We complete our previous(1, 2) demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,(4) including fine structure. We complete our previous derivation(3) of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.
We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with interactions among nearest and next-to-nearest neighbors, the interactions can be tuned as a function of range. We determine the exact ground state energy and wavefunction and obtain a part of the excitation spectrum.
Though not so widely appreciated in the literature, supersymmetric quantum mechanics provides an ideal playground for studying non-Abelian geometric phase, because supersymmetry always guarantees degeneracies in energy levels. In this paper we first present a simple supersymmetric model for a free particle on a circle with point-like interactions that exhibits $\mathscr{N} = 2$ supersymmetry and doubly degenerate energy levels. We then show that Berry's connection in this model is given by the Wu-Yang-like magnetic monopole in SU(2) Yang-Mills gauge theory. This article is largely based on our…
All-to-all connections are required in general quantum annealing machines to solve various combinatorial optimization problems. The Lechner, Hauke, and Zoller (LHZ) method, which is used to realize the all-to-all connections, requires many-body interactions in locally connected qubits. Because most of the qubit interactions are two-body interactions, Lechner also proposed the construction of each four-body interaction by six controlled-NOT (CNOT) gates between two qubits. However, it is difficult to construct many CNOT gates. Herein, we show more concrete sequences to produce four-body and thr…
We study a spin-gas model, where N_S system qubits are interacting with N_B bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decohenerce induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between baths that are coupled to different individual system qubit and compare Markovian with non-Markovian interactions. As examples we co…
We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler pr…
Analytically Exact Quantum Simulation of N-Body Interactions via Untunable Decentralized Hamiltonians for Implementing the Toric Code and Its Modifications
提出一种解析精确的量子模拟方法，通过迭代附加二体相互作用模拟 N 体相互作用，并应用于环面码及其变体的模拟，解决拓扑量子计算中的关键障碍。
Wavefunction structure is analyzed for dense interacting many-boson systems using Hamiltonian $H$, which is a sum of one-body $h(1)$ and an embedded GOE of $k$-body interaction $V(k)$ with strength $λ$. In the first analysis, a complete analytical description of the variance of the strength function as a function of $λ$ and $k$ is derived and the marker $λ_t$ defining thermalization region is obtained. In the strong coupling limit ($λ> λ_t$), the conditional $q$-normal density describes Gaussian to semi-circle transition in strength functions as body rank $k$ of the interaction increases. In t…
In a $m$ particle quantum system, one can have $k=1,\,2,\,\ldots,\,m$ body interactions. The rank of interactions and the nature of particles (fermions or bosons) can strongly affect the dynamics of the system. To explore this in detail, we study quenched quantum dynamics in many particle systems varying rank of interactions, both for fermionic and bosonic particles. We represent the system Hamiltonian by Fermionic Embedded Gaussian Orthogonal Ensembles (FEGOE) and Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) respectively. We show that generating function for $q$-Hermite polynomials …
Similar to interactions between dipoles, or van der Waals interactions, quadrupole-quadrupole interactions are interactions between quadrupoles. In this article, we study the quadrupole interactions between highly excited atoms or Rydberg atoms. In addition, unlike many other calculations, in which the primary focus was on the one-dimensional two-body quadrupole-quadrupole interactions, the primary aim of this article is to study the two-dimensional few-body quadrupole-quadrupole interactions. Specifically, the two-dimensional three-body interactions are investigated. This research has many ap…
In the present work, we present different two-body potentials which have oscillatory shapes with magnetic interactions. The eigenvalues and eigenfunctions are obtained for one of those problems using Nikiforov-Uvarov method.
We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold atoms, and realize a system dominated by elastic three-body interactions. Using this method, we show that it is possible to achieve the optimal scaling behavior predicted for interaction-based quantum metrology with three-body interactions. Specifically, we show that for ultracold atoms quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\bar n}^{-5/2}$ using homodyne quadrature interferometry, and ${\bar n}^{-7/…
In this Brief Report the extended Bose-Hubbard model with local two- and three-body interactions is studied by the exact diagonalization approach. The shapes of the first two insulating lobes are discussed and the values of the critical tunneling for which the insulating phase loses stability for repulsive and attractive three-body interactions are predicted.
We describe a method for engineering local $k+1$-body interactions ($k=1,2,3$) from two-body couplings in spin-${1}{2}$ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit abelian and non-abelian anyon excitations. The most complex of these, with $k=3$, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model …
We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges resonant 2-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive 3-body interaction is included. We find two categories of graphs, distinguished by the kind of 3-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like gra…
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a $Ξ$-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the me…
We consider the spectral problem for a family of $N$ point interactions of the same strength confined to a manifold with a rotational symmetry, a circle or a sphere, and ask for configurations that optimize the ground state energy of the corresponding singular Schrödinger operator. In case of the circle the principal eigenvalue is sharply maximized if the point interactions are distributed at equal distances. The analogous question for the sphere is much harder and reduces to a modification of Thomson problem; we have been able to indicate the unique maximizer configurations for $N=2,\,3,\,4,\…
Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing which combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong and long-range interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range multi-body interactions, consisting of two, three, and four-body …
The low-energy scattering of three bosons or distinguishable particles with short-range interactions is characterized by a fundamental parameter, the three-body scattering hypervolume. Its imaginary part is directly related to the three-body recombination rate in a quantum gas consisting of such particles. We derive an analytical formula of it for weak interactions, and perform its first numerical calculations for bosons with a variable nonzero-range potential. For attractive interactions, we identify several three-body resonances at which the three-body scattering hypervolume becomes divergen…
Quantum systems composed of $N$ distinct particles in $\R^2$ with two-body contact interactions of TMS type are shown to arise as limits - in the norm resolvent sense - of Schrödinger operators with suitably rescaled pair potentials.
Synthesizing many-body interaction Hamiltonian is a central task in quantum simulation. However, it is challenging to synthesize interactions including more than two spins. Borrowing tools from quantum optics, we synthesize five-body spin-exchange interaction in a superconducting quantum circuit by simultaneously exciting four independent qubits with time-energy correlated photon quadruples generated from a qudit. During the dynamic evolution of the five-body interaction, a Greenberger-Horne-Zeilinger state is generated in a single step with fidelity estimated to be $0.685$. We compare the inf…
