and discuss the possible relevance to its well-established continuous counterpart.
A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables us to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visualized as a periodic self-imaging phenomenon of the light beam along the waveguide array and explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight-binding lattice.
The quantum dynamics of interacting bosons in a one-dimensional (1D) system is investigated numerically. We consider dissipative and conservative two-particle interactions, and integrate the master equation describing the system dynamics via a time-evolving block-decimation (TEBD) algorithm. Our numerical simulations directly apply to stationary-light polaritons in systems where atoms and photons are confined to the hollow core of a photonic crystal fibre. We show that a two-particle loss term can drive an initially uncorrelated state into a regime where correlations effectively inhibit the dissipation of particles. The correlations induced by two-particle losses are compared with those generated by an elastic repulsion. For the considered time range, we find a similar behaviour in local density–density correlations but we find differences in non-local correlations.
Optical networks composed of interconnected waveguides are a versatile platform to simulate bosonic physical phenomena. Significant work in the non-interacting regime has demonstrated the capabilities of this platform to simulate many exotic effects such as photon transport in the presence of gauge fields, dynamics of quantum walks, and topological transition and dissipation phenomena. However, the extension of these concepts to simulating interacting quantum many-body phenomena such as the Bose-Hubbard and the fractional quantum Hall (FQH) physics has remained elusive. In this work, we address this problem and demonstrate a framework for quantum many-body simulation as well as drive and dissipation in photonic waveguides. Specifically, we show that for waveguide photons, a tunable on-site interaction can be simulated using a photon-number-selective phase gate. We propose an implementation of such a phase gate based on a three-level-atom-mediated photon subtraction and addition. We apply this approach to bosonic lattice models and propose circuits that can accurately simulate the Bose-Hubbard and FQH Hamiltonian as benchmarking examples. Moreover, we show how to simulate the Lindbladian evolution with engineered dissipators such that the steady state of the Lindbadlian corresponds to the ground state of desired Hamiltonians. Our scheme extends the waveguide photonic simulation platform to the strongly interacting quantum many-body regime while retaining all of its crucial advantages, such as single-site addressability, Hamiltonian parameter controllability, and hardware efficiency.
This work reveals that linear propagation of classical light beams can be used to simulate the nonlinear effect of SPDC leading to photon pair generation and quantum random walks of the generated biphotons. In particular, the authors demonstrate that the quantum correlations of biphotons generated in a quadratically nonlinear 1D waveguide array can be mapped onto a linear beam propagation in specially designed 2D array of coupled optical waveguides. This analogy enables us to simulate, with classical light, the quantum coincidence counts for biphotons including the regime of breaking a 1D Bell like inequality as indicated by positve values of the non-classicality.