Aharonov-Bohm Phase Research Articles

Sensing Aharonov-Bohm Phase Using a Multiply-Orbiting-Ion Interferometer.

Interferometers, which are built using spatially propagating light or matter waves, are commonly used to measure physical quantities. These measurements are made possible by exploiting the interference between waves traveling along different paths. This study introduces a novel approach to sensing of the Aharonov-Bohm phase, an ion matter-wave interferometer operating within a two-dimensional rotational trajectory in a trap potential. The ion orbitals in the nearly circular potential change rotation direction with time. This reversal of rotation direction results in a corresponding change in the interference phase. Our study is the first attempt to utilize propagating matter waves of an ion in constructing a two-dimensional interferometer for the measurement of physical quantities. Given that the scale factor of the interferometer to the cyclotron motion and the rotation of the system is common, the sensitivity to the Aharonov-Bohm phase in this study corresponds to a rotation sensitivity of approximately 300 rad/s. Besides advancing interferometry, our work also lays the foundation for future research into the use of ion matter waves in gyroscopic applications.

Nonreciprocal Acoustic Devices with Asymmetric Peierls Phases.

Nonreciprocity in acoustics is of paramount importance in many practical applications and has been experimentally realized using nonlinear media, moving fluids, or time modulation, which regrettably suffer from large volumes and high-power consumption, difficulty in integration, and inevitable vibrations or phase noise. In modern Hamiltonian theory, the violation of system's reciprocity can be achieved via asymmetric Peierls phases, which typically involves with non-Hermiticity or time-reversal symmetry breaking. Here, we propose a framework for designing nonreciprocal acoustic devices based on the asymmetric Peierls phases that can be fully controlled via active acoustic components. The fully controlled Peierls phases enable various high-performance acoustic devices, including non-Hermitian extensions of isolators, gyrators, and circulators, which are otherwise impossible in previous approaches that are bound by Hermiticity or passivity. We reveal that the transmission phases in isolators are equivalent to the Peierls phase plus a constant. The nonreciprocal phase delay in gyrators and the unirotational transmission behavior in circulators result from the gauge-invariant Aharonov-Bohm phases determined by Peierls phases. Our work not only uncovers multiple intriguing physics related to Peierls phases but also provides a general approach to compact, integratable, nonreciprocal acoustic devices.

Aharonov-Bohm effect in Generalized Electrodynamics

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.

Higgs-Confinement Continuity and Matching of Aharonov-Bohm Phases.

Some gauge theories with a spontaneously broken U(1) symmetry exhibit fractional Aharonov-Bohm (AB) phases around vortices in the Higgs regime. We discuss continuity between confining and Higgs regimes in such gauge theories with fundamental matter fields, focusing on the AB phases. By explicit calculations in relevant lattice models, we demonstrate that the AB phase is smoothly connected between the confining and Higgs regimes, supporting the Higgs-confinement continuity. This result provides new insight into phase structures of gauge theories with superfluidity, such as dense QCD.

Role of electromagnetic energy and momentum in the Aharonov–Bohm effect

We analyse the physical meaning of the Aharonov–Bohm (AB) phase based on its representation through electromagnetic (EM) potentials as a sum of four components, which, in addition to the known electric and magnetic phase components, contains two more terms recently disclosed by our team in the analysis of quantum phase effects for dipoles and charges, and which we named the complementary electric AB phase and the complementary magnetic AB phase. Using the complete expression for the AB phase, we reveal that the phase component, explicitly depending on time, is determined by the interactional electric energy, while the phase component, explicitly depending on the velocity of charge, is determined by the interactional EM momentum for an isolated system ‘source of EM field and charge’. These findings shed new light on the origin of the AB phase and, in particular, allow us to generalize the de Broglie relationship and the Heisenberg uncertainty relations for a charged particle in an EM field.

Is the Aharonov–Bohm phase shift for a non-closed path a measurable quantity?

Is the Aharonov–Bohm phase shift for a non-closed path a measurable quantity?

Concerning the direction of the Aharonov–Bohm deflection

The interaction of a solenoid with a passing charged particle can be treated within classical or quantum physics. If charged particles pass around both sides of a solenoid, there is an experimentally-observed Aharonov–Bohm deflection of the double-slit particle interference pattern between charges passing on opposite sides. Such a deflection can be obtained by a classical force calculation. Although the magnitude of the angular deflection agrees between the classical force calculation and the quantum topological theory, the direction of the predicted deflection is opposite. Here we point out the simple basis for the direction of the deflection based upon classical electrodynamics and based upon quantum theory. Also, we mention some deflection analogs, both the electrostatic deflection of the particle interference pattern and the optical analog of the classical calculation. The deflection direction involves an experimental question which is addressed rarely if ever. In the deflection direction, there is a direct experimental confrontation connected with the long-standing controversy involving the interpretation of the Aharonov–Bohm phase shift.

