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Ramesh VG, Peters KJH, Rodriguez SRK. Arcsine Laws of Light. PHYSICAL REVIEW LETTERS 2024; 132:133801. [PMID: 38613295 DOI: 10.1103/physrevlett.132.133801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2022] [Accepted: 02/06/2024] [Indexed: 04/14/2024]
Abstract
We demonstrate that the time-integrated light intensity transmitted by a coherently driven resonator obeys Lévy's arcsine laws-a cornerstone of extreme value statistics. We show that convergence to the arcsine distribution is algebraic, universal, and independent of nonequilibrium behavior due to nonconservative forces or nonadiabatic driving. We furthermore verify, numerically, that the arcsine laws hold in the presence of frequency noise and in Kerr-nonlinear resonators supporting non-Gaussian states. The arcsine laws imply a weak ergodicity breaking which can be leveraged to enhance the precision of resonant optical sensors with zero energy cost, as shown in our companion manuscript [V. G. Ramesh et al., companion paper, Phys. Rev. Res. (2024).PPRHAI2643-1564]. Finally, we discuss perspectives for probing the possible breakdown of the arcsine laws in systems with memory.
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Affiliation(s)
- V G Ramesh
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - K J H Peters
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - S R K Rodriguez
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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Luo L, Mi Z, Huang J, Ruan Z. Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields. SCIENCE ADVANCES 2023; 9:eadg6238. [PMID: 38039362 PMCID: PMC10691765 DOI: 10.1126/sciadv.adg6238] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 11/02/2023] [Indexed: 12/03/2023]
Abstract
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.
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Affiliation(s)
- Li Luo
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhiyi Mi
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Junyi Huang
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
- College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
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Alperin SN, Berloff NG. Emergence and Ordering of Polygonal Breathers in Polariton Condensates. PHYSICAL REVIEW LETTERS 2022; 129:015301. [PMID: 35841547 DOI: 10.1103/physrevlett.129.015301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
We show that the simultaneous driving of a polariton condensate with both nonresonant and nth order resonant pump frequencies allows for a generic mechanism of breather formation. From this we construct for the second order resonance a family of exotic breathers with nontrivial discrete order of rotational symmetry. Finally, we demonstrate the spontaneous emergence of both crystalline and glassy orderings of lattices of polygonal breathers, depending on the degree of polygonal excitations at the lattice sites.
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Affiliation(s)
- Samuel N Alperin
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Natalia G Berloff
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Skolkovo Institute of Science and Technology Novaya Street, 100, Skolkovo 143025, Russian Federation
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Fang Y, Huang J, Ruan Z. Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine. PHYSICAL REVIEW LETTERS 2021; 127:043902. [PMID: 34355963 DOI: 10.1103/physrevlett.127.043902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Statistical spin dynamics plays a key role in understanding the working principle for novel optical Ising machines. Here, we propose the gauge transformation for a spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Using gauge transformation, we experimentally evaluate the phase diagram of a high-dimensional spin-glass equilibrium system with 100 fully connected spins. We observe the presence of paramagnetic, ferromagnetic, and spin-glass phases and determine the critical temperature T_{c} and the critical probability p_{c} of the phase transitions, which agree well with the mean-field theory predictions. Thus, the approximation of the mean-field model is experimentally verified in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions even when the system is associated with optical aberrations and measurement uncertainty.
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Affiliation(s)
- Yisheng Fang
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Junyi Huang
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
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Stroev N, Berloff NG. Discrete Polynomial Optimization with Coherent Networks of Condensates and Complex Coupling Switching. PHYSICAL REVIEW LETTERS 2021; 126:050504. [PMID: 33605772 DOI: 10.1103/physrevlett.126.050504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 01/07/2021] [Indexed: 06/12/2023]
Abstract
Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation or coherence threshold have been recently proposed as efficient analog simulators of the two-local spin Hamiltonians with continuous or discrete degrees of freedom. We show that nonequilibrium condensates above the threshold arranged in an interacting network may realize k-local Hamiltonians with k>2 and lead to nontrivial phase configurations. Similarly, many gain-dissipative systems that can be manipulated by optical means can bring about the ground state of the k-local Hamiltonians and solve higher-order binary optimization problems. We show how to facilitate the search for the global solution by invoking complex couplings in the system and demonstrate the efficiency of the method on the sets of complex problems. This approach offers a highly flexible new kind of computation based on gain-dissipative simulators with complex coupling switching.
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Affiliation(s)
- Nikita Stroev
- Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld.1, Moscow, 121205 Russian Federation
| | - Natalia G Berloff
- Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld.1, Moscow, 121205 Russian Federation
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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Goto H, Endo K, Suzuki M, Sakai Y, Kanao T, Hamakawa Y, Hidaka R, Yamasaki M, Tatsumura K. High-performance combinatorial optimization based on classical mechanics. SCIENCE ADVANCES 2021; 7:eabe7953. [PMID: 33536219 PMCID: PMC11323291 DOI: 10.1126/sciadv.abe7953] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2020] [Accepted: 12/16/2020] [Indexed: 05/20/2023]
Abstract
Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.
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Affiliation(s)
- Hayato Goto
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan.
| | - Kotaro Endo
- Software Systems Research and Development Center, Toshiba Digital Solutions Corporation, 72-34 Horikawa-cho, Saiwai-ku, Kawasaki 212-8585, Japan
| | - Masaru Suzuki
- ICT Solutions Division, Toshiba Digital Solutions Corporation, 72-34 Horikawa-cho, Saiwai-ku, Kawasaki 212-8585, Japan
| | - Yoshisato Sakai
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
| | - Taro Kanao
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
| | - Yohei Hamakawa
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
| | - Ryo Hidaka
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
| | - Masaya Yamasaki
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
| | - Kosuke Tatsumura
- Corporate Research and Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan
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Geng Z, Peters KJH, Trichet AAP, Malmir K, Kolkowski R, Smith JM, Rodriguez SRK. Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity. PHYSICAL REVIEW LETTERS 2020; 124:153603. [PMID: 32357047 DOI: 10.1103/physrevlett.124.153603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Accepted: 03/31/2020] [Indexed: 06/11/2023]
Abstract
We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent -1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.
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Affiliation(s)
- Z Geng
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - K J H Peters
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - A A P Trichet
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - K Malmir
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - R Kolkowski
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - J M Smith
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - S R K Rodriguez
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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