Macroscopic Test of the Aharonov-Bohm Effect

The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in type-I AB effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.

Figure 1

Force versus phase. Electrons can follow two paths in an electron interferometer (lines) enclosing a solenoid (circle). The Aharonov-Bohm interference fringes (Signal) are thought to be due to a multiplicative phase factor (a). A force can shift the electron wave packet and cause similar interference fringes (b). The difference is that for a force, the fringes do not extend beyond the electron coherence length.

Figure 2

Experimental schematic. A laser induced electron pulse passes between solenoids. A time delay measurement establishes the presence or absence of forces on the electron.

Figure 3

Delay times. No delay for 40 eV electrons is observed as a function of solenoidal current, signaling the absence of a force consistent with the Aharonov-Bohm prediction. A force necessary to explain the AB effect would produce delays indicated with the red solid line [Eq. (4)]. The square, the triangle, and the diamond data point each correspond to a time-of-flight spectrum (inset).

Figure 4

Energy-time delays. Electron arrival times as a function of energy follow a ballistic behavior. The diamond, the triangle, and the square data point each correspond to a time-of-flight spectrum (inset). The time delay sensitivity is sufficient to detect the presence of forces necessary to explain the AB effect.