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Scientific Reports

Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems

Xiao-song Ma, Borivoje Dakić, Sebastian Kropatschek, William R. Naylor, Yang‐Hao Chan, Zhexuan Gong, L.-M. Duan, Anton Zeilinger, Philip John Walther

Published Jan 7, 2014• 18 citations
Publisher

Abstract

Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.

DOI
10.1038/srep03583

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Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.
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 interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology.
Quantum simulators are capable of calculating properties of quantum systems unfeasible for classical computers. Here we report the analog quantum simulation of arbitrary Heisenberg-type interactions among four spin-1/2 particles. This spin-1/2 tetramer is the two-dimensional archetype system whose ground state belongs to the class of valence-bond states. Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. We utilize the particular advantages of the precise single-particle addressability and a tunable measurement-induced interaction to obtain fundamental insights into entanglement dynamics among individual particles. We also directly extract ground-state energies and pair-wise quantum correlations, which enable our quantum simulator to investigate the frustration of entanglement. Remarkably, the pair-wise correlations are restricted by quantum monogamy.
In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤
We present design techniques for special optical lattices that allow quantum simulation of spin frustration in two-dimensional systems. By carefully overlaying optical lattices with different periods and orientations we are able to adjust the ratio between the nearest-neighbor and next-nearest-neighbor interaction strengths in a square spin lattice and realize frustration effects. We show that only laser beams of a single frequency are required and the parameter space reachable in our design is broad enough to study the important phases in the J1{J}_{1}J1​-J2{J}_{2}J2​ frustrated Heisenberg model and checkerboard antiferromagnet model. By using the polarization spectroscopy for detection, distinct quantum phases and quantum phase transition points can be characterized straightforwardly. Our design thus offers a suitable setup for simulation of frustrated spin systems.
The ability to simulate physical systems is essential for an understanding of their physical properties and advancing related technologies. However, simulating certain complex systems at scale, including many-body spin models, is often a significant challenge for conventional computing approaches. Quantum simulators, employing controlled quantum systems that mimic the dynamics of a target system, can offer a more efficient approach. This work demonstrates the use of photonic circuits for quantum simulation of disordered spin systems, where quantum properties such as superposition and interference can be leveraged for a more efficient simulation. We fabricate and characterize a low-loss silicon-on-insulator chip with a buried aluminum mirror and a reconfigurable interferometer, which is employed in conjunction with two input photons to map the dynamics of a spin Hamiltonian with four-body interactions. Our results demonstrate several characteristics associated with the target system, such as spin-degenerate ground states and phase transitions, confirming the device’s functionality as a quantum simulator of the spin system.