Surface Metrology from a Quantum Perspective

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Surface metrology is the branch of metrology that focuses on the minute features of physical surfaces, such as the surface’s primary form (overall shape), fractality (pattern changes at various levels of detail), and roughness (level of deviation from the normal vector of its ideal form).

Classical surface metrology techniques include contact measurement, which involves dragging a stylus over the surface with a piece of equipment called a profilometer, and non-contact measurements involving light waves, electrons, or photographic images.

Recent advances in quantum physics have opened up a new generation of metrology and surface metrology techniques, which enable much more precise measurements with higher resolution and greater sensitivity.

Overcoming the limitations of classical metrology

Quantum metrology and quantum surface metrology exploit the peculiar quantum mechanical effects of quantum entanglement and quantum squeezing.

Quantum entanglement is the observed tendency of multiple quantum particles becoming linked to one another regardless of the distance between them. Spinning one particle causes another entangled particle to spin as well.

Quantum squeezing moves the uncertainty of an entire system, from the area that the metrologist wants to measure to another part of the system that does not need to be measured, without having to reduce the overall uncertainty in the system. This is similar to squeezing the air from one end of a balloon to another.

Quantum surface metrology techniques that exploit these non-classical physical effects have recently been shown to overcome the extreme limit of image resolution, which is defined as the minimum distance between two light sources before they become indistinguishable from one another. This limitation is known as Rayleigh’s criterion.

Surface metrology with quantum entanglement

One quantum metrology technique utilizing the effect of quantum entanglement that overcomes the Rayleigh criterion involves the NOON state of light. The NOON state is a multipartite (containing multiple particles) state of photons (or theoretically any Bosonic field particle) in which the photons are related.

In the technique, the NOON state is achieved in a Mach-Zehnder interferometer to produce a surface measurement. In one study, it was shown that this technique could enhance accuracy in surface metrology as well as image resolution in quantum lithography (Kok, Braunstein and Dowling, 2004).

Techniques exploiting quantum entanglement in the NOON state can distinguish between light sources closer than the minimum possible distance set out in the Rayleigh criterion. It has been shown that using quantum entanglement-based techniques in multipartite systems such as this, is necessary to achieve maximum sensitivity in surface measurements (Tóth, 2012).

Surface metrology with quantum squeezing

A recent development from a team of physicists at the National Institute of Standards and Testing (NIST), utilizes quantum squeezing to “measure with greater sensitivity than could be achieved without quantum effects”, according to the study’s lead author (Ost, 2019).

The method traps a single ion 30 micrometers above a flat sapphire chip and controls it with gold electrons which cover the surface of the sapphire. Electric signals are used to achieve the squeezed state in the system and move the ion, and then to reverse the squeezing and generate magnetic fields which can be used to measure the motion (Burd et al., 2019).

This method was shown to ion motions of only 50 picometers (trillionths of a meter), and repeating the steps can produce even more minute surface measurements.

The new method put forward by the NIST team not only advances the burgeoning fields of quantum metrology, quantum surface metrology, and quantum information science, but it can also be applied to other sciences exploiting quantum mechanics such as quantum computing.

This is due to its previously unachieved levels of amplification, meaning that larger systems can be measured than were previously possible. This can help quantum computers operate much more quickly, and can also speed up the quantum simulation.


  • Burd, S.C., Srinivas, R., Bollinger, J.J., Wilson, A.C., Wineland, D.J., Leibfried, D., Slichter, D.H., and Allcock, D.T.C. (2019). Quantum amplification of mechanical oscillator motion. Science, 364(6446), pp.1163–1165.
  • Kok, P., Braunstein, S.L., and Dowling, J.P. (2004). Quantum lithography, entanglement, and Heisenberg-limited parameter estimation. Journal of Optics B: Quantum and Semiclassical Optics, 6(8), pp.S811–S815.
  • Ost, L. (2019). NIST Team Supersizes ‘Quantum Squeezing’ to Measure Ultrasmall Motion. [online] NIST. Available at: [Accessed 21 Sep. 2019].
  • Tóth, G. (2012). Multipartite entanglement and high-precision metrology. Physical Review A, 85(2).

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Ben Pilkington, MSt.

Written by

Ben Pilkington, MSt.

Ben Pilkington is a freelance writer, editor, and proofreader with a master’s degree in English literature from the University of Oxford. He is committed to clear and engaging written communication and enjoys telling complex, technical stories in a relevant and understandable way.


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