Jonas Neergaard-Nielsen PRO
Associate Professor @ DTU Physics, Denmark
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
E[1ex]=21mωx2+2m1p2=xˉ2+pˉ2
\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:
xˉ: mechanical oscillator position,
light field amplitude, etc.
Harmonic oscillators
Quantum harmonic oscillators
[x^,p^]=i
[\hat{x}, \hat{p}]=i
ΔxΔp≥21
\Delta x\Delta p \ge \frac{1}{2}
x,p→x^,p^
x,p \rightarrow \hat{x}, \hat{p}
Quantum harmonic oscillators
Quantum harmonic oscillators
∣0⟩
|0\rangle
∣1⟩
|1\rangle
∣2⟩
|2\rangle
∣3⟩
|3\rangle
∣4⟩
|4\rangle
∣6⟩
|6\rangle
∣7⟩
|7\rangle
∣5⟩
|5\rangle
a^
\hat{a}
a^†
\hat{a}^\dagger
↶
\curvearrowleft
↷
\curvearrowright
creation and annihilation operators
x^=2a^†+a^,p^=i2a^†−a^
\hat{x}=\frac{\hat{a}^\dagger+\hat{a}}{\sqrt{2}},\quad
\hat{p}=i\frac{\hat{a}^\dagger-\hat{a}}{\sqrt{2}}
∣n⟩
|n\rangle
a^†a^=n^
\hat{a}^\dagger\hat{a}=\hat{n}
photon number
En=⟨n^⟩+21
E_n = \langle \hat{n} \rangle + \frac{1}{2}
Quantum information: qubits
∣ψ⟩=cosθ∣0⟩logic+eiϕsinθ∣1⟩logic
|\psi\rangle = \cos\theta|0\rangle_\mathrm{logic} + e^{i\phi}\sin\theta|1\rangle_\mathrm{logic}
∣0⟩logic,∣1⟩logic:
|0\rangle_\mathrm{logic}, |1\rangle_\mathrm{logic}:
photon polarization
photon path
photon timing
photon number
...
∣1⟩logic
|1\rangle_\mathrm{logic}
∣0⟩logic
|0\rangle_\mathrm{logic}
∣ψ⟩
|\psi\rangle
qubit Bloch sphere
Photonic qubits
Not so easy to create single photons:
- very weak laser beam, ⟨n⟩≪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⟩⟨1∣
homodyne detection ∣x⟩⟨x∣
single photons
Gaussian states
2n 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 xθ
Gaussian states
Gaussian states and operations
Gaussian states: Gaussian (non-negative) Wigner function
Gaussian operations: transforming Gaussian states ↔ 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
ΔxΔp≥21
\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
- Set up a massively entangled cluster state
- Do measurement and feed-forward
- ...
- 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
H^int=−ℏg0a^†a^(b^+b^†)
\hat{H}_{\mathrm{int}} = -\hbar g_0 \hat{a}^\dagger\hat{a}(\hat{b}+\hat{b}^\dagger)
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
Thank you!
Quantum optics - macroscopic states Jonas Neergaard-Nielsen, bigQ / QPIT
Quantum optics - macroscopic states
By Jonas Neergaard-Nielsen
Quantum optics - macroscopic states
Modern Physics lecture given at DTU Physics, 25 April 2018
- 819
