Physicists have measured ‘negative time’ in the lab

As Homer tells us, Odysseus made an epic journey, against the odds, from Troy to his home in Ithaca. He visited many lands, but mostly dwelt with the nymph Calypso on her island.

We can imagine that his wife, Penelope, would have asked him about that particular time. Odysseus might have replied, “It was nothing. In fact, it was less than nothing. Negative five years I dwelt with Calypso. How else could I have arrived home after only ten years? If you don’t believe me, ask her.”

Quantum particles, it turns out, are just as wily as Odysseus, as we have shown in an experiment published in Physical Review Letters. Not only can their arrival time suggest that they dwelt with other particles for a negative amount of time, but if one asks those other particles, they will corroborate the story.

Photons dwelling with atoms

Our experiment used photons – quantum particles of light – and the against-the-odds journey they must undertake to pass straight through a cloud of rubidium atoms.

These atoms have a “resonance” with the photons, meaning the energy of the photon can be transferred temporarily to the atoms as an atomic excitation. This allows the photon to “dwell” in the atomic cloud for a time before being released.

For this resonance to be effective, the photon must have a well-defined energy, matching the amount of energy required to put a rubidium atom into an excited state.

But, by a form of Heisenberg’s famous uncertainty principle, if the energy of the photon is well defined then its timing must be uncertain: the pulse of light the photon occupies must have a long duration. This means we can’t know exactly when the photon enters the cloud, but we can know on average when it enters.

If a photon like this is fired into the cloud, the most likely outcome is that its energy will be transferred to the atoms, and then re-emitted as a photon travelling in a random direction. In such cases, the photon is scattered, and fails to arrive at its Ithaca.

Photon arrival times

But if the photon does make it straight through, a strange thing happens. Based on the average time when the photon enters the cloud, one can calculate the expected average time it would arrive at the far side of the cloud, assuming it travels at the speed of light (as photons usually do).

What one finds is that the photon actually arrives far earlier than that. In fact, it arrives so early it appears to have spent a negative amount of time inside the cloud – to exit, on average, before it enters.

This effect has been known for decades and was observed in a 1993 experiment. But physicists had mostly decided not to take this negative time seriously.

That’s because it can be explained by saying that only the very front of the long-duration pulse makes it straight through the atomic cloud, while the rest is scattered. This leads to a successful (non-scattered) photon arriving earlier than would be naively expected.

Asking the atoms

However, Aephraim Steinberg, one of the authors of that 1993 paper, was not so quick to accept this dismissal of the negative time as an artefact. In his laboratory at the University of Toronto, he wanted to find out what happened if one queried the rubidium atoms in the cloud to find out how long the photon had spent dwelling among them as an excitation. After an initial experiment with inconclusive results, he asked me, as a quantum theorist, for help in working out what to expect.

When we talk of querying the atoms, what this means in practice is continuously making a measurement on the atoms while the photon is passing through the cloud, to probe whether the photon’s energy is currently dwelling there. But there is a subtlety here: measurements in quantum physics inevitably disturb the system being measured.

If we were to make a precise measurement of whether the photon is dwelling in the atoms, at each instant of time, we would prevent the atoms from interacting with the photon. It is as if, merely by watching Calypso closely, we would stop her getting her hands on Odysseus (or vice versa). This is the well known quantum Zeno effect, which would destroy the very phenomenon we want to study.

Our experiment

The solution is to make, instead, a very imprecise (but still very accurately calibrated) measurement. That is the price paid to keep the disturbance negligible. Specifically, we fired a weak laser beam – unrelated to the single photon pulse – through the cloud of atoms, and measured small changes in the phase of the beam’s light to probe whether the atoms were excited.

Any single run of the experiment gives only a very rough indication of whether the photon dwelt in the atoms, but averaging millions of runs yields an accurate dwell time.

Amazingly, the result of this weak measurement of dwell time, when the photon goes straight through the cloud, exactly equals the negative time suggested by the photons’ average arrival time. Prior to our work, no-one suspected that these two times, measured in entirely different ways, would be equal.

Crucially, the negative value of the weakly measured dwell time cannot be explained by imagining that only the front of the photon’s pulse gets through, unlike the time inferred from the arrival time.

So what does this all mean? Is a time machine just around the corner?

Sadly, no. Our experiment is fully explained by standard physics.

But it does show that negative dwell time is not an artefact. However paradoxical it may seem, it has a directly measurable effect on the atomic cloud that the photon traverses. And it reminds us that there are still lands to discover on the odyssey that is quantum research.