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In a quest to build the most accurate quantum sensors in the world, scientists are constantly improving their performance. Making them more precise. More stable and reliable.��

But eventually, physical constraints will prevent further improvements.����

“You cannot pack more atoms in a quantum sensor because at some point, they start colliding and disturbing each other, affecting the performance of the sensor,” says Ana Maria Rey, a JILA and NIST fellow and professor adjoint of physics at the �鶹ӰԺ.��

Even the most precise sensors in the world are not fully isolated but subject to noise — subtle disturbances from the environment like vibrations, electromagnetic fields or temperature changes.��

So, Rey along with JILA Fellow James ��K. Thompson and colleagues from the Niels Bohr Institute, the Joint Quantum Institute and the Indian Institute of Technology Madras, asked; how can we improve the next generation of sensors despite these limitations?��

One promising idea is to use quantum entanglement, so atoms are connected to each other and working together as a system. When atoms are entangled, they share properties even when separated by distance. In principle, this allows for more precise measurements. But entangled atoms are still subject to noise.��

“Entangled states are well understood for estimating a single parameter, but our goal was to create an entangled state that is highly sensitive to a parameter difference between two nodes of a sensor network,” says Raphael Kaubruegger, a research associate at JILA.��

The researchers set out to identify a new class of entangled state that could filter out noise affecting both sensors. They then developed two ways to create these states inside an optical cavity, a pair of mirrors about one inch apart that bounce photons back and forth. They describe the state and two methods to create it in a published in Physical Review X.��

Lieb-Mattis state��

Photon exchange through an optical cavity links two atomic ensembles, creating a shared entangled state. This entanglement is designed to be insensitive to common noise while remaining highly sensitive to differential signals.

The entangled state they identified uses decoherence-free subspaces which are protected from certain types of disturbances to quiet noise affecting both sensors.����

Lasers are used to create coherent superposition between two internal states of an atom but to accomplish that, the laser’s frequency needs to exactly match the atomic transition.����

The challenge, as Rey explains, is that even the most precise lasers cannot maintain a stable frequency for long enough. These laser frequency instabilities generate a noise which is equally experienced by both sensors and currently one of the most detrimental errors in state-of-the-artclocks. “Ideally, one would like to prepare the atoms in a state that is insensitive to this type of noise,” says Rey.��

“The state we create is entanglement between these atoms, but in a way that you cannot distinguish which atom is in which ensemble,” says Rey. “They are fully symmetrized.”����

“After the fact, we realized this was the same kind of state people were thinking about to describe antiferromagnets, or quantum magnets,” says James Thompson, JILA and NIST fellow and professor adjoint of physics.��

In condensed matter physics, the Lieb-Mattis state describes a quantum version of an antiferromagnet, where two groups of atoms act like they point in opposite directions, but without the system picking one fixed direction in space.���� ��

A coherent and unitary approach��

One method the team developed to prepare the desired state involves entangling two nodes of a sensor network by engineering a “spin exchange,” by having the atoms send photons back and forth through an optical cavity. This leads to a state where each atom in one node is perfectly anticorrelated with an atom in the other. If one atom is “up,” the other atom is “down.”����

Thompson likens this approach to baseball, where each ensemble is a baseball team. The teams are throwing balls, or in this case photons, to each other. Every time a ball is thrown, the other team catches it. Thompson adds it’s important that we don’t know which player threw the ball or who caught it.����

“That’s what builds these links,” says Thompson. “If a ball is thrown, it is definitely caught.”��

The approach produces Heisenberg scaling, or the best possible precision scaling where all the atoms act as one quantum object.��

Losing a photon is not all that bad��

Optical cavities are not perfect. As Rey explains, sometimes you may lose a photon. The team’s second approach takes this into account.��

Inside the optical cavity, photons can bounce back and forth between very reflective mirrors about 100,000 times before they accidentally slip through to the other side.��

��“We are losing photons, but the important part is that the photons are lost in a collective way,” says Rey. ��

Because it’s impossible to tell which atom is to blame, this can create entanglement — driving them into a state where they cannot lose more photons.����

“At some point they get really good at not dropping the ball anymore,” says Thompson.����

“They go into a ‘dark state,’ or a state where the phases of the emitted photons completely cancel out, leading to what it is known as destructive interference,” adds Rey.����

What came as a surprise to the team, was initially they were trying to understand the detrimental effect of losing those photons. But as Rey explains, ultimately this type of dissipation actually led them to a state they wanted.����

“The state we initially wanted to prepare was one in which half the atoms are excited, but the system cannot collectively emit a photon,” adds Kaubruegger.��

Bridging theory with experiment for real-world applications��

The team’s proposed states can be created quickly, and more importantly, faster as the system gets larger, making them practical for scaling quantum sensors.��

“People have thought about this kind of state when you only have two atoms, which is cool, but you’d like to use more,” says Thompson. “It turns out, the more atoms you have, the better!”��

By making quantum sensors more precise, these entangled states could one day help guide navigation when GPS is unavailable or reveal hidden underground resources such as minerals, oil, or gas.����

Close collaborations between theorists and experimentalists have been key to this work. The groups inspire each other – and keep each other in check. Because they work so closely together, Kaubruegger says they have a deeper understanding of the challenges experimentalists face. ��

And now, the ball, so to speak, is in Thompson’s group’s hands; to demonstrate the state in experiment.��