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Heisenberg microscope, light force, and the "location" in quantum science
A microscope allows us to see tiny objects that are not visible to the naked eye. The eyepiece in the microscope collects the scattered light from the tiny object and sends it to the observer's eye. The photoreceptors in the eye convert the scattered light into electrical signals before relaying them to the observer's brain. The brain reconstructs the image of the tiny object by analyzing those electrical signals.
Quantum mechanics accurately describes the properties of tiny particles like electrons, neutrons, etc., known as subatomic particles. A founding principle of quantum mechanics is the Heisenberg Uncertainty principle which states that it is impossible to locate the position of a sub-atomic particle with 100% accuracy. We can only know the probability that a subatomic particle can be at a location but not where exactly it is. However, what is the big deal about needing to know the exact location? Well, everything around you, like the newspaper in your hand, your house, your car, etc., is located at some place known to you. When everything around you has a well-defined location, why doesn't a subatomic particle, which makes up all the stuff around us, have a well-defined location? The Heisenberg microscope was a thought experiment proposed to answer this question.
A Heisenberg microscope is used to see tiny subatomic particles like electrons, protons, etc. Let us assume that an electron is placed under the microscope. The observer can see the electron when the light scattered from the electron reaches the observer's eye through the microscope. In quantum mechanics, light is made up of a stream of particles known as photons. The scattering of photons by the electron can be imagined as a collision between billiard balls. When one moving billiard ball collides with the other at rest, both will move to different locations after the collision. During the collision, the moving ball will exert some force on the ball at rest. This force will move the ball at rest to a new location. Similarly, a photon scattered off the electron will move the electron to a new location. The force exerted by the photon on the electron in the scattering process is called light force.
On the other hand, the scattered photon goes in another direction (let us say towards the observer's eye). The scattered photon carries information about the location of the electron-photon collision. Hence the observer can infer, at best, the collision location but not the electron's new location after the collision. Simply put, the light scattered by the electron reveals where scattering took place at best but not the electron's location after scattering. Real-world objects, like your car, house, etc., are far heavier than the electron. The light force can not move them to a different location. So do not worry; your car is where it was parked.
The Heisenberg microscope was a thought experiment proposed in the late 1920s. Nearly nine decades later, technological advances led to synthesizing pico-gram mirrors that can simulate the physics of light force in a laboratory setting. The pico-gram mirror weighs roughly hundred-millionth of a single one-inch-long hair strand. The light reflected from these mirrors displaces them much like an electron in the Heisenberg microscope, and the reflected photon carries the information about the reflected location. The higher the number of photons reflected from the mirror, the higher the light force and the inaccuracy in the mirror position estimation. However, if only a few photons are reflected from the mirror, fewer photons carry the information about the mirror's location. The lower photon number translates into less information, increasing mirror position estimation inaccuracy. Optimizing the number of reflected photons leads to a standard quantum limit, the best possible accuracy in measuring the mirror position. The standard quantum limit, which arose from the light force, is not as fundamental as Heisenberg uncertainty and can be defeated.
My group recently developed a technique to overcome the standard quantum limit by taming the light force noise in the scattering process. This work is funded by Science and Engineering Research Board, India (SRG/2020/001167), and published in the Journal of Optical Society of America-B and Optics Letters. The idea is to exploit the simple harmonic motion properties of light. The back-and-forth swinging of the round bob through a metal rod attachment in a wall clock is a simple harmonic motion. Now imagine that the round bob in the wall clock is at rest. You may give it a slight jerk to move it away from its resting position. Then it will swing back and forth, returning to the same resting position again and again. The force returning the bob to its resting place is known as restoring force. A suitable simple harmonic motion of light is synthesized such that its restoring force cancels adverse light force effects in locating the mirror. This method led to an accuracy better than the standard quantum limit.
Even though the light force justifies the inability to locate a subatomic particle precisely using the Heisenberg microscope, it is not the complete story. Even a perfect microscope (no light force, no focussing errors, etc.) can not locate a subatomic particle with 100% accuracy. The Heisenberg Uncertainty principle is not an outcome of any known physical cause. It is far more profound, but that can be a story for some other time. Unlike the objects we see around us, the subatomic particles have no definite address.
Acknowledgements: The author thanks Prof. Thiruvikraman for several suggestions. Funding source: Science and Engineering Research Board, India (SRG/2020/001167).
References:
Sankar Davuluri, Quantum optomechanics without the radiation pressure force noise, Optics Letters 46, 904-907 (2021).
Sankar Davuluri, and Yong Li, Light as a quantum back-action nullifying meter, Journal of Optical Society of America B, 39, 3121 (2022)
sankar@hyderabad.bits-pilani.ac.in