I. Fuentes-Guridi, A. Carollo, S. Bose, V. Vedral
We calculate the Berry phase of a spin-1/2 particle in a magnetic field considering the quantum nature of the field. The phase reduces to the standard Berry phase in the semiclassical limit and eigenstate of the particle acquires a phase in the vacuum. We also show how to generate a vacuum induced Berry phase considering two quantized modes of the field which has a interesting physical interpretation.
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The quantum vacuum contribution to Berry's geometric phase of photon fields inside a noncoplanarly curved (coiled) fiber is considered by means of the second-quantization formulation. It is shown that the quantum vacuum Berry's phases of left- and right-handed circularly polarized light have the equal magnitudes but opposite signs, and are therefore eliminated entirely by each other. In order to realize such a novel vacuum effect, a scheme to separate the quantum vacuum Berry's phase of one polarized light from another by using the chiral medium fiber is suggested. We think the present study m…
Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquire the photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even the filed is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with cavity quantum electrodynamics (QED) system is desig…
We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a two-dimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the sta…
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, Ho…
With reference to the vacuum induced Berry phase (VIBP) obtained in the interaction of a spin-1/2 particle with quantized irradiation field under rotating-wave approximation (RWA), we present completely different treatment for the VIBP by a fully quantum mechanical treatment beyond the RWA, which gives a new definition of the VIBP and indicates the validity of RWA to be relevant not only to the energy conservation and comparison of characteristic parameters, but also to more subtle physics, such as the geometric property of the state evolution. Our result is of conceptual importance and also o…
Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum
本文构建多电极集成表面离子阱，在高真空悬浮并高速旋转纳米金刚石，实现 NV 电子自旋量子控制及旋转诱导 Berry 相位观测。
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Be…
We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the {\it rotating wave approximation} (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semi-classical energy surfaces which in a simple way brings out the phase space dynamics. With the RWA, a conical intersection between the surfaces em…
Ultra-sensitive magnetic sensor based on 3-dimensional rotation induced Berry phase
提出基于三维旋转诱导Berry相位测量直流磁场的新方法，理论证明14N核自旋静态磁场灵敏度可达10^(-7) T/Hz^(1/2)/N^(1/2)。
We in this Letter derive analytic formulas of Bell correlations in terms of quantum probability statistics under the assumption of measuring outcome-independence. For a spin-1/2 singlet state we find analytically that the violations of Bell-type inequalities are really related to the quantum non-local correlations. However, the Bell and Clauser-Horne-Shimony-Holt (CHSH) inequalities are always satisfied for the spin-1 singlet states. More generally the quantum non-locality does not lead to the violation of Bell and CHSH inequalities for the integer-spin singlet since the non-local interference…
Berry Phase in Non-Perturbative QED
本文研究QED$_4$中Berry相位及其拓扑效应，揭示红外区域存在非微扰的全局效应，超出局域或微扰描述范围。
We briefly review three ways that environmental noise can slow-down (or speed-up) quantum transitions; (i) Lamb shifts, (ii) over-damping and (iii) orthogonality catastrophe. We compare them with the quantum Zeno effect induced by observing the system. These effects are relevant to poor qubits (those strongly coupled to noise). We discuss Berry phases generated by the orthogonality catastrophe, and argue that noise may make it easier to observe Berry phases.
Quantum gyroscope based on three-dimensional rotation induced Berry phase
该研究利用钻石中的固态自旋缺陷作为传感量子比特，通过三维旋转诱导 Berry 阶段提高陀螺仪灵敏度，采用反迪阿巴托协议抑制非绝热泄漏，实现四阶灵敏度提升。
We present a general theoretical framework for the exact treatment of a hybrid system that is composed of a quantum subsystem and a classical subsystem. When the quantum subsystem is dynamically fast and the classical subsystem is slow, a vector potential is generated with a simple canonical transformation. This vector potential, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics; on the other hand, it yields a Lorentz-like force in the slow classical dynamics. In this way, the pure phase (Berry phase) of a wavefunction is linked to a physical force.
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to me…
We demonstrate that Berry phases may greatly affect the dynamics of spin-orbit coupled Bose-Einstein condensates. The effective model Hamiltonian under consideration is shown to be equivalent to the Exe Jahn-Teller model first introduced in molecular physics. The corresponding conical intersection is identified and the Berry phase acquired for a wave packet encircling the intersection studied. It is found that this phase manifests itself in the density profile of the condensate, making it a directly measurable quantity via time-of-flight detection. Moreover, the non-Abelian gauge structure of …
The energy eigenstates of a spin$-\frac{1}{2}$ particle in a magnetic field confined to a plane, define a planar spin. If the particle moves adiabatically around a loop in this plane, it picks up a topological Berry phase that can only be an integer multiple of $π$. We propose a neutron interferometry test of the Berry phase for a circulating planar spin induced by a magnetic field caused by a very long current-carrying straight wire perpendicular to the plane. This Berry phase causes destructive interference in the direction of the incoming beam of thermal neutrons moving through a triple-Lau…
Since the discovery of the Berry phase, there has been much interest in the study of topological effects in the fields of quantum mechanics and condensed matter physics. In this paper we investigate the persistent charge current in mesoscopic disorderd rings and compute the disorder averaged persistent current using the diagrammatic method. We find that within the adiabatic regime the average current oscillates as a function of the geometric flux which is related to the Berry phase.
