[Physics] What are quantum anharmonic oscillators

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I have just started studying about quantum computers (hardware side) and I am really confused about what is a quantum anharmonic oscillator. I have read somewhere that a qubit is the physical realization of a quantum anharmonic oscillator. How is it so?

Best Answer

Harmonic quantum oscillator has same displacement between each consecutive energy levels, i.e. : $$ E_{n+1} - E_n = \hbar\,\omega $$ In anharmonic quantum oscillator energy difference between next levels is not a constant and usual follows some non-linear form. Like in for example Morse_potential which helps to define molecule vibrational energy levels. Energy difference between consecutive levels in that case is : $$ E_{n+1}-E_{n}=\hbar\,\omega -\alpha(n+1)~\hbar^{2} \,\omega^{2} $$ So it's not constant, i.e. depends on exact energy level where you are starting from and is non-linear too,- follows a polynomial form of $a\,\omega-b\,\omega^2$. That's why it is anharmonic quantum oscillator.

Sometimes picture is worth a thousand words, so here it is - a graph with harmonic and Morse anharmonic oscillators depicted :

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