Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up new ways for simulating complex dynamics of e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.
Efimovian Phonon Production for an Analog Coasting Universe in Bose-Einstein Condensates
MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University（西安交通大学物理学院）；Institute of Theoretical Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University（山西大学理论物理研究所）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；The State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；New Cornerstone Science Laboratory, The Chinese University of Hong Kong（香港中文大学新基石科学实验室）；Hefei National Laboratory（合肥国家实验室）
Modeling the atomtronic analog of an optical polarizing beam splitter, a half-wave plate, and a quarter-wave plate for phonons of the motional state of two trapped atom
We calculate the resonance fluorescence signal of a two-level system coupled to a quantized phonon mode. By treating the phonons in the independent boson model and not performing any approximations in their description, we also have access to the state evolution of the phonons. We confirm the validity of our model by simulating the limit of an initial quasi-classical coherent phonon state, which can be compared to experimentally confirmed results in the semiclassical limit. In addition we predict photon scattering spectra in the limit of purely quantum mechanical phonon states by approaching t…
We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The…
We study a circularly moving impurity in an atomic condensate for the realisation of superradiance phenomena in tabletop experiments. The impurity is coupled to the density fluctuations of the condensate and, in a quantum field theory language, it serves as an analog of a detector for the quantum phonon field. For sufficiently large rotation speeds, the zero-point fluctuations of the phonon field induce a sizeable excitation rate of the detector even when the condensate is initially at rest in its ground state. For spatially confined condensates and harmonic detectors, such a superradiant emis…
We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean hereto…
We propose an efficient scheme for simulating the topological phases of matter based on silicon-vacancy (SiV) center arrays in phononic crystals. This phononic band gap structure allows for long-range spin-spin interactions with a tunable profile. Under a particular periodic microwave driving, the band-gap mediated spin-spin interaction can be further designed with the form of the Su-Schrieffer-Heeger (SSH) Hamiltonian. In momentum space, we investigate the topological characters of the SSH model, and show that the topological nontrivial phase can be obtained through modulating the periodic dr…
We propose an experimental architecture where an array of optical tweezers affords site-dependent control over the confining potential of a conventional radio-frequency ion trap. The site-dependent control enables programmable manipulation of phonon modes of ions, with many potential applications in quantum information processing (QIP) and thermodynamics. We describe protocols for programming the array of optical tweezers to attain a set of target phonon modes with high accuracy. We propose applications of such controls in simulating quantum thermodynamics of a particle of programmable effecti…
Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necess…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itiner…
Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons
Georg-August-Universität Göttingen（哥廷根大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
We propose and analyse an efficient scheme for simulating higher-order topological phases of matter in two dimensional (2D) spin-phononic crystal networks. We show that, through a specially designed periodic driving, one can selectively control and enhance the bipartite silicon-vacancy (SiV) center arrays, so as to obtain the chiral symmetry-protected spin-spin couplings. More importantly, the Floquet engineering spin-spin interactions support rich quantum phases associated with topological invariants. In momentum space, we analyze and simulate the topological nontrivial properties of the one-…
An analog of classical "hidden variables" for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical--like coins. The bijective map of the states corresponds to the presence of correlations of random classical--like variables associated with the coin positions "up" or "down" and the observables are mapped onto quantum observables described by Hermitian matrices. The connection of the classical--coin statistics with the statistical properties of qubits is found.
Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tD…
Acoustic waves, as science of sound, is an established field in physics. In analogy with light, engineers adapt tools from optic fields for manipulating sound waves to fight with cancer cells. Here we present a heat-gradient driven nanomachine concept for simultaneous emission of two phonons, i.e. a convertion of heat into a sonic wave output. Our theoretical work sheds light on nanoscale components or systems that could be used for future ultrasound devices.
Gauge magnetic fields have a close relation to breaking time-reversal symmetry in condensed matter. In the present of the gauge fields, we might observe nonreciprocal and topological transport. Inspired by these, there is a growing effort to realize exotic transport phenomena in optical and acoustic systems. However, due to charge neutrality, realizing analog magnetic flux for phonons in nanoscale systems is still challenging in both theoretical and experimental studies. Here we propose a novel mechanism to generate synthetic magnetic field for phonon lattice by Floquet engineering auxiliary q…
An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is l…
The analogy between quantum chemistry and light-front quantum field theory, first noted by Kenneth G. Wilson, serves as motivation to develop light-front quantum simulation of quantum field theory. We demonstrate how calculations of hadron structure can be performed on Noisy Intermediate-Scale Quantum devices within the Basis Light-Front Quantization framework. We calculate the light-front wave functions of pions using an effective light-front Hamiltonian in a basis representation on a current quantum processor. We use the Variational Quantum Eigensolver to find the ground state energy and wav…
This paper proposes a new general framework to build a one-to-one correspondence between quantum field theories in static 1+1 dimensional curved spacetime and quantum many-body systems. We show that a massless scalar field in an arbitrary 2-dimensional static spacetime is always equivalent to a site-dependent bosonic hopping model, while a massless Dirac field is equivalent to a site-dependent free Hubbard model or a site-dependent isotropic XY model. A possible experimental realization for such a correspondence in trapped ions system is suggested. As applications of the analogue gravity model…
We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate…
A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging, respectively. We demonstrate that these pronounced and interesting effects are also inherent in the dynamics of classical two-state systems. We discuss how such classical systems are realized using either mechanical, electrical, or optical resonators. In addition to the fundamental interest of such dynamical phenomena linking classical and quantum physics, we …
We investigate the multi-phonon interactions in a hybrid system composed of a nitrogen-vacancy center and a mechanical resonator.We show that, through appropriate sideband engineering analogy to the Mollow or Lamb-Dicke dynamics, the enhanced nonlinear interactions can dominate the coupled system. As an example, we show the preparation of nonclassical states of the mechanical motion and explore the quantum correlation of $n$-phonon with the engineered dissipation,based on the large multi-phonon coupling strength attainable in this sideband structure. This work takes full advantage of the struc…
Simulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here we exploit the mathematical analogies between a triangular spin lattice with Dzyaloshinskii-Moriya coupling on one edge and a three-level system driven by three fields in a loop configuation to emulate spin-transport effects. We show that the spin transport efficiency, seen in the three-level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. We demonstrate experimentally that phenomena characteristic to s…
We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon-electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn-Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular e…
The phonon analog of an optical laser has become the focus of research. We theoretically study phonon laser in a cavity magnomechanical system, which consist of a microwave cavity, a small ferromagnetic sphere and an uniform external bias magnetic field. This system can realize the phonon-magnon coupling and the cavity photon-magnon coupling via magnetostrictive interaction and magnetic dipole interaction respectively, the magnons are driven directly by a strong microwave field simultaneously. Frist, the intensity of driving magnetic field which can reach the threshold condition of phonon lase…
