A versatile approach to achieve enhanced quantum metrology with large Fock states

Collecting high-precision measurements can enable scientific and technological advances in many fields. In physics, high-precision measurements can reveal new phenomena and experimentally validate theories.

Enhanced quantum metrology techniques are emerging methods that enable the collection of precise measurements using nonclassical states. Although these techniques can theoretically outperform classical approaches, reliably manipulating nonclassical states to obtain high-precision measurements has so far proven challenging.

Researchers from the International Quantum Academy, Southern University of Science and Technology, and University of Science and Technology of China recently presented a new approach to achieve enhanced quantum metrology. Their proposed approach, introduced in Physics of naturehas been shown to enable the efficient generation of large Fock states with up to nearly 100 photons.

“Our recent research has mainly focused on high-precision measurement of weak microwave electromagnetic fields,” Yuan Xu, co-author of the paper, told Phys.org. “We found that microwave Fock states in a superconducting cavity are promising candidates because they exhibit ultrafine interference structural features in phase space.”

“A slight shift or displacement of these states induced by a weak microwave field can be detected with high precision thanks to the ultrafine interference patterns of the Fock states. The higher the number of photons in the Fock state, the finer the interference fringes presented and therefore the more precise the detection can be.”

To achieve a significant metrological gain over classical metrology techniques using the principles of quantum mechanics, Xu and his colleagues set out to design an approach that would allow generating Fock states with up to 100 photons. The method they propose relies on the use of two distinct types of photon number filters.

“We used two types of photon number filters (PNFs)—sinusoidal PNF and Gaussian PNF—to generate large Fock states using the photon number-dependent response of an auxiliary qubit coupled to the cavity,” Xu explains. “These PNFs can selectively filter specific photon numbers based on the state of the auxiliary qubit.”

To implement sinusoidal PNF, the researchers inserted a conditional rotation into a Ramsey-type sequence and projected the auxiliary qubit into the ground state. This operation acts as a lattice that periodically blocks specific numbers of photons from the cavity states.

In contrast, the second photon number filter used, called Gaussian PNF, applies a qubit flip pulse with a Gaussian envelope. This compresses the photon number distribution, focusing on a subspace centered around a desired Fock state.

“The combination of these two PNFs facilitates the efficient generation of large Fock states,” Xu said. “One of the main advantages of this method is its efficiency, as it enables the generation of large Fock states with a circuit depth that scales logarithmically with the number of photons, making it more efficient than previous proposals that required polynomial scaling.”

“Furthermore, this method is hardware efficient and more practical for generating Fock states with large numbers of photons, which is crucial for achieving improved quantum metrology with high precision.”

The team’s approach has so far proven to be a viable path to implement hardware-efficient quantum metrology, using large Fock states in a single bosonic mode. The approach is also very versatile and could therefore be easily extended to other physical platforms, such as mechanical and optical systems.

“We introduced a new quantum control method to generate Fock states with a substantial number of photons and set a new record for Fock state generation and metrology gain,” Xu said. “We successfully generated large Fock states containing up to 100 photons, which is an order of magnitude increase over previous demonstrations and is the largest microwave Fock states to our knowledge.”

In initial tests, the approach to implementing enhanced quantum metrology designed by Xu and colleagues proved to be significantly superior to classical metrology, achieving a metrological gain of 14.8 dB and thus approaching the Heisenberg limit.

Their work could soon make it possible to collect more precise measurements, potentially leading to exciting new discoveries and observations in various fields.

“First, our study benefits fundamental research by providing a testbed for theoretical predictions of highly nontrivial quantum effects in quantum optics and quantum mechanics,” Xu said. “Second, our single-mode quantum metrology with high hardware efficiency demonstrates remarkable potential for practical applications, including high-precision radiometry, weak force sensing, and dark matter search.”

The researchers hope that their recent research will contribute to the collection of increasingly precise measurements, paving the way for advances in various fields. In their future studies, they plan to continue advancing their method, focusing on two key areas of research.

“First, we now aim to further improve the coherence performance of the quantum system and develop scalable and high-precision quantum control techniques to deterministically generate Fock states with higher photon numbers, thereby achieving greater metrological gain,” Xu said.

“Second, we will explore important applications of the hardware-efficient quantum metrology scheme demonstrated here, particularly in areas such as weak electromagnetic field detection and dark matter searches.”

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