Detection of persistent current correlation in cavity-QED

We simulated the radiative response of a cavity quantum electrodynamics (QED) inductively coupled to the ring pierced by magnetic flux and analyzed its spectral dependence to get insight into persistent current dynamics. Current fluctuations in the ring induce changes in the microwave resonator: shifting the resonant frequency and changing its damping. We use the linear response theory and calculate the current response function by means of the Green function technique. Our model contains two quantum dots which divide the ring into two arms with different electron transfers. There are two opposite (symmetric and asymmetric) components of the persistent current, which interplay can be observed the response functions. The resonator reflectance shows characteristic shifts in the dispersive regime and avoided crossings at the resonance points. The magnitude of the resonator frequency shift is greater for coupling to the arm with higher transparency. Fluctuations of the symmetric component of the persistent current are relevant for a wide range of the Aharonov–Bohm phase ϕ, while the asymmetric component becomes dominant close to ϕ≈π (when the total persistent current changes its orientation).

Quantum Hall Bogoliubov interferometer

A quantum Hall interferometer containing a grounded superconducting terminal is proposed. This geometry allows to control the Andreev and normal scattering amplitudes of subgap Bogoliubov quasiparticles with the Aharonov-Bohm phase, as well as with the constrictions defining the interferometer loop. The conductance matrix of such a three-terminal NSN interference device exhibits a much richer behavior as compared to its two-terminal Fabry-P\'erot counterpart, which is illustrated by nontrivial behavior of nonlocal charge and heat responses. A single-edge version of the interferometer enables full on-demand control of the electron-hole superposition, including resonant enhancement of arbitrary small Andreev reflection probability up to 1, and can be used as a building block in future more complex interference setups.

Coupling sum rules and oblique corrections in gauge-Higgs unification

Abstract In grand-unified-theory-inspired SO(5) × U(1)X × SU(3)C gauge-Higgs unification (GHU) in the Randall–Sundrum warped spacetime, the W- and Z-couplings of all 4D fermion modes become nontrivial. The W- and Z-couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza–Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov–Bohm phase θH in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5- to 7-digit accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small.

Gate-Controlled Quantum Interference Effects in a Clean Single-Wall Carbon Nanotube p-n Junction.

The precise control and deep understanding of quantum interference in carbon nanotube (CNT) devices are particularly crucial not only for exploring quantum coherent phenomena in clean one-dimensional electronic systems, but also for developing carbon-based nanoelectronics or quantum devices. Here, we construct a double split-gate structure to explore the Aharonov-Bohm (AB) interference effect in individual single-wall CNT p-n junction devices. For the first time, we achieve the AB modulation of conductance with coaxial magnetic fields as low as 3T, where the flux through the tube is much smaller than the flux quantum. We further demonstrate direct electric-field control of the nonmonotonic magnetoconductance through a gate-tunable built-in electric field, which can be quantitatively understood in combination with the AB phase effect and Landau-Zener tunneling in a CNT p-n junction. Moreover, the nonmonotonic magnetoconductance behavior can be strongly enhanced in the presence of Fabry-Pérot resonances. Our Letter paves the way for exploring and manipulating quantum interference effects with combining magnetic and electric field controls.

Aharonov–Bohm effect with an effective complex-valued vector potential

The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov–Bohm (AB) scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the AB phase before the source is fully encircled. While this does not necessarily change the nonlocal status of the AB effect, it brings new insights into it. Moreover, we discuss how these results might have consequences for the correspondence principle, making complex vector potentials relevant to the study of classical systems.

Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect

A novel version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time varying, spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the 2-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric AB effect and the AC Stark effect.

Curved domain-wall fermion and its anomaly inflow

AbstractWe investigate the effect of a U(1) gauge field on lattice fermion systems with a curved domain-wall mass term. In the same way as the conventional flat domain-wall fermion, the chiral edge modes appear localized at the wall, whose Dirac operator contains the induced gravitational potential as well as the U(1) vector potential. In the case of anS1 domain-wall fermion on a two-dimensional flat lattice, we find a competition between the Aharonov–Bohm(AB) effect and a gravitational gap in the Dirac eigenvalue spectrum, which leads to an anomaly inthe time-reversal (T) symmetry. Our numerical result shows a good consistency with the Atiyah–Patodi–Singer index theorem on a disk inside the S1 domain wall, which describes the cancellation of the T anomaly between the bulk and edge. When the U(1) flux is squeezed inside one plaquette, and the AB phase takes a quantized value π mod $2\pi \mathbb {Z}$, the anomaly inflow drastically changes: the strong flux creates another domain wall around the flux to make the two zero modes coexist. This phenomenon is also observed in the S2 domain-wall fermion in the presence of a magnetic monopole. We find that the domain-wall creation around the monopole microscopically explains the Witten effect.

