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arXiv:1603.02669 · Nature Communications

Photonic simulation of entanglement growth and engineering after a spin chain quench

Ioannis Pitsios, Leonardo Banchi, Adil S. Rab, Marco Bentivegna, Debora Caprara, Andrea Crespi, Nicolò Spagnolo, Sougato Bose, Paolo Mataloni, Roberto Osellame, Fabio Sciarrino

Published Nov 13, 2017• 73 citations

Abstract

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.

DOI: 10.1038/s41467-017-01589-y

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The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.

Summary form only given. Photonic circuits represent a promising platform to perform quantum simulation of several different physical phenomena. Indeed, large progresses have been achieved in the last few years due to the technological advances enabled by integrated photonics, which allowed to achieve a significant increase in the size of the implemented systems. Notable examples of observed phenomena in integrated circuits include Anderson localization [1] and transport mechanisms [2].[4]). We discuss the photonic simulation of spin chain dynamics after a quench in a 5-site system [3]. Such dynamics present the feature of entangling distant spins in pairs starting from the input (separable) Neel state, thus obtaining an amount of entanglement which is proportional to the number of sites present in the system (volume law [4]). The verification of such increase in the amount of the generated entanglement provides a useful resource for several quantum information protocols, including quantum teleportation and quantum networking.

Multipartite entanglements are essential resources for proceeding tasks in quantum information science and technology. However, generating and verifying them present significant challenges, such as the stringent requirements for manipulations and the need for a huge number of building-blocks as the systems scale up. Here, we propose and experimentally demonstrate the heralded multipartite entanglements on a three-dimensional photonic chip. Integrated photonics provide a physically scalable way to achieve an extensive and adjustable architecture. Through sophisticated Hamiltonian engineering, we are able to control the coherent evolution of shared single photon in the multiple spatial modes, dynamically tuning the induced high-order W-states of different orders in a single photonic chip. Using an effective witness, we successfully observe and verify 61-partite quantum entanglements in a 121-site photonic lattice. Our results, together with the single-site-addressable platform, offer new insights into the accessible size of quantum entanglements and may facilitate the developments of large-scale quantum information processing applications.

The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many body localization (MBL). Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics have so far not been investigated. In this letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power

α

. Using a dynamical version of the strong disorder renormalization group (SDRG) we find for

α>α_c

that the entanglement entropy grows logarithmically with time and becomes smaller with larger

α

as

S(t) = S_p \ln(t)/(2α)

. Here,

S_p= 2 \ln2 -1

. We use numerical exact diagonalization (ED) simulations to verify our results for system sizes up to $ N\sim 16$ spins, yielding good agreement for sufficiently large

α> α_c \approx 1.8

. For

α<α_c

, we find that the entanglement entropy grows as a power-law with time,

S(t)\sim t^{γ(α)}

with

α> α_c \approx 1.8

a decaying function of the interaction exponent

α

.

Entanglement is one of the most vital properties of quantum mechanical systems, and it forms the backbone of quantum information technologies. Taking advantage of nano/microfabrication and particularly complementary metal-oxide-semiconductor manufacturing technologies, photonic integrated circuits (PICs) have emerged as a versatile platform for the generation, manipulation, and measurement of entangled photonic states. We summarize the recent progress of quantum entanglement on PICs, starting from the generation of nonentangled and entangled biphoton states, to the generation of entangled states of multiple photons, multiple dimensions, and multiple degrees of freedom, as well as their applications for quantum information processing.