On the energy of physical states in QED in the convariant gauge
Dan Solomon
在量子场论中，通常假定量子态的能量存在一个下限。在这里，它将表明，在QED的物理状态的能量没有下限在一个明显的协变规范。
In quantum field theory it is generally assumed that there is a lower bound to the energy of a quantum state. Here, it will be shown that there is no lower bound to the energy of physical states in QED in a manifestly covariant gauge.
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For over six decades, quantum electrodynamics (QED) in multipolar form has been an invaluable tool for understanding quantum-scale atomic and molecular interactions. However, its relation to the Poincare-gauge has been a recent topic of controversy and debate. It was claimed by Rousseau and Felbacq in the article Scientific Reports 7, 11115 (2017) that Hamiltonian multipolar QED is not the same as Poincare-gauge QED and that it is not generally equivalent to Coulomb-gauge QED. This claim has subsequently been refuted, but since both sides of the debate appear technically sound, a clear reconci…
We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the $U(1)$ theory for large $n$. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.
On the existence of negative energy states in QED in the temporal gauge
一般认为真空态是能量最低的量子态。然而，已经表明，这不是一个狄拉克-麦克斯韦场在时间规范的情况下。本文给出了另一个与以往工作不同的证明，证明了真空态不是时间规范中Dirac-Maxwell场的最低能态。
A quantum dipole interacting with an optical cavity is one of the key models in cavity quantum electrodynamics (cavity-QED). To treat this system theoretically, the typical approach is to truncate the dipole to two levels. However, it has been shown that in the ultrastrong-coupling regime, this truncation naively destroys gauge invariance. By truncating in a manner consistent with the gauge principle, we introduce master equations {for open systems} to compute gauge-invariant emission spectra, photon flux rates, and quantum correlation functions which show significant disagreement with previou…
In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are n…
In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The schemes consist of coupled transmons whose flux are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the fixed phase offset of each site on the complex coupling rate between coupled qubits. These configurations can be directly realised in a superconducting circuit and is easily extendable to a scalable lattice. Due to the intrinsic non-linearity of the transmon qubits such lattices would be an ideal…
Metrics and properties of optimal gauges in multimode cavity QED
本研究聚焦多模腔QED中截断希尔伯特空间计算的规范选择问题，提出最优规范的定义与性能度量方法，证明最优规范具有模式依赖性，且与光物纠缠最小的情形不对应。
Regularised Arbitrary Gauge non-Relativistic QED
开发了正则化任意规范非相对论量子电动力学，比较库仑与多极描述，分析正则化对微扰理论的影响，并讨论短程现象包括Dicke临界性。
New Angular Momentum Conservation Laws for Gauge Fields in QED
本文利用QED拉格朗日量和诺特定理推导出Dirac-Maxwell场的局部角动量守恒定律，并将其分解为自旋与轨道角动量密度的耦合运动方程，揭示了规范玻色子自旋相关的局部动力学。
Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincaré gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss i…
Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of p…
Waveguide QED in the Dipole Gauge
本文将规范选择分析扩展至波导 QED，证明偶极规范下的截断能产生准确结果，并利用单光子散射揭示了超强耦合下主共振 Lamb 移位、透射振幅不对称等新效应，最后提出了 circuit QED 实验测试方案。
Gauge invariance is the cornerstone of modern quantum field theory. Recently, it has been shown that the quantum Rabi model, describing the dipolar coupling between a two-level atom and a quantized electromagnetic field, violates this principle. This widely used model describes a plethora of quantum systems and physical processes under different interaction regimes. In the ultrastrong coupling regime, it provides predictions which drastically depend on the chosen gauge. This failure is attributed to the finite-level truncation of the matter system. We show that a careful application of the gau…
The stability of the QED vacuum in the temporal gauge
我们将研究在时间规范中QED真空的稳定性。一般认为真空态是能量最低的量子态。然而，它将表明，这是不是一个系统组成的费米子场耦合到一个量子化的电磁场的时间规范的情况下。将表明，在这种情况下，存在能量比真空态小的量子态。
Cavity QED models are analyzed in terms of field quadrature operators. We demonstrate that in such representation, the problem can be formulated in terms of effective gauge potentials. In this respect, it presents a completely new system in which gauge fields arise, possessing the advantages of purity, high control of system parameters as well as preparation and detection methods. Studying three well known models, it is shown that either Abelian or non-Abelian gauge potentials can be constructed. The non-Abelian characteristics are evidenced via numerical simulations utilizing experimental par…
We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulom…
Operator Gauge Symmetry in QED
本文将Kobe首先提出的算符规范变换应用于QED中的Maxwell方程和连续性方程。电磁场量子化后满足规范不变性。麦克斯韦方程组中的固有非线性是由于算子规范变换的非线性而得到的直接结果。通过定义第一类和第二类广义导数，得到了算符规范不变的麦克斯韦方程组和相应的电荷守恒。得到了实电荷和虚电荷的守恒律。场强张量中的附加项被解释为真空的电和磁极化。
We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating frame, where the matter is decoupled from the gauge constraints, we can express the gauge field operators in terms of dual operators. In two space dimensions, the dual representation is completely free of any local constraints. In three space dimensions, local constraints among the dual operators remain but involve only the gauge field degrees of freedom (and …
Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-…
Physical Fields in QED
讨论了量子电动力学的古普塔-布勒表述与库仑规范表述之间的联系。有人认为，这两个公式是没有连接的规范变换。库仑规范的状态空间也不能等同于古普塔-布莱希特空间的子空间。相反，通过绕道怀特曼重建定理提出了一个更间接的两个配方之间的联系。
We propose a scalable analog quantum simulator for quantum electrodynamics (QED) in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs inter-species spin-changing collisions in an ultra-cold atomic mixture trapped in an optical lattice. Building on the previous one-dimensional implementation scheme of Ref. [1] we engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle towards experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to pure gauge theory and discuss how the phenomenon of confineme…
The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other methods. So far, however, TN methods have mostly simulated lattice gauge theories in $(1+1)$ dimensions. The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled to a $U(1)$ gauge field, directly in the thermodynamic limit. With this idea in mind we first conside…
Truncation-Free Quantum Simulation of Pure-Gauge Compact QED Using Josephson Arrays
本文提出一种基于约瑟夫森阵列与格点QED局域希尔伯特空间精确类比的无截断量子模拟方法，可模拟准二维系统，并为连续规范群的超导电路模拟奠定基础。
The interplay of symmetry, topology, and many-body effects in the classification of possible phases of matter poses a formidable challenge that is attracting great attention in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work, we show that similar phenomena also appear in high-energy physics, where inter-particle interactions are mediated by gauge bosons, and constrained by a local gauge symmetry.…
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