Quantum optics with near lifetime-limited
quantum-dot transitions in a nanophotonic
waveguide
Henri Thyrrestrup,
∗,†
Gabija Kirˇsansk˙e,
†
Hanna Le Jeannic,
†
Tommaso
Pregnolato,
†
Liang Zhai,
†
Laust Raahauge,
†
Leonardo Midolo,
†
Nir Rotenberg,
†
Alisa Javadi,
†
R¨udiger Schott,
‡
Andreas D. Wieck,
‡
Arne Ludwig,
‡
Matthias C.
L¨obl,
¶
Immo S¨ollner,
¶
Richard J. Warburton,
¶
and Peter Lodahl
∗,†
†Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen,
Denmark
‡Lehrstuhl f¨ur Angewandte Festk¨orperphysik, Ruhr-Universit¨at Bochum, Universit¨atsstrasse
150, D-44780 Bochum, Germany
¶Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel,
Switzerland
E-mail: henri.nielsen@nbi.ku.dk; lodahl@nbi.ku.dk
Phone: +4535325306
Abstract
Establishing a highly efficient photon-emitter interface where the intrinsic linewidth
broadening is limited solely by spontaneous emission is a key step in quantum optics. It
opens a pathway to coherent light-matter interaction for, e.g., the generation of highly
indistinguishable photons, few-photon optical nonlinearities, and photon-emitter quan-
tum gates. However, residual broadening mechanisms are ubiquitous and need to be
1
arXiv:1711.10423v2 [quant-ph] 7 Feb 2018
combated. For solid-state emitters charge and nuclear spin noise is of importance and
the influence of photonic nanostructures on the broadening has not been clarified. We
present near lifetime-limited linewidths for quantum dots embedded in nanophotonic
waveguides through a resonant transmission experiment. It is found that the scat-
tering of single photons from the quantum dot can be obtained with an extinction of
66 ± 4%, which is limited by the coupling of the quantum dot to the nanostructure
rather than the linewidth broadening. This is obtained by embedding the quantum
dot in an electrically-contacted nanophotonic membrane. A clear pathway to obtain-
ing even larger single-photon extinction is laid out, i.e., the approach enables a fully
deterministic and coherent photon-emitter interface in the solid state that is operated
at optical frequencies.
In the optical domain, the high density of optical states implies that the interaction be-
tween a single optical mode and an emitter is usually weak. As a consequence, single-photon
sources, nonlinear photon-photon interactions, and photonic quantum gates are inefficient.
These limitations can be overcome by placing single quantum emitters in photonic nanos-
tructures where the routing of photons into a guided mode can be highly efficient. Addi-
tionally the interaction between a single photon and a single quantum emitter needs to be
coherent, which entails that a distinct phase relation is maintained when a single photon is
scattered from the emitter, i.e., incoherent broadening mechanisms must be efficiently sup-
pressed. Such a lifetime-limited photon-emitter interface enables indistinguishable single-
photon sources,
1–5
quantum optical nonlinearities at the single photon level
6–11
and may
find applications in quantum many-body physics.
12
Consequently, many different solid-state
quantum platforms are currently under development, each of which is based on a specific
quantum emitter
7,13–17
and with its own strengths and weaknesses. A coherent and determin-
istic photon-emitter interface may be a building block for complex architectures in quantum
communication, towards the ultimate goal of distributed photonic quantum networks.
18–20
Epitaxially grown quantum dots (QDs) embedded in GaAs membranes are the basis for a
particularly mature platform, as they are now routinely integrated into a variety of nanopho-
2
tonic structures.
21
By molding the photonic environment of QDs at their native nanoscale
the emitted single photons can be coupled to a guided mode with near-unity efficiency
22
and made highly indistinguishable.
3,5
The access to lifetime-limited resonance linewidths
is a stricter requirement than that of indistinguishability of subsequently emitted photons
since the former requires suppression of both slow drift (charge or spin noise)
23
and fast pure
dephasing (phonon decoherence).
24,25
Remarkably, this can be obtained by embedding QDs
in electrically-contacted bulk semiconductor structures.
26
However, exposed etched surfaces
present in nanophotonic structures may pose a problem since they could induce charge noise
in the samples. Here, we address this issue and demonstrate near lifetime-limited photon-QD
interaction in a nanophotonic waveguide. This is an essential step towards a deterministic
on-chip few-photon nonlinearity, which could form the basis of, e.g., a deterministic Bell-state
analyzer
27
and is a prerequisite for coupling multiple QDs.
Figure 1(a) shows the layout of the experiment. Two types of coherent measurements are
performed on a QD that is efficiently coupled to a waveguide: resonant fluorescence (RF)
and resonant transmission (RT) measurements. In RF, the QD is excited at the emitter’s
resonance frequency ω
0
from free-space and subsequently emits photons into the guided mode
with a probability determined by the β-factor. The photons are subsequently coupled out
of the waveguide at a distant location with a circular grating and detected.
