Jonas Neergaard-Nielsen PRO
Associate Professor @ DTU Physics, Denmark
Squeezing and
photon correlation measurements
on a telecom-wavelength OPO
ICQOQI 2017, Minsk - 24 Nov 2017
Jonas S. Neergaard-Nielsen
Technical University of Denmark (DTU)
Hybrid DV/CV optical QIP
Andersen, JSNN, van Loock, Furusawa, Nat. Phys. 11, 713 (2015)
Taking DV/CV Q. communication further
move to telecom wavelengths
send to fibres
transmit through installed networks
Outline
- Goal: hybrid teleportation
- Our hardware
- OPO output: squeezing and correlations
- Kennedy receiver
DV teleportation of CV states
Quantum teleportation
Bouwmeester et al., Nature 390, 575 (1997)
DV teleportation of qubits
Furusawa et al., Science 282, 706 (1998)
CV teleportation of coherent states
Takeda et al., Nature 500, 315 (2013)
CV teleportation of qubits
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 quantum scissors
Andersen & Ralph, PRL 111, 050504 (2013)
CV states: larger Hilbert space {0, 1, 2, 3, ...}
- split into multiple modes, each teleported by single-photon teleporter
Quantum scissors
Pegg et al., PRL 81, 1604 (1998)
Our hardware
Laser
NKT Koheras Basik X15
- 2 W amplified 1550 nm fibre laser
- low phase noise version
SHG + OPO
cavity-enhanced SPDC
- large squeezing possible
- well-defined spatial and spectral modes
- good mode-selectivity -> high purity in state tomography
SHG + OPO
bow-tie design
- relatively compact (32 cm long)
- low folding-angle (5°)
16 mm PPKTP crystal
- wedged - for easy tuning of dual polarization resonance
- Type 0 or Type II phase matching - crystal can easily be swapped
SHG + OPO
Nonlinearity
measured nonlinearity
P_{2\omega} = E_{NL} P_\omega^2
P2ω=ENLPω2
E_{NL} = \frac{64 d_{33}^2 L_c}{\epsilon_c c \lambda^3 n_z(\lambda) n_z(\lambda/2)} h(\Delta k)
ENL=ϵccλ3nz(λ)nz(λ/2)64d332Lch(Δk)
| method | E NL |
|---|---|
| single pass SHG | 0.34 %/W |
| resonant SHG | 0.30 %/W |
| intra-cavity loss (reflection dip) | 0.37 %/W |
| parametric gain | 0.30 %/W |
x = \sqrt{\frac{P_{\mathrm{pump}}}{P_{\mathrm{threshold}}}}
x=PthresholdPpump
\textrm{gain}=\frac{1}{(1-x)^{2}}
gain=(1−x)21
Effective nonlinearity - SHG conv. efficiency:
Boyd-Kleinman focusing and
phase matching function
P_\mathrm{threshold} = \frac{(T+\mathcal{L})^2}{4E_\mathrm{NL}}
Pthreshold=4ENL(T+L)2
FPGA locking
Red Pitaya FPGA + CPU
- 2x analog in + 2x out (14 bit, 125 MS/s)
- open source
- oscilloscope, spectrum analyzer, PID, ...
- "app store"
- 259€
FPGA locking
PyRPL (Python Red Pitaya Lockbox)
- extends Red Pitaya with new FPGA modules and Python GUI
- locking (e.g. PDH for cavity) becomes simple and very flexible
- developed by Leonhard Neuhaus and Samuel Deleglise at LKB, Paris
Homodyne detector
fibre 50/50 BS; output focused directly onto 99% efficient Ø=100 µm diodes by GRIN lens
Single photon detectors
Superconducting nanowire SPDs
developed by S. Miki, T. Yamashita, H. Terai at NICT, Kobe
S. Miki et al., Opt. Exp. 21, 10208 (2013)
Single photon detectors
Superconducting nanowire SPDs
developed by S. Miki, T. Yamashita, H. Terai at NICT, Kobe
Single photon detectors
OPO output:
Squeezing and photon correlations
Fibre-coupled squeezing
380 mW pump →
\epsilon/2\pi\approx 5.15\ \mathrm{MHz}
ϵ/2π≈5.15 MHz
S_{\pm}(f) = 1 \pm \frac{4\eta \epsilon\gamma}{(\gamma\mp\epsilon)^2+(2\pi f)^2}
S±(f)=1±(γ∓ϵ)2+(2πf)24ηϵγ
\eta_\mathrm{fc} \approx 0.95
ηfc≈0.95
fibre coupling efficiency
OPO photon correlations
Broad phase matching bandwidth ->
wide spectrum of correlated modes
Corresponding picture in time-domain:
Photons escaping once every round-trip time
OPO photon correlations
G^{(2)}(\tau) = \langle \hat{a}^\dag(t)\hat{a}^\dag(t+\tau)\hat{a}(t+\tau)\hat{a}(t)\rangle
G(2)(τ)=⟨a^†(t)a^†(t+τ)a^(t+τ)a^(t)⟩
Measure second order temporal correlations of Type 0 OPO output
OPO photon correlations
Exponential envelope: cavity decay
Comb structure: cavity round-trip time
"Tooth" shape: detector time response (+ 1/source bandwidth, but negligible)
OPO photon correlations
Lu & Ou, PRA 62, 033804 (2000)
Goto et al., PRA 68, 015803 (2003)
Zielińska & Mitchell, PRA 90, 063833 (2014)
Model:
time axis parameters:
- OPO decay rate
- cavity length/round-trip time
- detector jitter
- offset
count axis parameters:
- background (uncorrelated coinc.)
