The best clock in the world has no hands, no pendulum, no face or digital display. It is made of ultra-cold atoms trapped by light. This atomic clock is so precise that, had it begun ticking when Earth formed billions of years ago, it would not yet have gained or lost a second. Nonetheless, this incredible clock, and all atomic clocks, operate with collections of independent atoms, and as a result, their precision is limited by the fundamental laws of quantum mechanics. One way to get around this fundamental quantum imprecision is to entangle the atoms, or make them talk, in such a way that one cannot describe the individual atoms’ quantum states independently of one another. In this case it is possible to create the situation where the quantum noise of one atom in the clock 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. One type of entangled state is called a “squeezed state”, which can be visualized as if one had shaped the quantum noise in a way that is narrower in one direction at the expense of making the fuzziness in the adjacent direction worse. Squeezed states have been realized in several labs around the world at groundbreaking precision levels recorded by several physics institutes, including at JILA in Boulder, Colorado. However, squeezing is experimentally challenging to create and there is a need for a variety of “flavors” of squeezing for different types of quantum sensing tasks.
A new approach recently described in Physical Review Letters explores a new way to generate squeezing that is exponentially faster than previous experiments and generates a new flavor of entanglement: two-mode squeezing—a type of entanglement that is thought to be used for improving the best atomic clocks and for sensing how gravity changes the flow of time. This promising new approach was developed by a collaboration of JILA and NIST Fellows Ana Maria Rey and James K. Thompson, and their team members, along with Bhuvanesh Sundar, a former postdoctoral researcher at JILA now at Rigetti Computing, and former JILA research associate Dr. Robert Lewis-Swan, now an Assistant Professor at the University of Oklahoma.
Two-mode Squeezing
Squeezing is related to the Heisenberg Uncertainty Principle, which limits how accurately a researcher can measure two related properties—such as the momentum and position of a particle—such that researchers can only know more about either of the parameters than the other. Squeezing overcomes this limitation by making one of these variables more uncertain, allowing a more accurate measurement for one of the variables. “Squeezing has been used to improve the LIGO gravitational wave interferometer and the HAYSTAC dark matter detector,” Rey explained. “It would be great to now leverage entanglement for a quantum enhancement in a state-of-the-art atomic clock”.
As seasoned researchers looking at quantum entanglement, Rey’s and Thompson’s teams, along with Lewis-Swan, understood how important it is to develop new forms of squeezing, providing new tools for canceling noise sources and enabling more precise atomic clocks for more advanced technologies and probing the universe. “The idea was to design a protocol that generates entangled states with minimal fuss, that actually sort of stands up to challenges of typical experiments,” Lewis-Swan added. “It actively considers typical technical constraints present in the lab. Our guiding principle was that the less things we need to do in the experiment, the better, and what is simpler than having the atoms just sit in the dark talking to each other. By reducing the number of manipulations, we reduce the ability of unwanted noise to creep in.”
JILA has already generated record levels of spin squeezing. As Thompson explained: “My students have made squeezed state in that lab that have blown past the Standard Quantum Limit using light-matter interactions in optical cavities, but we work hard to achieve it by applying and measuring laser light.” In this new study, the researchers were curious if there were new squeezing approaches where the atoms just sit in the dark, swapping photons inside the cavity. By their predictions, the researchers believed this would reduce the experimental challenges for creating squeezing by orders of magnitude. “And not only that, but instead of just having vanilla-flavored squeezing, now we could have double-dutch chocolate squeezing called two-mode squeezing!” Thompson elaborated.
This type of squeezing suggested a new way to compare the accuracy of quantum sensors. As Lewis-Swan stated, “One of the outstanding challenges right now in quantum science is developing new ways to generate entanglement to build better quantum sensors, such as atomic clocks. There are many ways people have thought about creating one-mode squeezing relevant for clocks, but two-mode squeezing would enable one to compare the ticking rate of atomic clocks more precisely to measure how general relativity affects the rate at which time passes at different heights in Earth’s gravity.” This comparison can help with many different aspects of quantum sensing. “Instead of comparing the combined rate at which two clocks are both ticking, what you can compare now is the difference in the ticking rates more precisely,” Lewis-Swan continued. “This can be really useful to cancel common noise. And essentially, via the squeezing process, we can entangle two ensembles and use each of them as a clock with superb relative performance.”