Triply degenerate points (TDPs), which correspond to new types of topological semimetals, can support novel quasiparticles possessing effective integer spins while preserving Fermi statistics. Here by mapping the momentum space to the parameter space of a three-level system in a trapped ion, we experimentally explore the transitions between different types of TDPs driven by spin-tensor--momentum couplings. We observe the phase transitions between TDPs with different topological charges by measuring the Berry flux on a loop surrounding the gap-closing lines, and the jump of the Berry flux gives…
We investigate the geometric phase or Berry phase (BP) acquired by a spin-half which is both subject to a slowly varying magnetic field and weakly-coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original BP (for an isolated system) is the flux of a monopole-field through the loop traversed by the magnetic field, the environment-induced modification of the BP is the flux of a quadrupole-like field. We find that the environment-induced phase is complex, an…
Geometric phases are well known in classical electromagnetism and quantum mechanics since the early works of Pantcharatnam and Berry. Their origin relies on the geometric nature of state spaces and has been studied in many different systems such as spins, polarized light and atomic physics. Recent works have explored their application in interferometry and quantum computation. Earlier works suggest how to observe these phases in single quantum systems adiabatically driven by external classical devices or sources, where, by classical, we mean any system whose state does not change considerably …
Berry-Phase-Induced Chirality in Thermodynamics
研究通过耗散绝热扰动展开，揭示了Berry相诱导的非平衡手性工作差，阐明了量子几何在热力学几何表述中的作用。
Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped $Λ$-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are…
Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed to characterize the topology of these systems. While the topological classification of non-Hermitian systems is being developed, little attention has been paid to the impact of the new geometric phases on dynamics and transport. In this work, we derive the full set of semiclassical equations of motion for wave-packet dynamics in a system g…
The dynamical effects of topological charge in two-dimensional QED can be expressed in terms of a topological order parameter via a Berry phase construction. The Berry phase describes the electric charge polarization of the vacuum in a manner similar to the theory of polarization in topological insulators. The topological order parameter labels discrete vacua which differ by units of electric flux. Here the associated Berry connection is explicitly constructed from the Dirac Hamiltonian eigenstates by introducing a small attractive Thirring coupling, so that there is still a stable boson in th…
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. Here we demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by …
We propose a Berry phase effect on the chiral degrees of freedom of a triangular magnetic molecule. The phase is induced by adiabatically varying an external electric field in the plane of the molecule via a spin-electric coupling mechanism present in these frustrated magnetic molecules. The Berry phase effect depends on spin-orbit interaction splitting and on the electric dipole moment. By varying the amplitude of the applied electric field, the Berry phase difference between the two spin states can take any arbitrary value between zero and $π$, which can be measured as a phase shift between …
Note on Dirac monopole theory and Berry geometric phase
本工作通过将狄拉克单极子理论拓展到参数空间，利用双模哈密顿量模型可视化参数空间中的狄拉克弦，揭示其与贝里几何相位的内在联系，为相关研究提供统一框架。
Tracking Berry curvature effect in molecular dynamics by ultrafast magnetic x-ray scattering
针对分子动力学中Berry力效应难以探测的问题，提出利用自由电子激光的超快非共振磁性X射线散射圆二色性，重建光解离过程中瞬态空间自旋分离。
Influence of thermal bath on Pancharatnam-Berry phase in an accelerated frame
本文研究匀加速原子的 Pancharatnam-Berry 相位，发现场的热性质及 Unruh 热浴与真实热浴的交换对称性会影响相位，但实验所需高温超出当前技术能力。
We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincide…
Induced Berry Connection and Photonic Spin Hall Effect in Optical Dirac Theory
本文在光学狄拉克理论框架下建立了描述光子自旋轨道相互作用与自旋/轨道霍尔效应的场论模型，揭示螺旋路径挠率诱导的旋转耦合及几何相位中SAM与IOAM的联合贡献，并发现椭圆偏振与圆偏振光几何相位的差异。
The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wavefunction may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry-phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a small critical magnetic field is reached. This behavior results from turning on a $π$-Berry phase associated wit…
Topological transitions of the generalized Pancharatnam-Berry phase
本文利用光学平台实验演示并研究了单量子比特广义测量所诱导的广义 Pancharatnam-Berry 几何相位随测量强度发生的拓扑转变，证明其对协议推广和部分缺陷具有鲁棒性。
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