- effective # of excited spectral modes
- pump power
the only fixed
parameter when fitting
OPO photon correlations
P_\mathrm{pump} = 0.05\ \mathrm{mW}
Ppump=0.05 mW
\gamma/2\pi = 8.2 \pm0.1\ \mathrm{MHz}
γ/2π=8.2±0.1 MHz
l_\mathrm{cav} = 331.193\pm0.003\ \mathrm{mm}
lcav=331.193±0.003 mm
\sigma_{t,\mathrm{SSPD}} = 47.19\pm0.07\ \mathrm{ps}
σt,SSPD=47.19±0.07 ps
N_\textrm{SPDC
pairs}= 1198 \pm 4
NSPDC pairs=1198±4
low pump power
OPO photon correlations
P_\mathrm{pump} = 0.05\ \mathrm{mW}
Ppump=0.05 mW
\gamma/2\pi = 7.8 \pm0.1\ \mathrm{MHz}
γ/2π=7.8±0.1 MHz
l_\mathrm{cav} = 331.168\pm0.001\ \mathrm{mm}
lcav=331.168±0.001 mm
\sigma_{t,\mathrm{SSPD}} = 40.74\pm0.06\ \mathrm{ps}
σt,SSPD=40.74±0.06 ps
N_\textrm{SPDC
pairs}= 38 \pm 1
NSPDC pairs=38±1
insert 100 GHz DWDM filter - background reduced
OPO photon correlations
P_\mathrm{pump} = 100\ \mathrm{mW}
Ppump=100 mW
\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
γ/2π=7.1±0.5 MHz
l_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
lcav=331.162±0.009 mm
\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
σt,SSPD=46.7±0.3 ps
N_\textrm{SPDC
pairs}= 40.6 \pm 0.3
NSPDC pairs=40.6±0.3
high pump power,
DWDM filter
OPO photon correlations
P_\mathrm{pump} = 100\ \mathrm{mW}
Ppump=100 mW
\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
γ/2π=7.1±0.5 MHz
l_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
lcav=331.162±0.009 mm
\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
σt,SSPD=46.7±0.3 ps
N_\textrm{SPDC
pairs}= 40.6 \pm 0.3
NSPDC pairs=40.6±0.3
high pump power,
DWDM filter
Kennedy receiver
The problem
Single-rail encoding of photonic qubits:
|0\rangle_\mathrm{logic} \equiv |0\ \mathrm{photons}\rangle
∣0⟩logic≡∣0 photons⟩
|1\rangle_\mathrm{logic} \equiv |1\ \mathrm{photons}\rangle
∣1⟩logic≡∣1 photons⟩
These states can be distinguished by a photon detector
- but what about the conjugate basis?
|+\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle + |1\rangle)
∣+⟩=21(∣0⟩+∣1⟩)
|-\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle - |1\rangle)
∣−⟩=21(∣0⟩−∣1⟩)
Orthogonal, but no practical measurement can distinguish them perfectly
Photon counting: 50% error rate
Homodyning: 10% error rate
Kennedy receiver
Phase space displacement before photon counting
Known from BPSK discrimination
e.g. Tsujino et al., PRL 106, 250503 (2011)
7% error rate possible
Implementation
Detector tomography with coherent probe states
Proof-of-principle: we compensate all losses and detector efficiency
see also Zhang et al., Nat. Phot. 6, 364 (2012)
Results
reconstructed POVM with
optimal displacement
S. Izumi, JSNN, U.L. Andersen - under submission
Ulrik Lund Andersen
Xueshi Guo
Mikkel V. Larsen
Casper R. Breum
Shuro Izumi
Thank you!
Squeezing and photon correlation measurements on a telecom-wavelength OPO ICQOQI 2017, Minsk - 24 Nov 2017 Jonas S. Neergaard-Nielsen Technical University of Denmark (DTU)
Squeezing and photon correlation measurements on a telecom-wavelength OPO
By Jonas Neergaard-Nielsen
Squeezing and photon correlation measurements on a telecom-wavelength OPO
Presented at ICQOQI 2017 in Minsk, Belarus.
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