Entangling atomic pairs in two different ensembles
To generate squeezing expeditiously, the researchers leveraged a process known as bosonic pair creation. “The bosonic pair creation idea is well known in quantum physics,” stated Lewis-Swan. “It’s decades old and is pivotal for a lot of different applications in quantum science, from quantum communication to metrology and information processing. Here, we’re leveraging bosonic stimulation, where once you produce one pair, it’s easier and easier to produce more pairs. So basically, the number of pairs increases exponentially fast, and those pairs are entangled in a very useful way.”
Bosonic pair production is important in several different subfields of physics. As Rey elaborated, “Indeed pair production appears in many contexts in physics and keeps finding a wide range of applications in quantum technologies. For example, it manifests in high-energy physics when electron-positron pairs are spontaneously created in the presence of a strong electric field. In general relativity, in the so-called Unruh thermal radiation—or generation of thermal radiation from vacuum when viewed in an accelerating reference frame.” Engineering pair creation in a fully controllable clock could therefore be fascinating and useful for many different applications.
Even though pair creation is well known, what was missing was a feasible mechanism to generate it in state-of-the-art clocks, and more importantly, how to take advantage of the generated squeezed states for metrology in the presence of real sources of decoherence that disrupt the utility of the prepared state. Within the collaboration, first author Bhuvanesh Sundar looked at this particular problem, and thanks to the resulting calculations, the researchers could map out the best operating regimes for which an experiment can generate squeezing. “The ultimate limit that one can achieve for squeezing is called the Heisenberg limit,” Sundar elaborated. “We calculated how much squeezing we can generate by balancing the amount of unwanted environmental noise that creeps into the system versus how much entanglement we can try and create. We found out that the optimal scaling using pair creation doesn’t quite reach the Heisenberg limit, but nevertheless it is still better than (or comparable to) other competitive protocols that researchers have used in the labs in the past.”
Beyond those calculations, the researchers also figured out multiple ways to take advantage of the squeezing. “In the past we have focused on finding ways to generate squeezing among a single large ensemble of atoms by having them essentially play catch with each other,” Lewis-Swan added. “One atom throws a photon into the cavity and another catches it. Here, the way we engineer pair production by using the internal electronic structure of the atoms leads us to naturally think about the atoms as being grouped into a pair of distinct ensembles that we can separately address. We can tune our system such that when an atom in one ensemble throws a photon it can only be caught by an atom in the other ensemble. This allows us to effectively make two entangled ensembles which can be used in parallel for precise measurements.”
The simplicity of the researchers’ protocol enables better scalability and facilitates experimental implementation, opening the door to advances in clock sensitivity and bandwidth, not only for improved traditional timekeeping applications, but also gravitational wave detection, precision tests of fundamental physics, and the search for new physics beyond the standard model.
Now that the protocol has been published, the researchers hope the next steps will be to test the protocol in a laboratory setting. “We would like to test these protocols in the lab,” Sundar added. “The ideas require minimal ingredients, so it should be possible in labs like Thompson’s. But you could also apply this to trapped ions or other systems that people use to build clocks.” As Thompson himself has had a history of working on squeezed states, he is looking forward to putting this new protocol into action. “It will be a lot of fun to think of these same ideas can be used to extend our recent squeezed matter-wave interferometer to make two-mode squeezed matter-wave interferometers for inertial sensing and gravimetry,” he stated. With atomic clocks and other quantum sensors being used around the world today, improving the sensitivity of these devices allows us to glean more information about our environment and can improve other technologies we use regularly in our society.
Written by Kenna Hughes-Castleberry, JILA Science Communicator