Quantum optics -
macroscopic states

Jonas Neergaard-Nielsen, bigQ / QPIT

Quantum optics

\begin{aligned}E &= \frac{1}{2} m \omega x^2+\frac{1}{2m}p^2 \cr[1ex] &= \bar{x}^2 + \bar{p}^2 \end{aligned}

\begin{aligned}E &= \frac{1}{2} m \omega x^2+\frac{1}{2m}p^2 \cr[1ex] &= \bar{x}^2 + \bar{p}^2 \end{aligned}

energy, in normalised, unit-less variables:

$\bar{x}$ : mechanical oscillator position,

light field amplitude, etc.

|0\rangle

|0\rangle

|1\rangle

|1\rangle

|2\rangle

|2\rangle

|3\rangle

|3\rangle

|4\rangle

|4\rangle

|6\rangle

|6\rangle

|7\rangle

|7\rangle

|5\rangle

|5\rangle

\hat{a}

\hat{a}

\hat{a}^\dagger

\hat{a}^\dagger

\curvearrowleft

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\curvearrowright

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creation and annihilation operators

\hat{x}=\frac{\hat{a}^\dagger+\hat{a}}{\sqrt{2}},\quad \hat{p}=i\frac{\hat{a}^\dagger-\hat{a}}{\sqrt{2}}

\hat{x}=\frac{\hat{a}^\dagger+\hat{a}}{\sqrt{2}},\quad \hat{p}=i\frac{\hat{a}^\dagger-\hat{a}}{\sqrt{2}}

|n\rangle

|n\rangle

\hat{a}^\dagger\hat{a}=\hat{n}

\hat{a}^\dagger\hat{a}=\hat{n}

photon number

E_n = \langle \hat{n} \rangle + \frac{1}{2}

E_n = \langle \hat{n} \rangle + \frac{1}{2}

|\psi\rangle = \cos\theta|0\rangle_\mathrm{logic} + e^{i\phi}\sin\theta|1\rangle_\mathrm{logic}

|\psi\rangle = \cos\theta|0\rangle_\mathrm{logic} + e^{i\phi}\sin\theta|1\rangle_\mathrm{logic}

|0\rangle_\mathrm{logic}, |1\rangle_\mathrm{logic}:

|0\rangle_\mathrm{logic}, |1\rangle_\mathrm{logic}:

photon polarization

photon path

photon timing

photon number

...

|1\rangle_\mathrm{logic}

|1\rangle_\mathrm{logic}

|0\rangle_\mathrm{logic}

|0\rangle_\mathrm{logic}

|\psi\rangle

|\psi\rangle

qubit Bloch sphere