VOLUME 71 19 JULY 1993 Nondispersive Phase of the Aharonov-Bohm ENect NUMBER 3 Gerald Badurek, ' Harald Weinfurter, Roland Gahler, Achim Kollmar, Stefan Wehinger, and Anton Zeilinger Institut fi ir Kernph'ysik, Technische Universitat Wien, A l02-0 Wien, Austria Institut fiir Experimentalphysik, Universitat Innsbruck, A 6020 Inn-sbruck, Austria Reaktorstation Garching d. Technische Universitat Mu'nchen, D-8046 Garching, Germany Institut fu rFestkor'perforschung, Forschungszentrum Ju lich, D'-5170 Ju'lich, Germany (Received 19 April 1993) An essential signature of the topological nature of all Aharonov-Bohm type phases is that they are nondispersive, i.e. , independent of the velocity (wavelength) of the interfering particles. This implies that an Aharonov-Bohm phase shift can greatly exceed the usual limit given by the coherence length of the interfering beams. We report the results of a polarized neutron experiment demonstrating this prop- erty for a spin-rotation analog of the scalar Aharonov-Bohm effect. PACS nUmbers: 03.65.Bz In 1959 Aharonov and Bohm [11 published their famous proposals on the influence of electromagnetic po- tentials in electron interference experiments, known since then as the Aharonov-Bohm (AB) eII'ects. Unlike classi- cal physics where potentials are considered merely as con- venient mathematical tools to calculate electromagnetic fields of force by solving Maxwell's equations, the AB eftects reveal the much deeper physical significance of po- tentials in quantum mechanics. They are illustrious ex- amples of quantum nonlocality, because they predict an observable phase shift of the electron's de Broglie wave packet which depends on fields in regions of space-time not accessible to the interfering electron. Hence there is no force acting on the particle and the phase shift is en- tirely due to nonzero potentials, namely, the vector poten- tial A(r) in the so-called magnetic (or "vector") AB eAect and the scalar potential p in the less often cited electric (or "scalar" ) AB eII'ect (Fig. 1). An essential feature of both Aharonov-Bohm eff'ects is their nondisper- sivity, which implies that none of the AB eA'ects should lead to any measurable positiona1 shift or spread of the electron wave packet. This is a consequence of the topo- logica1 nature of the eA'ect. Moreover, such a positional shift would provide a means to detect, by observing just one of the interfering beams, the presence of an elec- tromagnetic field without having to invoke the topology of the whole arrangement [2j. Therefore an AB phase shows up only as an overall phase factor of the wave packet and thus it is only observable in an interference experiment. We emphasize that in contrast a phase shift due to, say, transmission through a static potential well is VEC TOR AB- SCALAR AB- F= C TRO/V NEUTRON FIG. 1. The Aharonov-Bohm effects for electrons (top) and their analogs for neutrons (bottom). The solenoid used in the vector (or magnetic) AB effect for electrons (top left) is re- placed in its neutron counterpart by a line charge (bottom left). In the scalar AB effect a time-dependent Hamiltonian is provid- ed either by properly switched Faraday cages in the electron case (top right) or by switched magnetic fields in the neutron analog (bottom right). 0031-9007/93/71 (3)/307 (5) $06.00 1993 The American Physical Society 307