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arXiv:2211.09805 · APL Quantum

Programmable photonic system for quantum simulation in arbitrary topologies

Ben Bartlett, Olivia Y. Long, Avik Dutt, Shanhui Fan

Published Feb 23, 2024• 4 citations
arXivHTMLPDF

Abstract

Synthetic dimensions have generated great interest for studying many types of topological, quantum, and many-body physics, and they offer a flexible platform for simulation of interesting physical systems, especially in high dimensions. In this paper, we describe a programmable photonic device capable of emulating the dynamics of a broad class of Hamiltonians in lattices with arbitrary topologies and dimensions. We derive a correspondence between the physics of the device and the Hamiltonians of interest, and we simulate the physics of the device to observe a wide variety of physical phenomena, including chiral states in a Hall ladder, effective gauge potentials, and oscillations in high-dimensional lattices. Our proposed device opens new possibilities for studying topological and many-body physics in near-term experimental platforms.

DOI
10.1063/5.0181151

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Synthetic dimensions have generated great interest for studying many types of topological, quantum, and many-body physics, and they offer a flexible platform for simulation of interesting physical systems, especially in high dimensions. In this paper, we describe a programmable photonic device capable of emulating the dynamics of a broad class of Hamiltonians in lattices with arbitrary topologies and dimensions. We derive a correspondence between the physics of the device and the Hamiltonians of interest, and we simulate the physics of the device to observe a wide variety of physical phenomena, including chiral states in a Hall ladder, effective gauge potentials, and oscillations in high-dimensional lattices. Our proposed device opens new possibilities for studying topological and many-body physics in near-term experimental platforms.
Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.
The evenly spaced modes of an electromagnetic resonator are coupled to each other by appropriate time modulation, leading to dynamics analogous to those of particles hopping between different sites of a lattice. This substitution of a real spatial dimension of a lattice with a ``synthetic'' dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and readout of a highly multimoded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator's free spectral range and observing propagation of photon wave packets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wave packets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation.
We investigate the use of programmable optical lattices for quantum simulation of Hubbard models, determining analytic expressions for the hopping and Hubbard UUU, finding that they are suitable for emulating strongly correlated systems with arbitrary structures, including those with a multiple site basis and impurities. Programmable potentials are highly flexible, with the ability to control the depth and shape of individual sites in the optical lattice dynamically. Quantum simulators of Hubbard models with (1) an arbitrary basis are required to represent many real materials of contemporary interest, (2) broken translational symmetry are needed to study impurity physics, and (3) dynamical lattices are needed to investigate strong correlations out of equilibrium. We derive analytic expressions for Hubbard Hamiltonians in programmable potential systems. We find experimental parameters for quantum simulation of Hubbard models with an arbitrary basis, concluding that programmable optical lattices are suitable for this purpose. Finally, we demonstrate how programmable optical lattices can be used for quantum simulation of ionic Hubbard models, and thus the onset of charge transfer insulating states, in parameter regimes that are currently inaccessible to experiment.
Synthetic dimensions are powerful tools for quantum simulation and computation. They are realized by harnessing internal or external degrees of freedom of an atom or molecule, which can mimic the motion of an electron in a real-space lattice potential. Such degrees of freedom are highly tunable and can be engineered to create configurations difficult to access or realize in real space. Some of the exciting possibilities include realizing higher dimensions systems[1, 2, 3], nontrivial real space[4, 5] and band structure[6, 7] topologies and artificial gauge fields[8, 9]. Experiments have utilized various degrees of freedom to create synthetic dimensions, such as motional[10, 11], spin[8, 12, 13, 14] and rotational[15] levels of atoms and molecules, and frequency modes, spatial modes, and arrival times in photonic systems[16]. Atomic synthetic dimensions have demonstrated artificial gauge fields, spin-orbit coupling, chiral edge states using Raman-coupled ground magnetic sublevels[8, 12, 17] of atoms, and phenomena such as Anderson localization using two-photon Bragg transitions by coupling free-particle momentum states[18]. Here, we harness the Rydberg levels of 84Sr to realize a synthetic lattice for studying quantum matter. Resonant millimeter-wave (mm-wave) radiation coupling Rydberg levels |i⟩ and |j⟩ with amplitude Ωij (Rabi frequency) are described by the same Hamiltonian as a particle tunneling between lattice sites |i⟩ and |j⟩ with tunneling amplitude Jij = Ωij /2. The mathematical equivalence to particles moving in a real-space lattice enables Rydberg levels to function as a synthetic spatial dimension. Rydberg-atom synthetic dimensions offer control over connectivity, tunneling rates and on-site potentials, which allows for the creation of a broad range of synthetic dimensional system. The capabilities of such a system are demonstrated by realizing the famous Su-Schrieffer-Heeger (SSH) model[19] and studying its topologically protected edge states(TPS).
The recent emerging field of synthetic dimension in photonics offers a variety of opportunities for manipulating different internal degrees of freedom of photons such as the spectrum of light. While nonlinear optical effects can be incorporated into these photonic systems with synthetic dimensions, these nonlinear effects typically result in long-range interactions along the frequency axis. Thus, it has been difficult to use the synthetic dimension concept to study a large class of Hamiltonians that involves local interactions. Here we show that a Hamiltonian that is locally interacting along the synthetic dimension can be achieved in a dynamically modulated ring resonator incorporating χ ( 3 ) nonlinearity, provided that the group velocity dispersion of the waveguide forming the ring is specifically designed. As a demonstration we numerically implement a Bose–Hubbard model and explore photon blockade effect in the synthetic frequency space. Our work opens new possibilities for studying fundamental many-body physics in the synthetic space in photonics, with potential applications in optical quantum communication and quantum computation.
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum simulations in high dimensions, synthetic dimensions have since demonstrated advantages in designing novel Hamiltonians and manipulating quantum or optical states for exploring topological physics, and for applications in computing and information processing. Here we provide a comprehensive overview of progress in synthetic dimensions across photonic, atomic, and other physical platforms over the past decade. We showcase different approaches used to construct synthetic dimensions and highlight key physical phenomena enabled by the advantage of such a framework. By offering a unified perspective on developments in this field, we aim to provide insights into how synthetic dimensions can bridge fundamental physics and applied technologies, fostering interdisciplinary engagement in quantum simulation, atomic and photonic engineering, and information processing.