Scientists Demonstrate How to Speed Up Frequency Measurement

An accurate analog clock tick-tick-ticks with a well-known frequency and constant precision: one tick per second. The longer it is let tick, the better it is to test its accuracy — 10 times as long corresponds to a ten-fold enhancement in any frequency uncertainty. However, is there a faster way to determine a frequency?

It turns out there is, in a recent discovery featured this week in Physical Review Letters via a partnership between Washington University in St. Louis and the University of Rochester.

The speed-up in frequency measurement is obtained from quantum mechanics. When a quantum bit is employed for measuring the frequency of a signal, the strange rules of quantum mechanics permit the frequency measurement to be a lot more accurate. The technique hinges on the potential to put the quantum bit in a superposition of its two quantum states, and then move these states around in time along with the signal.

Kater Murch, Assistant Professor of Physics in Arts & Sciences at Washington University, in colaboration with Arts & Sciences Graduate Student Mahdi Naghiloo and Theory Collaborator Andrew Jordan of the University of Rochester defined the technique as a “quantum magic trick.”

It’s reminiscent of the magic tricks that involve a ball placed under one of two cups and the cups are shuffled around — except this time, the ball can be under both cups at the same time. The resulting speedup in frequency measurement is astonishing. Now, by measuring for 10 times as long, the frequency uncertainty can be reduced by a factor of 100 — enabling enhanced resolution of the frequency beyond any other technique of its kind. Earlier theory work published by the Jordan group this year has proven in two separate papers that the technique applied in this paper is the theoretical optimum that quantum mechanics allows.

Kater Murch, Assistant Professor of Physics in Arts & Sciences, Washington University

The experiment was completed with the help of a superconducting quantum system where an external oscillating signal with unknown frequency led to the quantum system undergoing periodic changes. The application of quantum pulses on top of the oscillating signal allowed the state of the system to be controlled so that the last readout of the quantum system became greatly sensitive to the accurate value of the oscillation frequency.

The fundamental physical source of the advantage is linked to the fact that the energy of the quantum system is time-dependent, which leads to the quantum states corresponding to varied frequencies in order to accelerate away from each other, giving improved distinguishability in a given time.

According to Jordan, this method allowed improved resolution of the frequency beyond any other technique of its kind.

This work is considered to be just one example of how the new field of quantum technologies makes use of the laws of quantum physics for technological benefit over classical physics, Jordan stated. Other examples include quantum sensing, quantum computing and quantum simulation. For those fields, the exploitation of quantum physics offers advantages such as the factoring of large numbers, a speed up of database search or the rapid simulation of difficult molecules.

Such fine-scale measurement of the frequency of a periodic signal is considered to be the basic ingredient in various applications, including the analysis of light emitted from stars, MRI medical imaging devices, and, of course, clock precision. Accelerating these measurements in a manner demonstrated by Murch and Jordan could have profound impacts in many areas.

Murch and Naghiloo employed GPS and timekeeping, and such constantly progressing technologies, as examples of the significance of their findings.

“Nowadays, most of us carry a phone in our pocket that is capable of telling us almost exactly where we are on Earth using the Global Positioning System,” Murch said. “The way this works is that your phone receives signals from several different satellites, and by timing the relative arrival of these signals it infers your position. The accuracy of the timing directly relates to the accuracy of your position — a relationship between timekeeping and navigation that has persisted for hundreds of years.

“Well before GPS, a sailor who wanted to know his location would navigate by the stars. In the Northern Hemisphere, the height of the north star will tell you your latitude, but to know your longitude, you need to keep track of the time. As the night goes on, the stars circle around the north star — the height of any star above the horizon is related to the local time, and by comparing this time to a clock set to Greenwich Mean Time, the time difference gives your longitude.” Murch added.

The vitality of frequency advances is highlighted by nautical timekeeping.

“In the 1700s, accurate clocks were the main limitation to ocean navigation,” Murch said. “The Scilly naval disaster of 1707 — one of the worst disasters in British naval history — was widely blamed on poor navigation, prompting the British government to invest heavily in precise clocks. The resulting chronometers transformed marine navigation and greatly accelerated the age of discovery.

Advances in timekeeping continue to have profound impact on technology and fundamental science. Quantum tools, such as the quantum speedup in frequency measurement that we discovered, are necessary to push these technologies forward. This is an exciting time for quantum physics because these quantum resources are increasingly leading to practical advantages over traditional measurement approaches.

Kater Murch, Assistant Professor of Physics in Arts & Sciences, Washington University