Quantum limits to precision measurement

Continuous-wave (CW) interferometers and oscillators lie at the core of many modern precision measurements including atomic clocks and ground and space based gravitational wave detectors. As with all measurements, quantum mechanics sets the ultimate limit on the precision of these devices. In interferometers employing only classical sources of light, such as thermal sources and lasers, sensitivity is bounded by “standard quantum limit” (SQL) scaling. However, using quantum light sources, such as squeezed light, we can achieve precision beyond the SQL and achieve “Heisenberg scaling”, where the available quantum resources are used with maximal efficiency. Prior to our work, a variety of theoretical and technical challenges have prevented any CW interferometer from approaching Heisenberg scaling. I will show that it is possible to achieve Heisenberg scaling in a CW interferometer using squeezed light and homodyne detection. I will discuss a recent experimental demonstration, which has achieved sensitivity in line with theoretical predictions [1]. These results demonstrate that we can approach the Heisenberg limit in CW interferometers using existing technology. Similarly, the frequency stability of feedback oscillators using only classical sources of light is bounded by the “Schawlow-Townes limit”, a SQL for these devices. I will show theoretically that this limit can be evaded through quantum engineering and discuss an ongoing experiment at MIT to demonstrate the resulting frequency stability enhancement [2,3].
[1] H. A. Loughlin et. al., Heisenberg Scaling in a Continuous-Wave Interferometer, arXiv:2509.25384 (2025).
[2] H. A. Loughlin and V. Sudhir, Quantum Noise and Its Evasion in Feedback Oscillators, Nature Communications 14, 7083 (2023).
[3] H. A. Loughlin and V. Sudhir, A Generalized Schawlow-Townes Limit, arXiv:2501.11861 (2025).