A self-interfering clock as a “which path” witness

Abstract

We experimentally demonstrate a new interferometry paradigm: a self-interfering clock. We split a clock into two spatially separated wave packets, and observe an interference pattern with a stable phase showing that the splitting was coherent, i.e., the clock was in two places simultaneously. We then make the clock wave packets "tick" at different rates to simulate a proper time lag. The entanglement between the clock's time and its path yields "which path" information, which affects the visibility of the clock's self-interference. By contrast, in standard interferometry, time cannot yield "which path" information. As a clock we use an atom prepared in a superposition of two spin states. This first proof-of-principle experiment may have far-reaching implications for the study of time and general relativity and their impact on fundamental quantum effects such as decoherence and wave packet collapse. Two-slit interferometry of quanta, such as photons and electrons, figured prominently in the Bohr-Einstein debates on the consistency of quantum theory [1, 2]. A fundamental principle emerging from those debates-intimately related to the uncertainty principle-is that "which path" information about the quanta passing through slits blocks their interference. At the climax of the debates, Einstein claimed that a clock, emitting a photon at a precise time while being weighed on a spring scale to measure the change in its massenergy, could evade the uncertainty principle. Yet Bohr showed that the clock's gravitational redshift introduced enough uncertainty in the emission time to satisfy the uncertainty principle. Inspired by the subtle role time may play in quantum mechanics, we have now sent a clock through a spatial interferometer. The proof-of-principle experiment described below presents clock interferometry as a new tool for studying the interplay of general relativity[3] and quantum mechanics [4].Quantum mechanics cannot fully describe a self-interfering clock in a gravitational field.If the paths of a clock through an interferometer have different heights, then general relativity predicts that the clock must "tick" slower along the lower path. However, time in quantum mechanics is a global parameter, which cannot differ between paths. In standard interferometry (e.g.[5]), a difference in height between two paths affects their relative phase and shifts their interference pattern; but in clock interferometry, a time differential between paths yields "which path" information, degrading the visibility of the interference pattern [6]. It follows that, while standard interferometry may probe general relativity [7][8][9] In principle, any system evolving with a well defined period can be a clock. In our experiment, we utilize a quantum two-level system. Specifically, each clock is a 87 Rb atom in a superposition of two Zeeman sublevels, the m F = 1 and m F = 2 sublevels of the F = 2 hyperfine state.The general scheme of the clock interferometer is shown in Fig. 1 atoms 90 µm below the chip surface). Initially, af...

Bi-chromatic adiabatic shells for atom interferometry

“…. Close to resonance, m F remain good quantum numbers and we can find the eigenenergies: For small Ω 2,1 , Ω 1,2 the time averaged potential resulting from equation (C.7) is well approximated by equation (3). Notice however that we did not account for the spatial dependence of the quadrupole field, since we have assumed a homogeneous field aligned with e ẑ , which is only a fair approximation for small clouds at the bottom of the trap.…”

Time dilation in quantum systems and decoherence

“…The effect described in [1] for a two-level system was recently experimentally simulated with a BEC [26]. In this experiment, a Stern-Gerlach type matter-wave interferometer on an atom chip was utilized, and an external inhomogeneous magnetic field was applied to simulate the effect of time dilation on the spin precession of the system.…”

“…. In a recent experiment, the above predictions have been simulated in a BEC interference setup in the presence of inhomogeneous magnetic fields [26].…”

Erratum and Addendum: Atom interferometry and the gravitational redshift (2011 Class. Quantum Grav. 28 145018)

“…As a matter of interest, we add that a version of the experiment proposed in [1] has been recently performed and is reported in [2]. Because of the experimental difficulty of detecting the gravitational slowing down of clocks within the small size of their atom chip, the authors of [2] simulate gravity by introducing a relative slowing down of clocks in one interferometric arm using a magnetic field gradient.…”