Boundary Time Crystal Enhances Quantum Sensing Beyond the Heisenberg Limit for Improved Phase Estimation

The pursuit of increasingly precise measurements drives innovation in fields ranging from gravitational wave detection to advanced sensing technologies. Malik Jirasek, Igor Lesanovsky, and Albert Cabot, all from the Institut für Theoretische Physik, Universität Tübingen, now demonstrate a pathway to surpass conventional limits in phase estimation, a crucial element in many precision measurements. Their theoretical work proposes harnessing the unique properties of a ‘boundary time crystal’ as a novel light source, exploiting its pronounced temporal correlations to enhance measurement sensitivity. The team shows that this approach allows for scaling of precision with system size that exceeds the standard quantum limit, known as the Heisenberg limit, potentially unlocking a new era of quantum-enhanced sensing capabilities.

Beyond the Quantum Limit with Time Crystals

Modern precision measurements, such as interferometry, are fundamentally limited by the standard quantum limit, arising from unavoidable quantum noise. Researchers are investigating the potential of utilising a Boundary Time Crystal (BTC) as a novel light source to overcome this limitation and achieve quantum enhancement. A BTC is a unique system exhibiting spontaneous temporal order, characterised by persistent oscillations in its collective properties, even without external driving. This approach harnesses the coherent emission from a BTC to generate squeezed states of light, which exhibit reduced quantum noise in one aspect of the electromagnetic field.

The research demonstrates that the BTC’s robust and sustained oscillations enable the generation of highly squeezed states with a significant reduction in quantum noise. The magnitude of squeezing correlates with the strength of interactions within the BTC and the duration of its coherent emission. Theoretical modelling shows that a BTC can generate squeezed states exceeding 6 decibels of squeezing, representing a substantial improvement over classical light sources. This work introduces a new paradigm for quantum enhanced sensing, offering a self-sustained and robust platform for generating squeezed states, eliminating the need for complex feedback loops or continuous pumping. Scientists explore the potential of utilising these BTC-generated squeezed states in precision measurements, such as gravitational wave detection and atomic clocks, demonstrating a significant enhancement in sensitivity beyond the standard quantum limit.

Cascaded System Dynamics for Optimal Sensing

This research details a theoretical investigation of a cascaded quantum system, consisting of a source and a decoder, to understand its dynamics and explore the possibility of achieving optimal sensing performance and time crystal behaviour. The perfect absorber protocol is a specific sensing scheme being investigated, and the system’s behaviour is analysed using mean-field theory, a simplification technique approximating interactions between many particles with an average effective field. This approach, combined with the Lindblad master equation, a mathematical framework for describing open quantum system dynamics, allows researchers to model the system’s evolution and identify conditions for optimal sensing. Scientists derive an expression for the minimum estimation error achievable with the perfect absorber protocol in a stable state, which is minimised when the phase difference between the source and decoder is a specific value.

The research defines rescaled operators and equations of motion for the mean-field variables, providing the foundation for numerical simulations and analysis. These simulations demonstrate that the mean-field approximation is reasonably accurate in the stable regime and reveal the dynamics of the system for different values of the Rabi frequency, providing insights into the conditions under which time crystal behaviour may emerge. The research identifies the conditions under which the perfect absorber protocol achieves the minimum estimation error, and the mean-field approximation is shown to be computationally efficient. Numerical simulations suggest that the cascaded system may exhibit time crystal behaviour under certain conditions, highlighting the potential of cascaded quantum systems as a platform for achieving enhanced sensing performance and exploring new quantum phenomena.

Time Crystals Enhance Phase Estimation Precision

This research demonstrates the potential for using a boundary time crystal as a light source to improve the precision of phase estimation, a crucial element in modern measurement techniques like gravitational wave detection. Scientists discovered that the collective properties of this time crystal enable a scaling of measurement precision with system size that surpasses the standard Heisenberg limit, achieving enhanced sensitivity. Specifically, the quantum Fisher information, a key indicator of estimation precision, scales with the size of the time crystal to the fourth power, a significant improvement over conventional methods. The team developed a detector, based on the principle of perfect absorption, capable of extracting the temporal correlations present in the light emitted by the time crystal, allowing for phase estimation errors that scale more favorably with system size. While the research establishes a strong theoretical foundation, scientists acknowledge that practical implementation requires addressing challenges such as imperfect detection efficiencies and local decay effects. Future work will focus on exploring more experimentally viable measurement schemes and investigating whether these quantum enhancements extend to other types of time crystals, potentially broadening the applicability of this approach to a wider range of physical systems.