Shaking Schroedinger’s cat
You've probably heard about Schrödinger's cat, which famously is trapped in a box with a kill mechanism that is activated if a radioactive atom decays, releasing radiation. The act of looking in the box collapses the atom's wave function — the mathematical description of its state –from a "superposition" of states to a definite state, which either kills the cat or let's it live to see another day.
But did you know that if you peek into the cat box frequently — thousands of times a second — you can either delay the fateful choice or, conversely, accelerate it? The delay is known as the quantum Zeno effect and the acceleration as the quantum anti-Zeno effect.
The quantum Zeno effect was named by analogy with the arrow paradox conceived by the Greek philosopher Zeno: At any given instant of time, an arrow in flight is motionless; how then can it move? Similarly, if an atom could be continually measured to see if it is still in its initial state, it would always be found to be in that state.
Both the Zeno and an the anti-Zeno effects are real and happen to real atoms. But how does this work? How can measurement either delay or accelerate the decay of the radioactive atom? What is "measurement," anyway?
The physicist's answer is that in order to obtain information about a quantum system, the system must be strongly coupled to the environment for a brief period of time. So the goal of measurement is to obtain information, but the strong coupling to the environment means that the act of measurement also necessarily disturbs the quantum system.
But what if the system was disturbed but no information was passed to the outside world? What would happen then? Would the atom still exhibit the Zeno and anti-Zeno effects?
Kater Murch's group at Washington University in St. Louis has been exploring these questions with an artificial atom called a qubit. To test the role of measurement in the Zeno effects, they devised a new type of measurement interaction that disturbs the atom but learns nothing about its state, which they call a "quasimeasurement."
They report in the June 14, 2017, issue of Physical Review Letters that quasimeasurements, like measurements, cause Zeno effects. Potentially the new understanding of the nature of measurement in quantum mechanics could led to new ways of controlling quantum systems.
The quantum Zeno effect was first proposed as a thought experiment by the British mathematician Alan Turing in 1958, although it wasn't rigorously described until 1977 or observed in the laboratory until 1989.
The original explanation for the Zeno effect was that measurement of an atom in its excited state collapses it back onto its excited state, resetting the clock of its decay process. So if an atom is measured often enough, it will never decay to a lower energy state but instead remain 'frozen' in its excited state.
The opposite effect, in which frequent measurement accelerates decay, wasn't formulated until 1997. But this anti-Zeno effect is actually much more common in nature. Frequent measurements of a radioactive atomic nucleus or excited molecule, for example, speed up the emission of radiation or light.
In the meantime, another explanation for the effect has emerged. "Atomic decay rates depend on the density of possible energy states, or electromagnetic modes, at a given energy," Murch said." In order for the atom to decay, it must emit a photon into one of these modes. More modes means more ways to decay, and therefore faster decay."
Measurement disturbs the energy levels of the atom, and this disturbance shifts the energy levels in such a way that there are fewer electromagnetic modes at the appropriate energy, leading to the Zeno effect, or more modes at the appropriate energy, leading to the anti-Zeno effect.
"What stands out about this explanation," Murch sajd, "is that it is the disturbance and not the collapse that leads to the Zeno effects.
"Measurement is all about acquiring information about a system, but measurement invariably involves disturbance," Murch said. "So measurement means information gained and disturbance (back action)."
Murch's group, including graduate students Patrick Harrington and Jonathan Monroe, constructed experiments to provoke the Zeno effects and to nail down the roles of information and disturbance in creating them.
They used a thermal bath of photons centered at a specific energy to decrease or increase the density of electromagnetic states available to their artificial atom. They then used standard measurements to check on the state of the atom once every microsecond.
When the thermal bath of photons was centered at the same energy as the transition energy of the atom, the disturbance of the measurement reduced the average number of electromagnetic modes at the transition energy, slowing decay. When the thermal bath of photons was centered on an energy different from the transition energy of the atom, the measurements increased the number of electromagnetic modes available to the atom, accelerating decay.
"These measurements constitute the first observation of the two Zeno effects on a single quantum system," Murch said.
To study the role of information in the Zeno effects, the physicists turned to "quasimeasurement," the new type of measurement interaction that only disturbs.
Would quasimeasurements also cause the Zeno effects? "According to the original conception of the Zeno effect they should not, because there is no collapse back to the excited state. But the explanation of the effects that invokes the density of available states predicts they should still occur," Murch said.
"To be honest, we were not completely sure what we would find. But days of data taking conclusively showed that the quasimeasurements caused the Zeno effects in the same way as the usual measurements. This means it is really the disturbance of the measurement and not the collapse of the wave function that leads to these effects."
What does this mean for Schrödinger's cat? "The Zeno effect says that if we check on the cat, we reset the atom's decay clock, keeping the cat alive," said Harrington. "Unfortunately for the cat, frequent checks might also accelerate the atom's decay, killing the cat more quickly." In other words, the cat is subject to the Zeno effects.
"The twist, however, is that because the Zeno effects have to do with disturbance and not information," Harrington said, "it isn't even necessary to look inside the box to provoke them. The same effects will occur if you just shake the box."
This research was funded by NSF grant PHY-1607156 and ONR grant
No. 12114811. Murch also receives support from the Sloan Foundation.