Physicists in Australia and the UK have found a new way to manipulate Heisenberg’s uncertainty principle in experiments on the vibrational mode of a trapped ion. Although still at the laboratory stage, the work, which uses tools developed for error correction in quantum computing, could lead to improvements in ultra-precise sensor technologies like those used in navigation, medicine and even astronomy.
“Heisenberg’s principle says that if two operators – for example, position x and momentum, p – do not commute, then one cannot simultaneously measure both of them to absolute precision,” explains team leader Ting Rei Tan of the University of Sydney’s Nano Institute. “Our result shows that one can instead construct new operators – namely ‘modular position’ x̂ and ‘modular momentum’ p̂. These operators can be made to commute, meaning that we can circumvent the usual limitation imposed by the uncertainty principle.”
The modular measurements, he says, give the true measurement of displacements in position and momentum of the particle if the distance is less than a specific length l, known as the modular length. In the new work, they measured x̂ = x mod lx and p̂ = p mod lp, where lx and lp are the modular length in position and momentum.
“Since the two modular operators x̂ and p̂ commute, this means that they are now bounded by an uncertainty principle where the product is larger or equal to 0 (instead of the usual ℏ/2),” adds team member Christophe Valahu. “This is how we can use them to sense position and momentum below the standard quantum limit. The catch, however, is that this scheme only works if the signal being measured is within the sensing range defined by the modular lengths.”
The researchers stress that Heisenberg’s uncertainty principle is in no way “broken” by this approach, but it does mean that when observables associated with these new operators are measured, the precision of these measurements is not limited by this principle. “What we did was to simply push the uncertainty to a sensing range that is relatively unimportant for our measurement to obtain a better precision at finer details,” Valahu tells Physics World.
This concept, Tan explains, is related to an older method known as quantum squeezing that also works by shifting uncertainties around. The difference is that in squeezing, one reshapes the probability, reducing the spread in position at the cost of enlarging the spread of momentum, or vice versa. “In our scheme, we instead redistribute the probability, reducing the uncertainties of position and momentum within a defined sensing range, at the cost of an increased uncertainty if the signal is not guaranteed to lie within this range,” Tan explains. “We effectively push the unavoidable quantum uncertainty to places we don’t care about (that is, big, coarse jumps in position and momentum) so the fine details we do care about can be measured more precisely.
“Thus, as long as we know the signal is small (which is almost always the case for precision measurements), modular measurements give us the correct answer.”
Repurposed ideas and techniques
The particle being measured in Tan and colleagues’ experiment was a 171Yb+ ion trapped in a so-called grid state, which is a subclass of error-correctable logical state for quantum bits, or qubits. The researchers then used a quantum phase estimation protocol to measure the signal they imprinted onto this state, which acts as a sensor.
This measurement scheme is similar to one that is commonly used to measure small errors in the logical qubit state of a quantum computer. “The difference is that in this case, the ‘error’ corresponds to a signal that we want to estimate, which displaces the ion in position and momentum,” says Tan. “This idea was first proposed in a theoretical study.”
Towards ultra-precise quantum sensors
The Sydney researchers hope their result will motivate the development of next-generation precision quantum sensors. Being able to detect extremely small changes is important for many applications of quantum sensing, including navigating environments where GPS isn’t effective (such as on submarines, underground or in space). It could also be useful for biological and medical imaging, materials analysis and gravitational systems.
Their immediate goal, however, is to further improve the sensitivity of their sensor, which is currently about 14 x10-24 N/Hz1/2, and calculate its limit. “It would be interesting if we could push that to the 10-27 N level (which, admittedly, will not be easy) since this level of sensitivity could be relevant in areas like the search for dark matter,” Tan says.
Another direction for future research, he adds, is to extend the scheme to other pairs of observables. “Indeed, we have already taken some steps towards this: in the latter part of our present study, which is published in Science Advances, we constructed a modular number operator and a modular phase operator to demonstrate that the strategy can be extended beyond position and momentum.”
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