In RT, the QD is excited through the waveguide by a weak laser and the interference
between the scattered and incident photons is recorded. RT measurements on a QD were first
reported in Ref. 28. For a QD ideally coupled to the waveguide (β = 1) and in the absence
of dephasing (Γ
d
= 0), the scattered and incident light interferes destructively and incident
single photons resonant with the QD transition are reflected, as sketched in Figure 1(c).
When detuned off-resonance, the photons do not interact with the QD and are consequently
transmitted. A finite pure dephasing rate Γ
d
effectively smears out the energy levels and
partially destroys the quantum coherence between the scattered and transmitted photons.
This allows on-resonance photons to be transmitted and broadens the QD resonance, cf.
3
illustration in Figure 1(c).
The resonant scattering leads to a Lorentzian extinction dip in the transmission spectrum,
whose depth depends on the effective emitter-waveguide coupling efficiency β and the pure
dephasing rate of the emitter Γ
d
. Here β 6= 1 is due to the photons that are not scattered
into the waveguide mode, including the fraction of photons that are emitted into the phonon
sideband.
29,30
The power dependent transmission intensity on resonance is given by
6
T = 1 +
(β −2)β
(1 + 2γ
r
)(1 + S)
, (1)
where γ
r
= Γ
d
/Γ is the pure dephasing rate relative to the homogeneous linewidth Γ and
S = n
τ
/n
c
quantifies the effective saturation of the QD transition. n
τ
is the mean photon
number of photons within the lifetime of the emitter input field that is normalized by a
critical input flux
n
c
=
1 + 2γ
r
4β
2
, (2)
which represents the number of photons in the waveguide within the lifetime of the emitter
resulting in an excited state population of 1/4 for the QD. The corresponding width of the
Lorentzian trough is given by
Γ
RT
= (Γ + 2Γ
d
)
√
1 + S. (3)
We note that a larger dephasing rate Γ
d
causes the extinction dip to both widen and lessen,
as resonant photons that would otherwise be reflected are transmitted instead. In contrast,
a non-ideal coupling (β < 1) only reduces the depth for a fixed decay rate. It is therefore
possible to extract both β and Γ
d
in the weak excitation limit (n
τ
n
c
) from Eq. (1) if
the homogeneous linewidth Γ is known independently from lifetime measurements. The β
2
dependence of T in Eq. (1) makes the minimum transmission a sensitive probe of the effective
β-factor whereas the dephasing rate Γ
d
can be extracted from the measured linewidth. At
4
larger incident powers the QD transition is power broadened, as seen from Eq. (3), and
results in a decrease of the transmission extinction.
In the following experiment the waveguide sample featured weak reflections from the ter-
mination ends, meaning that weak cavity resonances were modulating the spectral response
of the system. Consequently, the transmission response has a Fano spectral character,
6,31,32
which slightly modifies the Lorentzian profile that Eq. (3) describes. See Supplementary
Information for detailed expressions for the Fano resonances that were used to model the
experimental data.
The experiment is conducted on a single QD located near the center of a 600 nm wide
and 175 nm thick planar GaAs nanobeam waveguide. The width was chosen to maintain
a relatively large separation between the QD and nearby interfaces while still supporting
a well-confined mode (see Figure 1(b)) with a large β-factor above 0.5. The waveguide
supports three guided modes and the higher order modes can largely be filtered out via
photonic elements on the chip (see Supplementary Information). The studied QD is located
approximately 15 µm away from the collection grating, which is a second-order circular Bragg
grating optimized for a wavelength of 920 nm,
33
cf. Figure 1(a) with a full SEM image of the
sample shown in Supplementary Information. The QD layer with a density of around 1 µm
−2
is embedded in a p-i-n diode (see Ref. 5 for details) and held at a temperature of 1.7 K in order
to stabilize the local charge environment and to suppress phonon broadening.
25,29,30
Charge
stabilization is essential in order to achieve narrow optical linewidths.
34
We consider a bright
neutral exciton line X
0
of the QD with an emission wavelength of 920.86 nm at 0.2 V, cf.
Figure 2(a) with other charge states being visible at longer wavelengths. The external bias
enables tuning of the QD transition energy. The decay rate of the QD is measured by time
correlated single photon counting on an avalanche photo diode (APD) with a response time
of 50 ps where the QD is excited by a picosecond-pulsed laser tuned to the p-shell at 905.8 nm.
Excitation in the p-shell prevents the excitation of free carriers, which could shield the QD
from the applied field and thus potentially modify the decay rate. The measured decay curve
5
