In the world of quantum technology, measuring with extreme accuracy is key. Despite impressive developments, state-of-the-art matter-wave interferometers and clocks still operate with collections of independent atoms, and the fundamental laws of quantum mechanics limit their precision.
One way to get around this fundamental quantum fuzziness is to entangle the atoms or make them talk so that one cannot independently describe their quantum states. In this case, it is possible to create a situation where the quantum noise of one atom in a sensor can be partially canceled by the quantum noise of another atom such that the total noise is quieter than one would expect for independent atoms. This type of entangled state is called a “squeezed state,” which can be visualized as if one had made a clock hand narrower to tell the time more precisely, a precision that comes at the expense of making the fuzziness along the clock hand worse. However, preparing spin-squeezed states is no easy feat.
Up to now, there have been two leading ways to generate squeezed states, using atoms that interact with light. One way, unitary evolution, is by transforming an initially uncorrelated (not entangled) state into a spin-squeezed state via dynamical evolution via a specific type of unitary interaction. One can imagine the initially uncorrelated state as a round piece of dough where your hand slowly squeezes the dough in one direction while making the other direction wider.
The other way is to perform quantum nondemolition measurements (QND) that allow one to pre-measure the quantum noise and subtract it from the final measurement outcome. The QND approach has currently realized the largest amounts of observed squeezing between the two methods, but it is not clear which protocol is actually optimal, given fundamental experimental constraints, or even if it would be better to use both protocols at the same time.
This is why JILA and NIST Fellows and University of Colorado Boulder Physics professors Ana Maria Rey and James K. Thompson and their teams wanted to guide the community on which protocol is best to use under fundamental and realistic experimental conditions. Their results, published in Physical Review Research, revealed that when measurement efficiency is greater than 19%, the QND measurement protocol outperformed unitary dynamical evolution. This finding can have big implications for quantum metrology.
“We were able to build a sort of map, where, if you have this experiment with these specific parameters, here’s what you should do,” explains first author former JILA graduate student Diego Barberena, now a postdoc at the University of Cambridge. “I think that it's beneficial to have all the results together in a single place because they are scattered all over the literature and written in ways that may be easier to parse for some physicists but not others, given the technical language of each different experiment. So, we’re happy to give people a paper where all protocols are in one place.”
A Tale of Two Methods
Squeezing is related to the Heisenberg Uncertainty Principle, which limits how accurately a researcher can measure two related properties simultaneously—such as the momentum and position of a particle—where the more researchers know about one parameter than the other. Squeezing overcomes this limitation by making one of these variables more uncertain, or less known, allowing a more accurate measurement of one of the variables.
Within quantum research, unitary evolution and QND are two of the most commonly used methods to create spin-squeezing in atoms. Both revolve around an ensemble of atoms placed in an optical cavity. By measuring the light leaking out of the cavity in QND experiments, the researchers can determine if the atoms are in a spin-squeezed state or not.
In the unitary evolution method, atoms interact by exchanging photons inside the optical cavity while swapping their internal levels or spins, a process that allow them to evolve in a controlled, predictable way which shapes their noise distribution in a specific desirable way: from a circle to an ellipse. This process is governed by a well-defined set of rules that describe the system's evolution, and no external measurements are involved, meaning the researchers didn’t observe or measure the light leakage during the experiment.
“You send the laser into the system, and then you let the atoms do their own thing,” says Barberena. “We call it unitary evolution because the atoms are evolving via their interactions. They are already in a setup where the evolution alone would help enhance measurement precision.”
In contrast, QND uses a different method to measure quantum dynamics.
Thompson elaborates, “QND measurements are very special. They involve measuring the light that leaks from the optical cavity to gather information about how many atoms are in which quantum state without knowing which atoms are in which quantum state.”
This measurement projects or collapses the original quantum state into a state with less quantum noise, with the measurement outcome telling the experimentalist which quantum state they have available to use.
“We have used both methods to generate squeezing here at JILA and NIST. Given that both approaches seem to work, it would be great to understand with certainty which one is the best one to use,” adds Rey.
Trading Off Efficiencies
To compare the two methods, researchers developed a detailed simulation that modeled how atoms interact with a shared light field inside an optical cavity. In this simulation, they accounted for real-world factors such as quantum noise, imperfect optical cavities, decoherence, and a crucial parameter known as quantum efficiency. Quantum efficiency refers to the fraction of all the information that is accessible to the experimentalist.
“Quantum efficiency is basically a quantity describing how well you can measure a system,” adds former JILA graduate student Anjun Chu, second author and now a postdoctoral fellow at the University of Chicago. “It revolves around the percentage of light leakage that can be measured out of the cavity. The efficiency is one, if you can perfectly detect all photons coming out of the cavity. In this case, it would be better to turn off unitary evolution and focus only on QND. If the efficiency is zero, you’re measuring no light, so you get no information from a measurement. In this case, it would be better to suppress the light leakage and let the system evolve near unitary. Between zero and one, there is a combination of measurement and unitary evolution. We are trying to determine which of the two methods or their combination would win.”
The simulation tested different levels of quantum efficiency to see how both methods performed under various conditions. The results showed that when quantum efficiency was above 19%, the QND method outperformed unitary evolution in generating spin-squeezed states. This was because the high efficiency allowed the QND process to gather enough information from the system to reduce uncertainty and improve precision. Below that threshold, unitary evolution was more effective.
Thompson notes, “In previous experimental work, we achieved net quantum efficiencies above 30%, and it is just a matter of technology development to achieve >90%. However, in quantum sensing, one often juggles many competing requirements that might make unitary evolution more advantageous. Now we know when to switch between one approach versus the other.”
The researchers also found that the combination of QND and unitary evolution did not provide the distinct advantage they expected, suggesting that one or the other method should be favored instead.
Improvements in Precision Measurement
This result is significant for quantum metrology, where the goal is to achieve more accurate measurements than the standard quantum limit (SQL)—the fundamental limit of precision achievable with uncorrelated particles—which can be achieved using spin-squeezed states.
“I think this paper is a helpful guideline for future experiments,” says Chu. “A researcher is going to want to know what the best way is to generate spin-squeezing. We give a very straightforward answer: look at the quantum efficiency of the experiment.”
This research was supported by the National Science Foundation (NSF), the NSF-Funded center Q-SEnSE and NIST.
Written by Kenna Hughes-Castleberry, JILA Science Communicator
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