- quantumtech.blog/2023/01/17/quantum-computing-with-neutral-atoms/ OK this one hits it:So we understand that it is truly like the classical computer analog vs digital case.
As Alex Keesling, CEO of QuEra told me, "... whereas in gate-based [digital] quantum computing the focus is on the sequence of the gates, in analog quantum processing it's more about the position of the atoms and where you place them so they can mirror real life problems. We arrange the atoms and define the forces that drive them and then measure the result... so it’s a geometric encoding of the problem itself."
- thequantuminsider.com/2022/06/28/why-analog-neutral-atoms-quantum-computing-is-a-promising-direction-for-early-quantum-advantage on The Quantum Insider useless article mostly by Pasqal
Relates particle momentum and its wavelength, or equivalently, energy and frequency.
Particle wavelength can be for example measured very directly on a double-slit experiment.
So if we take for example electrons of different speeds, we should be able to see the diffraction pattern change accordingly.
What you see along a line or plane in a wave interference.
Notably used for the pattern of the double-slit experiment.
This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.
Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
- Compton scattering, also suggests that photons carry momentum
- photoelectric effect
- single photon production and detection experiments
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.
Proportionality factor in the Planck-Einstein relation between light energy and frequency.
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
Experiments explained:
- via the Schrödinger equation solution for the hydrogen atom it predicts:
- spectral line basic lines, plus Zeeman effect
- Schrödinger equation solution for the helium atom: perturbative solutions give good approximations to the energy levels
- double-slit experiment: I think we have a closed solution for the max and min probabilities on the measurement wall, and they match experiments
Experiments not explained: those that the Dirac equation explains like:
- fine structure
- spontaneous emission coefficients
To get some intuition on the equation on the consequences of the equation, have a look at:
The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.
Then, with that in mind, the general form of the Schrödinger equation is:where:
- is the reduced Planck constant
- is the wave function
- is the time
- is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
The argument of could be anything, e.g.:Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
- we could have preferred polar coordinates instead of linear ones if the potential were symmetric around a point
- we could have more than one particle, e.g. solutions of the Schrodinger equation for two electrons, which would have e.g. and for different particles. No matter how many particles there are, we have just a single , we just add more arguments to it.
- we could have even more generalized coordinates. This is much in the spirit of Hamiltonian mechanics or generalized coordinates
The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.
This experiment seems to be really hard to do, and so there aren't many super clear demonstration videos with full experimental setup description out there unfortunately.
Wikipedia has a good summary at: en.wikipedia.org/wiki/Double-slit_experiment#Overview
For single-photon non-double-slit experiments see: single photon production and detection experiments. Those are basically a pre-requisite to this.
photon experiments:
- aapt.scitation.org/doi/full/10.1119/1.4955173 "Video recording true single-photon double-slit interference" by Aspden and Padgetta (2016). Abstract says using spontaneous parametric down-conversion detection of the second photon to know when to turn the camera on
electron experiments: single electron double slit experiment.
Non-elementary particle:
- 2019-10-08: 25,000 Daltons
- interactive.quantumnano.at/letsgo/ awesome interactive demo that allows you to control many parameters on a lab. Written in Flash unfortunately, in 2015... what a lack of future proofing!
You can't get more direct than this in terms of proving that photons exist!
The particular case of the double-slit experiment will be discussed at: single particle double slit experiment.
Production:
Detectors are generally called photomultipliers:
Bibliography:
- iopscience.iop.org/book/978-0-7503-3063-3.pdf Quantum Mechanics in the Single Photon Laboratory by Waseem, Ilahi and Anwar (2020)
Can be used as a very precise magnetometer.
There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.