Observation of a gravitational Aharonov-Bohm effect

Gravitational interference The Aharonov-Bohm effect is a quantum mechanical effect in which a magnetic field affects the phase of an electron wave as it propagates along a wire. Atom interferometry exploits the wave characteristic of atoms to measure tiny differences in phase as they take different paths through the arms of an interferometer. Overstreet et al . split a cloud of cold rubidium atoms into two atomic wave packets about 25 centimeters apart and subjected one of the wave packets to gravitational interaction with a large mass (see the Perspective by Roura). The authors state that the observed phase shift is consistent with a gravitational Aharonov-Bohm effect. —ISO

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

Anyons and the double copy

We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimensions by introducing a non-trivial mixing of the topological graviton and the dilaton. Finally, we show that the celebrated Aharonov-Bohm phase can be derived directly from the constructed on-shell amplitude, and that it too enjoys a simple double copy to its gravitational counterpart.

An investigation of Aharonov-Bohm effect towards the potential use for the gravitational wave detection

We investigate an alternative way to detect the gravitational wave using the concept of Aharonov-Bohm experiment in curved space-time. Our system consists of an electron beam which is split into two beams passing opposite sides of the solenoid and producing interference patterns. The change in interference patterns can be observed if the system is perturbed by the gravitational wave, and can be used to trace back to the nature of the gravitational wave. This system is described by the cylindrical coordinate in Minkowski space-time where we set the incoming wave propagating in the z-direction, perpendicular to the solenoid’s cross-section. We found that the perturbation on the cross-section area due to gravitational strength is not strong enough to significantly change the phase shift. Contrarily, by changing the magnetic field generated by the current inside the solenoid, the results suggest that the significant phase shift could potentially be detected if the gravitational wave is allowed to propagate in the direction that is perpendicular to z-direction.

Spin-dependent transport through helical Aharonov-Bohm interferometer

We discuss spin-dependent transport via tunneling Aharonov-Bohm interferometer formed by helical edge states tunnel-coupled to helical leads. We focus on the experimentally relevant high-temperature case as compared to the level spacing and obtain the full 4×4 matrix of transmission coefficients in the presence of magnetic impurities. We show that spin conserving and spin-flip transmission coefficients of the setup can be effectively tuned by the magnetic flux. These features are attractive due to possible applications for spintronics, magnetic field detection, and quantum computing.

Random-Gate-Voltage Induced Al’tshuler–Aronov–Spivak Effect in Topological Edge States

Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the random-gate-voltage induced Φ 0/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ 0/2-period Al’tshuler–Aronov–Spivak oscillation proportional to sin2(2πΦ/Φ 0) by quenching theΦ 0-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.

The topological counterparts of non-Hermitian SSH models

Inspired by the relevance between the asymmetric coupling amplitude and the imaginary gauge field, we construct the counterpart of the non-Hermitian SSH model. The idea is the nonzero imaginary magnetic flux vanishing when the boundary condition changes from periodic to open. The zero imaginary magnetic flux of the counterpart leads to the eliminating of the non-Hermitian skin effect and the non-Hermitian Aharonov-Bohm effect which ensures the recovery of the conventional bulk-boundary correspondence from the non-Bloch bulk-boundary correspondence. We explain how some the non-Hermitian models can be transformed to the non-Hermitian SSH models and how the non-reciprocal hopping in the non-Hermitian SSH models can be transformed from one term to the other terms by the similarity transformations. We elaborate why the effective imaginary magnetic flux disappears due to the interplay of the non-reciprocal hoppings in the partner of the non-Hermitian SSH model. As the results, we obtain the topological invariants of the non-Hermitian SSH model in analytical form defined in conventional Brillouin zone. The non-Hermitian SSH model in domain configuration on a chain is discussed with this method. The technique gives an alternative way to study the topological properties of non-Hermitian systems.