On the Quantization of AB Phase in Nonlinear Systems.

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

Quantum phase effects for electrically charged particles: Updated analysis

We present an updated analysis of the total expression for the Aharonov-Bohm (AB) phase of a charged particle in an electromagnetic field, which we previously obtained through the superposition principle for quantum phases of charges and dipoles (Sci. Rep., 8 (2018) 11937), and here we re-derive it directly in the framework of the general approach, when the source, the electromagnetic field and the charged particle are quantized. The disclosure of the full set of quantum phase effects for a moving charged particle allows an important update of the wave-particle duality concept by generalizing the de Broglie relationship, where the wave vector associated with the particle is proportional to the vector sum of the mechanical and interactional electromagnetic momenta.

Quantization conditions and the double copy

We formulate Wilson loop observables as products of eikonal Wilson lines given in terms of on-shell scattering amplitudes. We derive the eikonal phases for dyons in both gauge theory and gravity, which we use to derive the Dirac-Schwinger-Zwanziger quantization condition and its relativistic gravitational (Taub-NUT) counterpart via the double copy. We also compute the Wilson loop for an anyon-anyon system, obtaining a relativistic generalisation of the Aharonov-Bohm phase for gravitational anyons.

Universality in anomaly flow

Abstract Universality in anomaly flow by an Aharonov–Bohm phase θH is shown in the flat M4 × (S1/Z2) spacetime and in the Randall–Sundrum (RS) warped space. We analyze the SU(2) gauge theory with doublet fermions. With orbifold boundary conditions the U(1) part of the gauge symmetry remains unbroken at θH = 0 and π. Chiral anomalies smoothly vary with θH in the RS space. It is shown that the anomaly coefficients associated with this anomaly flow are expressed in terms of the values of the wave functions of the gauge fields at the UV and IR branes in the RS space. The anomaly coefficients depend on θH, the warp factor of the RS space, and the orbifold boundary conditions for fermions, but not on the bulk mass parameters of fermions.

The Aharonov–Bohm effect in a closed flux line

The Aharonov–Bohm (AB) effect was convincingly demonstrated using a micro-sized toroidal magnet but it is almost always explained using an infinitely-long solenoid or an infinitely-long flux line. The main reason for this is that the formal treatment of the AB effect considering a toroidal configuration turns out to be too cumbersome. But if the micro-sized toroidal magnet is modelled by a closed flux line of arbitrary shape and size then the formal treatment of the AB effect is exact, considerably simplified, and well-justified. Here we present such a treatment that covers in detail the electromagnetic, topological, and quantum-mechanical aspects of this effect. We demonstrate that the AB phase in a closed flux line is determined by a linking number and has the same form as the AB phase in an infinitely-long flux line which is determined by a winding number. We explicitly show that the two-slit interference shift associated with the AB effect in a closed flux line is the same as that associated with an infinitely-long flux line. We emphasise the topological nature of the AB phase in a closed flux line by demonstrating that this phase is invariant under deformations of the charge path, deformations of the closed flux line, simultaneous deformations of the charge path and the closed flux line, and the interchange between the charge path and the closed flux line. We also discuss the local and nonlocal interpretations of the AB effect in a closed flux line and introduce a non-singular gauge in which the vector potential vanishes in all space except on the surface surrounded by the closed flux line, implying that this vector potential is zero along the trajectory of the charged particle except on the crossing point where this trajectory intersects the surface bounded by the closed flux line, a result that questions the alleged physical significance of the vector potential and thereby the local interpretation of the AB effect.

Robustness of quantum Hall interferometry

Fabry-P\'{e}rot interferometry has emerged as a tool to probe anyon statistics in the quantum Hall effect. The interference phase is interpreted as a combination of a quantized statistical phase and an Aharonov-Bohm phase, proportional to the device area and the charge of the anyons propagating along the device edge. This interpretation faces two challenges. First, the edge states have a finite width and hence the device area is ill-defined. Second, multiple localized anyons may be present in states that overlap with the edge, and it may not be clear whether a second anyon traveling along the edge will go inside or outside the region with a localized anyon and therefore whether or not it should pick up a statistical phase. We show how one may overcome both challenges. In a case where only one chiral edge mode passes through the constrictions defining the interferometer, as when electrons in a constriction are in a Laughlin state with $\nu=1/(2n+1)$ or the integer state at $\nu=1$, we show that the interference phase can be directly related to the total electron charge contained in the interferometer. This holds for arbitrary electron-electron interactions and holds even if the bulk of the interferometer has a higher electron density than the region of the constrictions. In contrast to the device area or to the number of anyons inside a propagating edge channel, the total charge is well-defined. We examine, at the microscopic level, how the relation between charge and phase is maintained when there is a soft confining potential and disorder near the edge of the interferometer, and we discuss briefly the complications that can occur when multiple chiral modes can pass through the constriction.