Aharonov-Bohm Experiment Research Articles

Aharonov-Bohm experiments in magnetic field without the Landau levels

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field, where an electron produces so called synchrotron radiation. In other words, the photons are emitted from the points of the electron trajectory and it means that the trajectory of electron is visible in the synchrotron radiation spectrum. The axiomatic system of quantum mechanics does not enable to define the trajectory of the elementary particle. The two-slit experiment and the AB experiment in magnetic field are the missing experiments of quantum mechanics. The extension of the discussion to the cosmical rays moving in the magnetic field of the Saturn magnetosphere and its rings is mentioned. It is related to the probe CASSINI.

Selective Area Growth of PbTe Nanowire Networks on InP

AbstractHybrid semiconductor–superconductor nanowires are promising candidates as quantum information processing devices. The need for scalability and complex designs calls for the development of selective area growth techniques. Here, the growth of large scale lead telluride (PbTe) networks is introduced by molecular beam epitaxy. The group IV‐VI lead‐salt semiconductor is an attractive material choice due to its large dielectric constant, strong spin‐orbit coupling, and high carrier mobility. A crystal re‐orientation process during the initial growth stages leads to single crystalline nanowire networks despite a large lattice mismatch, different crystal structure, and diverging thermal expansion coefficient to the indium phosphide (InP) substrate. The high quality of the resulting material is confirmed by Hall bar measurements, indicating mobilities up to 5600 cm2 (Vs)−1, and Aharonov–Bohm experiments, indicating a low‐temperature phase coherence length exceeding 21 µm. Together, these properties show the high potential of the system as a basis for topological networks.

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.

Multi-valued vortex solutions to the Schrödinger equation and radiation

This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie–Bohm, hydrodynamic, or stochastic models of quantum mechanics where the physical basis for single-valuedness has been questioned. It first constructs a large class of multi-valued wave functions based on knotted vortex filaments familiar in fluid mechanics, and then it argues that for free particles, these systems will likely radiate electromagnetic radiation if they are charged or have multipolar moments, and only if they are single-valued will they definitely be radiationless. Thus, it is proposed that electromagnetic radiation is possibly the mechanism that causes quantum wave functions to relax to states of single-valuedness, and that multi-valued states might possibly exist in nature for transient periods of time. If true, this would be a modification to the standard quantum mechanical formalism. A prediction is made that electrons in vector Aharonov–Bohm experiments should radiate energy at a rate dependent on the solenoid’s magnetic flux.

Detecting dark matter with Aharonov-Bohm

While the evidence for dark matter continues to grow, the nature of dark matter remains a mystery. A dark U(1)D gauge theory can have a small kinetic mixing with the visible photon which provides a portal to the dark sector. Magnetic monopoles of the dark U(1)D can obtain small magnetic couplings to our photon through this kinetic mixing. This coupling is only manifest below the mass of the dark photon; at these scales the monopoles are bound together by tubes of dark magnetic flux. These flux tubes can produce phase shifts in Aharonov-Bohm type experiments. We outline how this scenario might be realized, examine the existing constraints, and quantify the experimental sensitivity required to detect magnetic dipole dark matter in this novel way.

Line of magnetic monopoles and an extension of the Aharonov–Bohm effect

In the Landau problem on the two-dimensional plane, physical displacement of a charged particle (i.e., magnetic translation) can be induced by an in-plane electric field. The geometric phase accompanying such magnetic translation around a closed path differs from the topological phase of Aharonov and Bohm in two essential aspects: The particle is in direct contact with the magnetic field and the geometric phase has an opposite sign from the Aharonov–Bohm phase. We show that magnetic translation on the two-dimensional cylinder implemented by the Schrödinger time evolution truly leads to the Aharonov–Bohm effect. The magnetic field normal to the cylinder’s surface corresponds to a line of magnetic monopoles of uniform density whose simulation is currently under investigation in cold atom physics. In order to characterize the quantum problem, one needs to specify the value of the magnetic flux (modulo the flux unit) that threads but not in touch with the cylinder. A general closed path on the cylinder may enclose both the Aharonov–Bohm flux and the local magnetic field that is in direct contact with the charged particle. This suggests an extension of the Aharonov–Bohm experiment that naturally takes into account both the geometric phase due to local interaction with the magnetic field and the topological phase of Aharonov and Bohm.

