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Scientists Take New Approach to the PDH Method

Scientist John “Jan” Hall is regarded as a seminal figure in the history of laser frequency stabilization and laser-based precision measurement in the atomic and laser physics sectors. Hall’s research focused on developing novel techniques for handling steady lasers that were groundbreaking in their day. His research established the technical framework for detecting the minuscule fractional change in distance caused by a passing gravitational wave. In 2005, he was granted the Nobel Prize in Physics for his research on laser arrays.

Lasers Enable Enhanced and Simplified Precision Measurement Scheme
A schematic of a laser going through an AOM, which sends sound waves into a silicon cavity. Image Credit: Kenna Hughes-Castleberry/JILA/Ye and Hall Groups

Using this as a starting point, JILA and NIST Fellow Jun Ye and his group set out on a bold mission to push the limits of precise measurement further. This time, they concentrated on a particular approach that is crucial to laser frequency stabilization and precision optical interferometry: the Pound-Drever-Hall (PDH) method, which was created by scientists R. V. Pound, Ronald Drever, and Hall himself.

Although the PDH method has been used for decades by physicists to guarantee that their laser frequency is “locked” to an artificial or quantum reference, residual amplitude modulation (RAM), a limitation resulting from the frequency modulation process itself, can still impact the stability and precision of the laser’s measurements.

In a recent Optica study, Ye’s team, along with JILA electronic staff member Ivan Ryger and Hall, created a novel strategy for the PDH method, decreasing RAM to never-before-seen minimum levels while making the system more resilient and simpler.

Enhancing the PDH approach can lead to breakthroughs in a variety of scientific domains since it is used in investigations such as optical clocks and gravitational wave interferometers.

A Dive into Laser ‘Locking’

The PDH approach was published in 1983 and has been used and cited thousands of times since then.

Setting up a PDH lock is something you might learn in an undergraduate lab course; that is just how central it is doing all the experiments we do in atomic physics.

Dhruv Kedar, Study Co-First Author and PhD Student, Joint Institute for Laboratory Astrophysics

To accurately quantify the laser frequency or phase variations, the PDH method employs a frequency modulation technique. A primary light beam, referred to as the “carrier,” is surrounded by extra light signals, or unique “sidebands,” thanks to frequency modulation.

Any minute variations in the frequency or phase of the primary light beam concerning a reference can be measured by comparing these sidebands to the main carrier. This method is particularly helpful as it can reject mistakes and unwanted noise and is quite sensitive.

These coupled light beams may then be used by physicists to investigate various situations, such a mirror-based optical cavity. The researchers need to “lock” the laser to the cavity or use a certain frequency for it to probe the cavity to do this.

Kedar added, “What that means is that you are trying to lock your laser to the center of your resonance.”

This enables the laser to achieve cutting-edge stability levels, particularly crucial when attempting to discern minute variations in the optical length or tracking quantum dynamics, including energy shifts or spin fluctuations in atoms and molecules.

Regretfully, a laser does not always remain steady after it is “locked.”

In resonance with the center of the optical cavity, as noise like RAM can change the relative offsets of the reference light beams and introduces frequency shift. The RAM can contaminate your PDH error signal.

Zhibin Yao, Study Co-First Author and Postdoctoral Researcher, Joint Institute for Laboratory Astrophysics

As the JILA scientists and others in the laser physics community soon discovered, lowering this RAM is essential to enhancing the PDH technique’s stability and, therefore, their laser observations. It has taken a while to solve the RAM issue, but the new strategy would make the battle much simpler.

Reducing RAM via EOMs and AOMs

The PDH locking mechanism depends on the two-reference light “sidebands”. The JILA researchers were required to utilize a frequency modulator, either an acousto-optic modulator (AOM) or an electro-optic modulator (EOM), to produce the “sidebands.”

Electric fields applied to optical crystals have historically been used by EOMs in a variety of optical systems to alter the phase of laser light passing through the crystal. There are crystals whose refractive index changes when an electric field is applied, and these crystals regulate the laser phase. EOMs could easily add sidebands to the carrier beam with this procedure.

However, variations in the environment may readily change the effective phase modulation of the crystal used in EOMs, which introduces RAM into the PDH error signal and reduces its stability. Even small quantities of RAM can create undesirable variations in situations when ultra-high accuracy is needed, such as when running an atomic clock or an optical timescale.

Kedar added, “EOMs add sidebands to the carrier laser in the optical domain, which is more challenging for us to control. So instead, we can try to generate these sidebands in the electronic domain and translate them to the optical by using an AOM.

AOMs, which regulate laser light using sound waves, are a more recent method of RAM reduction. A sound wave’s diffraction pattern, produced when it passes through a transparent material like a crystal, causes the laser light to bend in different ways. The changes in refractive index of this sound wave-altered medium function as a series of small prisms, modifying the path and, consequently, the frequency of a light beam as it travels through it.

If you want to control the amplitude of each sideband, you control the amplitude of the main tone that you are generating in the microwave domain via the AOM,” Kedar further stated.

Since AOM does not modify the laser frequency based on the electro-optic effect, it creates substantially less RAM noise than EOM, lowering the total RAM level of the system. All of the beams exiting the AOM crystal can be joined in a single optical fiber, placing all frequency shift beams into a single, common spatial mode profile.

Comparing EOM and AOM

Kedar, Yao, Ye, and the rest of the team conducted an experiment utilizing both their enhanced AOM setup and the conventional EOM to compare the benefits of this novel PDH technique. They discovered they could lower the RAM levels to a tiny number of parts per million using the AOM.

Not to mention, this method gives you a lot more control over the relative strengths of the carrier and the two sidebands. When the carrier gets vanishingly tiny, the AOM advantage becomes much more evident.

Kedar noted, “Instead of parts per million, you can do like 0.2 parts per million, which seems like a small improvement, but that is kind of toeing the line for acceptable levels of RAM for us. Even though this RAM level is so small, it's still a significant roadblock to improving our cavities and making them slightly better. That extra factor of two or three is enormously helpful in pushing the frontiers of state-of-the-art laser stabilization.

The simple use of AOM instead of EOM proposes a solution that even Hall would be pleased with.

Kedar concluded, “It is simple enough that, in principle, someone can look at this scheme and see it as a natural method to interrogate a spectral feature. In the end, this speaks to the research style that Jan and Jun both create: a very elegant, simple solution.

Journal Reference:

Kedar, D., et. al. (2023) Synthetic FM triplet for AM-free precision laser stabilization and spectroscopy. Optica. doi:10.1364/OPTICA.507655


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