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

  1. Goal: hybrid teleportation
  2. Our hardware
  3. OPO output: squeezing and correlations
  4. 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=ENLPω2P_{2\omega} = E_{NL} P_\omega^2
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=64d332Lcϵccλ3nz(λ)nz(λ/2)h(Δk)E_{NL} = \frac{64 d_{33}^2 L_c}{\epsilon_c c \lambda^3 n_z(\lambda) n_z(\lambda/2)} h(\Delta k)
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=PpumpPthresholdx = \sqrt{\frac{P_{\mathrm{pump}}}{P_{\mathrm{threshold}}}}
\textrm{gain}=\frac{1}{(1-x)^{2}}
gain=1(1−x)2\textrm{gain}=\frac{1}{(1-x)^{2}}

Effective nonlinearity - SHG conv. efficiency:

Boyd-Kleinman focusing and

phase matching function

P_\mathrm{threshold} = \frac{(T+\mathcal{L})^2}{4E_\mathrm{NL}}
Pthreshold=(T+L)24ENLP_\mathrm{threshold} = \frac{(T+\mathcal{L})^2}{4E_\mathrm{NL}}

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

http://pyrpl.readthedocs.io

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\epsilon/2\pi\approx 5.15\ \mathrm{MHz}
S_{\pm}(f) = 1 \pm \frac{4\eta \epsilon\gamma}{(\gamma\mp\epsilon)^2+(2\pi f)^2}
S±(f)=1±4ηϵγ(γ∓ϵ)2+(2πf)2S_{\pm}(f) = 1 \pm \frac{4\eta \epsilon\gamma}{(\gamma\mp\epsilon)^2+(2\pi f)^2}
\eta_\mathrm{fc} \approx 0.95
ηfc≈0.95\eta_\mathrm{fc} \approx 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)⟩G^{(2)}(\tau) = \langle \hat{a}^\dag(t)\hat{a}^\dag(t+\tau)\hat{a}(t+\tau)\hat{a}(t)\rangle

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 mWP_\mathrm{pump} = 0.05\ \mathrm{mW}
\gamma/2\pi = 8.2 \pm0.1\ \mathrm{MHz}
γ/2π=8.2±0.1 MHz\gamma/2\pi = 8.2 \pm0.1\ \mathrm{MHz}
l_\mathrm{cav} = 331.193\pm0.003\ \mathrm{mm}
lcav=331.193±0.003 mml_\mathrm{cav} = 331.193\pm0.003\ \mathrm{mm}
\sigma_{t,\mathrm{SSPD}} = 47.19\pm0.07\ \mathrm{ps}
σt,SSPD=47.19±0.07 ps\sigma_{t,\mathrm{SSPD}} = 47.19\pm0.07\ \mathrm{ps}
N_\textrm{SPDC pairs}= 1198 \pm 4
NSPDC pairs=1198±4N_\textrm{SPDC pairs}= 1198 \pm 4

low pump power

OPO photon correlations

P_\mathrm{pump} = 0.05\ \mathrm{mW}
Ppump=0.05 mWP_\mathrm{pump} = 0.05\ \mathrm{mW}
\gamma/2\pi = 7.8 \pm0.1\ \mathrm{MHz}
γ/2π=7.8±0.1 MHz\gamma/2\pi = 7.8 \pm0.1\ \mathrm{MHz}
l_\mathrm{cav} = 331.168\pm0.001\ \mathrm{mm}
lcav=331.168±0.001 mml_\mathrm{cav} = 331.168\pm0.001\ \mathrm{mm}
\sigma_{t,\mathrm{SSPD}} = 40.74\pm0.06\ \mathrm{ps}
σt,SSPD=40.74±0.06 ps\sigma_{t,\mathrm{SSPD}} = 40.74\pm0.06\ \mathrm{ps}
N_\textrm{SPDC pairs}= 38 \pm 1
NSPDC pairs=38±1N_\textrm{SPDC pairs}= 38 \pm 1

insert 100 GHz DWDM filter - background reduced

OPO photon correlations

P_\mathrm{pump} = 100\ \mathrm{mW}
Ppump=100 mWP_\mathrm{pump} = 100\ \mathrm{mW}
\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
γ/2π=7.1±0.5 MHz\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
l_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
lcav=331.162±0.009 mml_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
σt,SSPD=46.7±0.3 ps\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
N_\textrm{SPDC pairs}= 40.6 \pm 0.3
NSPDC pairs=40.6±0.3N_\textrm{SPDC pairs}= 40.6 \pm 0.3

high pump power,

DWDM filter

OPO photon correlations

P_\mathrm{pump} = 100\ \mathrm{mW}
Ppump=100 mWP_\mathrm{pump} = 100\ \mathrm{mW}
\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
γ/2π=7.1±0.5 MHz\gamma/2\pi = 7.1 \pm0.5\ \mathrm{MHz}
l_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
lcav=331.162±0.009 mml_\mathrm{cav} = 331.162\pm0.009\ \mathrm{mm}
\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
σt,SSPD=46.7±0.3 ps\sigma_{t,\mathrm{SSPD}} = 46.7\pm0.3\ \mathrm{ps}
N_\textrm{SPDC pairs}= 40.6 \pm 0.3
NSPDC pairs=40.6±0.3N_\textrm{SPDC pairs}= 40.6 \pm 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⟩|0\rangle_\mathrm{logic} \equiv |0\ \mathrm{photons}\rangle
|1\rangle_\mathrm{logic} \equiv |1\ \mathrm{photons}\rangle
∣1⟩logic≡∣1 photons⟩|1\rangle_\mathrm{logic} \equiv |1\ \mathrm{photons}\rangle

These states can be distinguished by a photon detector

- but what about the conjugate basis?

|+\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle + |1\rangle)
∣+⟩=12(∣0⟩+∣1⟩)|+\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle + |1\rangle)
|-\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle - |1\rangle)
∣−⟩=12(∣0⟩−∣1⟩)|-\rangle = \tfrac{1}{\sqrt{2}} (|0\rangle - |1\rangle)

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!