Particle and wave:

Quantum information processing

with non-Gaussian light

Jonas Neergaard-Nielsen, bigQ - DTU Physics

Vision:

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

DNRF Center for Macroscopic Quantum States

quadrature operators:

x,p \rightarrow \hat{x}, \hat{p}

continuous variables for light

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

quadrature operators:

quadrature operators:

x,p \rightarrow \hat{x}, \hat{p}

Gaussian states:   Gaussian Wigner functions

squeezed

thermal

coherent

Gaussian operations:   maintain Gaussianity

  • most light is naturally Gaussian
  • easy to do (experiment)
  • easy to describe (theory)
  • deterministic

quadrature squeezing

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

quadrature squeezing

    squeezer (OPO)

applications of squeezed light

sensing:

  • enhanced sensitivity in quantum-limited measurements, e.g. LIGO

 

quantum information:

  • quantum teleportation
  • state encoding

LIGO collaboration, Nature Photonics 7, 613 (2013)

squeezed posters - please enjoy tonight!

Casper Rubæk Breum

Distributed phase sensing

with 4-mode entanglement

Jens Arnbak

Extreme squeezing - towards 20 dB

Gaussian CV-QIP

  • most light is naturally Gaussian
  • easy to do (experiment)
  • easy to describe (theory)
  • deterministic
  • NO universal quantum computation
  • NO entanglement distillation
  • NO error correction of Gaussian noise

Many experimental successes:

  • quantum key distribution
  • teleportation
  • quantum memory
  • various gates
  • cluster state generation
  • ...

non-Gaussian element needed to complete CV-QIP

+

the simplest:  single photon detector

entanglement distillation by photon detection

H Takahashi, JSNN, M Takeuchi, M Takeoka, K Hayasaka, A Furusawa & M Sasaki, Nature Photonics 4, 178 (2010)

create non-Gaussian states by subtracting photons

JSNN, BM Nielsen, C Hettich, K Mølmer & ES Polzik, PRL 97, 083604 (2006)

- and many others since then

\hat{S}|0\rangle \rightarrow \hat{a}\hat{S}|0\rangle\propto\hat{S}|1\rangle

squeezed qubits

\cos\frac{\theta}{2} \hat{S} |0\rangle + e^{i\phi} \sin\frac{\theta}{2} \hat{S} |1\rangle
\hat{S} |0\rangle
\hat{S} |1\rangle

ambiguous photon subtraction (PS) 

arbitrary superposition of PS and no-PS squeezed vacuum:

JSNN, M Takeuchi, K Wakui, H Takahashi, K Hayasaka,

M Takeoka & M Sasaki, PRL 105, 053602 (2010)

Schrödinger kittens

Squeezed photon is very similar to small-amplitude "Schrödinger cat" state, a superposition of clearly distinguishable coherent states

\hat{S}|1\rangle
|\alpha\rangle - |{-\alpha}\rangle

towards macroscopic quantum superpositions

larger states

more modes

massive physical systems

larger states

more modes

massive physical systems

micro-macro entangled states

micro-macro entangled states

UL Andersen & JSNN, PRA 88, 022337 (2013)

|\Psi\rangle = (|0\rangle + |1\rangle)|\psi^+\rangle + (|0\rangle - |1\rangle)|\psi^-\rangle
|\psi^-\rangle
|\psi^+\rangle

larger states

more modes

massive physical systems

non-Gaussian cluster states

non-Gaussian cluster states

measurement-based quantum computation paradigm:

multimode-entanglement + measurement and feed-forward

Implement with temporal and spatial modes in fibres

- based on scheme by N. Menicucci, demonstrated in A. Furusawa lab:

S Yokoyama et al., Nature Photonics 7,  982 (2013)

non-Gaussian cluster states

larger states

more modes

massive physical systems

"mechanical kittens"

"mechanical kittens"

grand goal: bring mechanical object in superposition of being "here" and "there"

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

cavity opto-mechanical interaction: radiation pressure / phase shift

"mechanical kittens"

"mechanical kittens"

blessing and curse: large superpositions are extremely fragile and sensitive to e.g. phase noise - may be used for probing decoherence effects

UB Hoff, J Kollath-Bönig, JSNN, UL Andersen, PRL 117, 143601 (2016)

conclusion

non-Gaussian quantum optics have rich applications in

fundamental quantum mechanics

and quantum information processing

QPIT / bigQ

Xueshi Guo

Shuro Izumi

Dennis Høj

Kristian-Rasmussen

Jan Bilek

Casper Breum

Joost van der Heijden

Ulrik Andersen

Mikkel Larsen, Ulrich Hoff, Jens Arnbak

Thank you!