Revisiting the Marton, Simpson, and Suddeth experimental confirmation of the Aharonov–Bohm effect

We perform an “archeological” study of one of the original experiments used as evidence for the static, time-independent Aharonov–Bohm effect. Since the experiment in question [1] involved a time varying magnetic field we show that there are problems with the explanation of this experiment as a confirmation of the static Aharonov–Bohm effect – specifically the previous analysis ignored the electric field which arises in conjunction with a time-varying magnetic flux. We further argue that the results of this experiment do in fact conform exactly to the recent prediction [2,3] of a cancellation between the magnetic and electric phase shifts for the time-dependent Aharonov–Bohm effect. To resolve this issue a new time-dependent Aharonov–Bohm experiment is called for.

Non-reciprocal phase shift induced by an effective magnetic flux for light

Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials.

Nonlocal phases of local quantum mechanical wavefunctions in static and time-dependent Aharonov–Bohm experiments

We show that the standard Dirac phase factor is not the only solution of the usual gauge transformation equations. The full form of a general gauge function (that connects systems that move in different sets of scalar and vector potentials), apart from Dirac phases (spatial or temporal integrals over potentials), also contains terms of classical fields that act nonlocally (in spacetime) on the local solutions of the time-dependent Schrödinger equation. As a result, the phases of wavefunctions in the Schrödinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in specific ways that are fully explored. These contributions go beyond the usual Aharonov–Bohm effects (magnetic or electric). (i) Application to cases of particles passing through full static magnetic or electric fields leads to cancellations of Aharonov–Bohm phases at the observation point; these cancellations are linked to behaviors at the semiclassical level (i.e. the old Werner and Brill experimental observations, or their ‘electric analogs’—or to more recent reports of Batelaan and Tonomura) but are shown to be far more general (true not only for narrow wavepackets but also for completely delocalized (spread-out) quantum states). By using these cancellations, certain previously unnoticed sign-errors in the literature are corrected. (ii) Application to time-dependent situations provides a remedy for erroneous results in the literature (concerning an uncritical use of Dirac phase factors) and leads to phases that contain an Aharonov–Bohm part and a field-nonlocal part: their competition is shown to recover relativistic causality in earlier ‘paradoxes’ (such as the van Kampen thought-experiment), while a more general consideration indicates that the temporal nonlocalities found here demonstrate in part a causal propagation of phases of quantum mechanical wavefunctions in the Schrödinger picture. This may open a new and direct way to address time-dependent double-slit experiments and the associated causal issues.

Two-Slit and Aharonov-Bohm Experiments in Magnetic Field

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. In such a case the electron moving in the magnetic field produces so called synchrotron radiation. In other words the photons are emitted from the points of the electron trajectory and it means that the trajectory of electron is visible in the synchrotron radiation spectrum. The axiomatic system of quantum mechanics does not enable to define the trajectory of the elementary particle. The two-slit experiment and AB experiment in a magnetic field was never performed and it means that they are the missing experiments of quantum mechanics. The extension of the discussion to the cosmical rays moving in the magnetic field of the Saturn magnetosphere and its rings is mentioned. It is related to the probe CASSINI. The solution of the problem in the framework of the hydrodynamical model of quantum mechanics and the nonlinear quantum mechanics is also mentioned.

Electron lifetime in Luttinger liquids

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp(-t/\tau_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys $\tau_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T\tau_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.

Domain-Wall Induced Phase Shifts in Spin Waves

We study the interaction between two important features of ferromagnetic nanoparticles: magnetic domain walls and spin waves. Micromagnetic simulations reveal that magnetostatic spin waves change their phase as they pass through domain walls. Similar to an Aharonov-Bohm experiment, we suggest to probe this effect by splitting the waves on different branches of a ring. The interference of merging waves depends on the domain walls in the branches. A controlled manipulation of spin-wave phases could be the first step towards nanoscaled ferromagnetic devices performing logical operations based on spin-wave propagation.

Novel interference effects and a new quantum phase in mesoscopic systems

Mesoscopic systems have provided an opportunity to study quantum effects beyond the atomic realm. In these systems quantum coherence prevails over the entire sample. We discuss several novel effects related to persistent currents in open systems which do not have analogues in closed systems. Some phenomena arising simultaneously due to two non-classical effects namely, Aharonov-Bohm effect and quantum tunneling are presented. Simple analysis of sharp phase jumps observed in double-slit Aharonov-Bohm experiments is given. Some consequences of parity violation are elaborated. Finally, we briefly describe the dephasing of Aharonov-Bohm oscillations in Aharonov-Bohm ring geometry due to spin-flip scattering in one of the arms. Several experimental manifestations of these phenomena and their applications are given.

