Editorial Feature

Quantum Advances in Time-Keeping

From the grandfather clock to the world's most advanced timekeeper, oscillations are influenced by environmental noise. Eliminating such environmental effects can improve clock precision. According to a study published in Nature Communications, surpassing the constraints on an oscillator's precision caused by quantum noise is possible by manipulating or "squeezing" the states that give rise to this noise.

quantum time, quantum timekeeping

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Importance of Feedback Oscillators in Contemporary Society

Feedback oscillators are prevalent in contemporary society and serve as essential markers in various fields. They defined the thresholds for measuring distances through radar, lidar, or the detection of gravitational waves and for measuring time with optical atomic clocks.

The reliability of these clocks not only limits the efficiency of information processors, both classical and quantum, and communication systems but also shapes our exploration of new physics, from low-energy research to high-energy colliders.

Moreover, they play a pivotal role in comprehending our planet, the universe, and even modern economic practices that rely on precise timekeeping (such as GPS systems and financial markets)

The accuracy of a clock depends on its stability, which is affected by external noise. For example, a light breeze can disrupt the motion of a pendulum, whereas heat can interfere with the atomic oscillations in an atomic clock. Reducing these environmental influences can improve the precision of the clock, but there is a limit to the extent to which this can be done.

Quantum Limits and Sub-Standard Quantum Limit (SQL) Oscillators

In photodetection, there is a fundamental limit known as shot noise that mimics classical fluctuations and is linked to Poissonian photoelectron statistics. This is the quantum limit or SQL of detection and is often referred to as quantum noise. Thermal noise, on the other hand, has origins similar to quantum noise but occurs at lower frequencies.

Feedback oscillators, which use an amplifier with some of their output fed back to its input, can provide stable references for synchronization and standardization. The laser, as an oscillator, can be constrained by quantum fluctuations, leading to frequency instability defined by the Schawlow-Townes formula, which sets limits on the laser linewidth. 

The application of this formula extends to a wide range of feedback oscillators, including those beyond the lasers. In addition, techniques such as squeezing can be used to create oscillators with line widths that are smaller than the Schawlow-Townes limit, resulting in sub-SQL oscillators.

Extending the Schawlow-Townes Limit

A study conducted by MIT researchers showed that the Schawlow-Townes limit extends to a broader range of feedback oscillators, which are constructed because of the positive feedback of the broadband amplifier’s output.

The origin of the Schawlow-Townes limit was identified, and the theory of quantum noise was extended in amplifiers to oscillators, bridging the gap between the classical electronic theory of the feedback oscillator and the quantum electronics of the laser.

The insights gained were utilized to devise methods for circumventing the Schawlow-Townes limitation by controlling the quantum states of the oscillators. The researchers discovered that techniques such as entanglement, squeezing, and phase-sensitive amplification in feedback oscillators enabled stability beyond the Schawlow-Townes limit, presenting a new approach for achieving ultra-stable oscillators.

Investigating Oscillator Stability with Laser-Like Setup

In this study, oscillator stability was investigated using a laser-like setup comprising an amplifier, delay line, and coupler. Analyzing the system's behavior through equations unveiled the origin of the quantum noise.

The primary aim was to understand the source of quantum fluctuations within a system by framing it as an oscillator problem. This approach identified the amplifier and coupler as critical areas that facilitate signal extraction from the oscillator.

This study demonstrated that surpassing the quantum limit was achievable through quantum squeezing, a technique that reduces quantum fluctuations in one system by proportionally increasing them in another system. The present strategy focuses on mitigating noise in specific sources, namely, amplifiers and couplers.

Introducing a phase-sensitive amplifier into the feedback loop notably reduced the oscillator's phase quadrature spectrum compared with input-mode squeezing or correlation under specific levels of squeezing. However, a phase-insensitive amplifier aligned with quantum principles effectively decreases the oscillator output phase noise without amplifying the amplitude noise.

The use of a laser allows the manipulation of quantum fluctuations in the coupler, enhancing the precision and timing of the emitted laser beam oscillations. However, this improvement comes at the expense of increased noise in the laser power.

The origin of the Schawlow-Townes limit was identified in the oscillator frequency stability, a principle applicable across diverse feedback oscillators. Specifically, the quantum-noise-limited, phase-insensitive oscillator is part of a broader restriction known as the Standard Quantum Limit (SQL) for the oscillator's outgoing field.

This SQL delineates the fundamental balance between oscillation frequency and amplitude in various feedback loops. However, advanced techniques, such as squeezed vacuum, Einstein-Podolsky-Rosen (EPR) entanglement, and phase-sensitive amplification, offer the possibility of surpassing this constraint, marking the emergence of a new class of stable oscillators.


In conclusion, the advancement of timekeeping technology from ancient mechanisms, such as the grandfather clock, to modern atomic clocks, has consistently faced the challenge of environmental noise. The precision of these timekeepers is crucial across various sectors, including information processing, communication systems, and the scientific exploration of the universe.

The key obstacles in timekeeping are overcoming inherent limitations such as quantum noise and defining the precision of feedback oscillators. Recent studies, including one by MIT researchers, have revealed the roots of the Schawlow-Townes limit, a fundamental barrier to oscillator stability due to quantum noise. By manipulating quantum states through techniques such as squeezing and entanglement, researchers have made breakthroughs in creating ultra-stable oscillators that surpass this limit.

This work demonstrated that the Schawlow-Townes limit applies to a broader range of feedback oscillators, specifically those that utilize positive feedback from the output of a broadband amplifier.

Consequently, the root cause of the ST limit was clarified, extending the theory of quantum noise in amplifiers to include oscillators and connecting the classical electronic theory of feedback oscillators with the quantum electronics of lasers.

These findings offer new possibilities for the development of stable timekeeping devices and technological advancements. By bridging the gap between classical electronic theory and quantum electronics, the present study offers a promising path toward achieving unprecedented accuracy in timekeeping systems. As we continue to explore and apply these insights, the future of precise timekeeping appears brighter than ever.

More from AZoQuantum: Why We Need Generalized Quantum Standards

References and Further Reading 

Loughlin, H.A., Sudhir, V. Quantum noise and its evasion in feedback oscillators. Nat Commun 14, 7083 (2023). https://doi.org/10.1038/s41467-023-42739-9

With a quantum “squeeze,” clocks could keep even more precise time, MIT researchers propose. Accessed on 19 December, 2023.

Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.

Bhavna Kaveti

Written by

Bhavna Kaveti

Bhavna Kaveti is a science writer based in Hyderabad, India. She has a Masters in Pharmaceutical Chemistry from Vellore Institute of Technology, India, and a Ph.D. in Organic and Medicinal Chemistry from Universidad de Guanajuato, Mexico. Her research work involved designing and synthesizing heterocycle-based bioactive molecules, where she had exposure to both multistep and multicomponent synthesis. During her doctoral studies, she worked on synthesizing various linked and fused heterocycle-based peptidomimetic molecules that are anticipated to have a bioactive potential for further functionalization. While working on her thesis and research papers, she explored her passion for scientific writing and communications.


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