Not every day does “time” get into misbehavior, but in a new experiment, photons passing through a fog of ultracold rubidium-85 atoms were shown to spend a negative duration in an excited atomic state. The outcome, confirmed by beautifully sensitive weak measurements, adds a new nuance to the already bizarre landscape of quantum mechanics and suggests that there are deeper relations between light–matter interactions and the intangible property of contextuality.
The result came out of research by Aephraim Steinberg and his team at the University of Toronto, working in conjunction with theorists such as Howard Wiseman of Griffith University. The team’s approach was to fire isolated photons into a cloud of atoms and monitor continuously for excitations in the atoms with a weak probe beam. They could estimate the mean time spent by a transmitted photon in an excited atomic state by summing the probe’s phase shifts over time. The unexpected twist was that the calculations indicated and the experiment verified that this excitation time could be negative, with results like (–0.82 ± 0.31)𝜏₀ for narrowband pulses, where 𝜏₀ is the necessarily positive average excitation time for all photons.
Wiseman makes a distinction between this quantity and the more common group delay, which may be negative in some dispersive media. In group delay, the illusion is created because the front of a pulse departs before the peak arrives, with the peak itself usually absorbed or scattered. In this case, though, the measurement is aimed at the true time a transmitted photon spends in the medium, whether it be exciting an atom or not a nuance that involved discarding the long-standing assumption that excited photons are inevitably lost to scattering. “Forward-scattered photons actually contribute a lot to the average measurement,” Wiseman observes.
The experimental apparatus required ultimate stability. Two opposing laser beams interacted with atoms cooled to 60–70 µK: one transported the photons to be tested, the other executed the weak measurement by measuring minuscule phase changes caused by atomic excitations. The weak measurement methodology based on the theory established by Yakir Aharonov and co-workers enables partial information extraction without quantum state collapse, making it perfect for measuring transient effects such as excitation times.
Aside from the temporal weirdness, the result crosses with the idea of contextuality, a characteristic of quantum systems where measurement results vary based on the collection of other compatible measurements that are made. Newcastle University’s Jonte Hance, not participating in the research, warns against taking “negative time” too literally while pointing to its quantum importance: contextuality, a resource that can impart quantum computational superiority over classical approaches, is signaled by anomalous weak values of excitation time. Contextuality has been demonstrated to be required for beating classical algorithms in measurement-based quantum computing, connecting this optical demonstration to future architectures.
The physical basis for the negative time is related to interference among probability amplitudes of various paths of photons those that excite atoms and get forward-scattered, and those which do not. In quantum optics, this type of interference can generate counterintuitive values for a measurement, such as weak values that fall outside of the eigenvalue range. Analogous effects are seen in man-made photonic systems where group delay is controlled, e.g., slow-light materials or resonator arrays, but again the effect is inherently built into the light–atom coupling.
From a detection perspective, the measurement needed to resolve the weak probe’s signal from noise, similar to issues with ultrastrong coupling photodetection where bare photon operators are no longer representative of observable excitations. In either instance, the relevant operators are given relative to the dressed eigenstates of the interacting full system, so that the measured quantities are representative of physical, detectable phenomenon as opposed to mathematical artifacts.
Steinberg concedes that previous work had the tendency to “sweep under the rug” the negative numbers that occurred in theory and simply regarded them as an artifact of the formalism. The new findings compel a rethinking: “Those negative numbers appear to have more physical significance than we would previously have attributed to them,” he says. That reassessment could lead to avenues of taking advantage of such anomalous times in quantum sensing, in which sensitivity can be increased by leveraging interference effects in weak measurements.
For quantum researchers, the experiment serves as a reminder that even simple quantities such as “time spent” in a state can baffle classical intuition when operationally defined in the quantum regime. And for theorists probing the foundations, it gives an experimental grounding to connect temporal anomalies, weak measurement theory, and contextuality three threads that, braided together, may demonstrate new possibilities in quantum information science.