Scalar Aharonov-Bohm effect with longitudinally polarized neutrons

In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a ``dual'' scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper.

A unified approach to Aharonov-Bohm, Aharonov-Casher and which-path experiments

A unified approach to Aharonov-Bohm, Aharonov-Casher and which-path experiments is presented, using an enlarged Hilbert space. This Hilbert space contains quasi-periodic Aharonov-Bohm wavefunctions R(x+2) = R(x)exp(i) with various values of . Thus it can describe which-path Aharonov-Bohm experiments where the phase is uncertain due to decoherence that occurs as a result of the observation of the paths of the electric charges. The same Hilbert space contains quasi-periodic Aharonov-Casher wavefunctions which describe magnetic flux tubes winding around an electric charge and which are related through a Fourier transform to the Aharonov-Bohm wavefunctions. The duality between these two phenomena is discussed. The decoherence occuring in which-path experiments is studied quantitatively. Magnetic and electric superselection rules, appropriate for the Aharonov-Bohm and Aharonov-Casher experiments correspondingly, are also discussed.

Generalized Aharonov-Bohm effect, homotopy classes and Hausdorff dimension

We suggest as gedanken experiment a generalization of the Aharonov-Bohm experiment, based on an array of solenoids. This experiment allows us in principle to measure the decomposition into homotopy classes of the quantum mechanical propagator. This yields information on the geometry of the average path of propagation and allows us to determine its Hausdorff dimension.

Aharonov-Bohm order parameters for non-Abelian gauge theories.

The Aharonov-Bohm effect has been invoked to probe the phase structure of a gauge theory. Yet in the case of non-Abelian gauge theories, it proves difficult to formulate a general procedure that unambiguously specifies the realization of the gauge symmetry, e.g. the unbroken subgroup. In this paper, we propose a set of order parameters that will do the job. We articulate the fact that any useful Aharonov-Bohm experiment necessarily proceeds in two stages: calibration and measurement. World sheets of virtual cosmic string loops can wrap around test charges, thus changing their states relative to other charges in the universe. Consequently, repeated flux measurements with test charges will not necessarily agree. This was the main stumbling block to previous attempts to construct order parameters for non-Abelian gauge theories. In those works, the particles that one uses for calibration and subsequent measurement are stored in {\em separate} ``boxes''. By storing all test particles in the {\em same} ``box'', we show how quantum fluctuations can be overcome. The importance of gauge fixing is also emphasized.

Quantum Particle on a Rotating Loop: Topological Quenching due to a Coriolis-Aharonov-Bohm Effect.

A particle is assumed to move along a one-dimensional loop such as an ellipse that rotates in a plane. Because of the centrifugal force the particle is subjected to a symmetric double-well potential. Classically, the Coriolis force does not affect the motion of the particle, whereas the corresponding term in the Lagrangian influences the properties of the quantum system: its ground state turns out to be degenerate for a discrete set of angular velocities. The analogy between a constant magnetic field and a uniform rotation is used to propose, in addition, a variant of the Aharonov-Bohm experiment, which can be performed also with neutral particles.

Path-integral treatment of ring-shaped topological defects

Explicit path integration is carried out in a space with a ring-shaped topological defect using toroidal coordinates. The toroidal Aharonov-Bohm experiment is taken as an example.

The double slit experiment, the Aharonov-Bohm effect, and a new quantum potential theory: Towards a realistic interpretation of quantum mechanics

In this paper, a new proposal of the quantum potential theory is presented, along with a discussion of the two-slit interference experiment and the Aharonov-Bohm effect, which are explicitly calculated within the scheme adopted. The present formulation holds the notion of particle trajectory and follows the interpretation suggested by de Broglie and Bohm, the quantum potential being a manifestation of the quantum wave. This wave always satisfies the Schrodinger equation and is considered as areal and separate entity from the particle with which is associated. In our approach we try to circumvent some conceptual difficulties that prevent the de Broglie-Bohm's theory from fulfilling a complete objective program. New effects are predicted, specially for the Aharonov-Bohm experiment in the regime of high magnetic fields, and a setup for their detection is proposed.