Quantum optics -
macroscopic states

Jonas Neergaard-Nielsen, bigQ / QPIT

  • experimental quantum optics

  • labs in 309 basement

  • ~30 people​

...to radically advance our understanding of macroscopic quantum effects and to exploit these macroscopic effects for demonstrating quantum supremacy

=

DNRF Center of Excellence

2018–2024

Quantum optics

recap / introduction

Harmonic oscillators

\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.

Harmonic oscillators

Quantum harmonic oscillators

[\hat{x}, \hat{p}]=i
\Delta x\Delta p \ge \frac{1}{2}
x,p \rightarrow \hat{x}, \hat{p}

Quantum harmonic oscillators

Quantum harmonic oscillators

|0\rangle
|1\rangle
|2\rangle
|3\rangle
|4\rangle
|6\rangle
|7\rangle
|5\rangle
\hat{a}
\hat{a}^\dagger
\curvearrowleft
\curvearrowright

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

photon number

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

Quantum information: qubits

|\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}:

photon polarization

photon path

photon timing

photon number

...

|1\rangle_\mathrm{logic}
|0\rangle_\mathrm{logic}
|\psi\rangle

qubit Bloch sphere

Photonic qubits

Not so easy to create single photons:

  • very weak laser beam, \(\langle n \rangle \ll 1\), and post-selection
  • down-conversion (pair production) and heralded photon detection
  • quantum dots, etc.

Continuous variables
quantum optics & information

DV vs. CV

Optical DV vs. CV

photon detection \( |1\rangle\langle1| \)

homodyne detection \( |x\rangle\langle x| \)

single photons

Gaussian states

\(2^n\) dimensional

infinite dimensional

probabilistic

deterministic

Wigner function

\(W(x,p)\): quasi-probability distribution of quantum state in phase space

can be negative - a sign of strong non-classicality

Quantum state tomography

reconstruct a state's Wigner function by tomographic \(x\) measurements

homodyne detection of \(x_\theta\)

Gaussian states

Gaussian states and operations

Gaussian states: Gaussian (non-negative) Wigner function

Gaussian operations: transforming Gaussian states \(\leftrightarrow\) Gaussian states

  • most light is naturally Gaussian
  • easy to do (experiment)
  • easy to describe (theory)
  • deterministic
  • no entanglement increase by local Gaussian operations
  • no universal quantum computation

only the noise product is lower bounded

Squeezing

\Delta x\Delta p \ge \frac{1}{2}

Squeezer (OPO)

Hybrid CV-DV

include photon-level operation on CV states

Single photon detectors

Schrödinger kitten states

subtract a photon from a squeezed vacuum state - becomes non-Gaussian

the result resembles a superposition of coherent state ~ small "Schrödinger cat"

Kittens in the wild, 2012

Squeezed qubits

many other uses, e.g. entanglement distillation

Increase entanglement by subtraction

Other non-Gaussian states

Project #1

DV teleportation of CV states

(Casper)

Quantum teleportation

DV states

CV states

Bouwmeester et al. 1997

Takeda et al. 2013

Furusawa et al. 1998

DV teleportation

(single photons)

CV teleportation

(two-mode squeezing)

Parallel single photon teleporters

CV states: larger Hilbert space {0, 1, 2, 3, ...}

- split into multiple modes, each teleported by single-photon teleporter

Project #2

Cluster states for optical quantum computers

(Mikkel)

Measurement-based QC

  1. Set up a massively entangled cluster state
  2. Do measurement and feed-forward
  3. ...
  4. Profit!

Optical MBQC

Implementation

Use temporal and spatial light modes

Fibre-based setup (?) - fast switches available

[ sketch ]

Project #3

Mechanical kittens

(Dennis)

Opto-mechanical interaction

\hat{H}_{\mathrm{int}} = -\hbar g_0 \hat{a}^\dagger\hat{a}(\hat{b}+\hat{b}^\dagger)
image/svg+xml

Radiation pressure / phase shift

High Q-factor micro-membranes

Experimental scheme (heavily simplified)

Protocol

m = 1

m = 2

m = 3

with 1 thermal phonon

with 5% optical loss

10 dB squeezing

80% detector eff.

Simulated states

Conclusion

Einstein agreed with Schrödinger - a cat in superposition is nonsense...

 

- but perhaps we can put Einstein on a superposed swing?

Xueshi Guo

Mikkel V. Larsen

Casper R. Breum

Shuro Izumi

The Team

+ former colleagues at NBI (Copenhagen) and NICT (Tokyo)

QPIT / bigQ

blog.bigq.dk

Thank you!