Abstract
Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.
Highlights
The idea of time-domain interferometry can be traced back to the seminal paper by Moshinsky [2] on diffraction in time
In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time
The authors of Robert et al [12] were well aware of the theoretical difficulties one will encounter in a realistic modeling of their experiment
Summary
The idea of time-domain interferometry can be traced back to the seminal paper by Moshinsky [2] on diffraction in time. After (or before) having detected a photon one could perform a direct measurement of the atomic position, revealing location of the source at the moment of emission, and destroying the interference This was not a typical Young experiment, but rather its which-way version [13,14,15]. The authors of Robert et al [12] were well aware of the theoretical difficulties one will encounter in a realistic modeling of their experiment They wrote: “In conclusion it seems that an interference phenomenon characterized by a wavelength close to the Lyman α one does occur in the optical emission. 3. One should be able to distinguish between states inside and outside of the interaction zone, so there must exist at least one position state |3 , corresponding to the region of space where spontaneous emission occurs. The result is generic and should be observable in a large variety of quantum systems
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