On-demand semiconductor source of
entangled photons with high efficiency
and indistinguishability
Hui Wang, Hai Hu, T. H. Chung, Qin Jian, Xiaoxia Yang, Jin-Peng Li, Ren-Ze Liu,
Han-Sen Zhong, Yu-Ming He, Xing Ding, Yu-Hao Deng, C. Schneider, Qing Dai,
Yong-Heng Huo, Sven Höfling, Chao-Yang Lu and Jian-Wei Pan
1
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern
Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
2
CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and
Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026,
China
3
Nanophotonics Research Division, CAS Center for Excellence in Nanoscience, National
Center for Nanoscience and Technology, Beijing, 100190, China
4
Technische Physik, Physikalisches Instität and Wilhelm Conrad Röntgen-Center for
Complex Material Systems, Universitat Würzburg, Am Hubland, D-97074 Würzburg,
Germany
5
SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews, KY16 9SS,
United Kingdom
Abstract:
An outstanding goal in quantum optics and scalable photonic quantum technology
is to develop a source that each time emits one and only one entangled photon pair
with simultaneously high entanglement fidelity, extraction efficiency, and photon
indistinguishability. By coherent two-photon excitation of a single InGaAs quantum
dot coupled to a circular Bragg grating bullseye cavity with broadband Purcell
enhancement, we generate entangled photon pairs with a state fidelity of 0.90(1),
single-photon extraction efficiency of 0.79(1), and photon indistinguishability up to
0.93(1) simultaneously. Our work will open up many applications in high-efficiency
multi-photon experiments and solid-state quantum repeaters.
Quantum entanglement [1] between flying photons [2] are central in the Bell test [3]
of the contradiction between local hidden variable theory and quantum mechanics [4].
Aside from the fundamental interest, the entangled photons have been recognized as
the elementary resources in quantum key distribution [5], quantum teleportation [6],
quantum metrology [7] and quantum computing [8]. There has been a strong interest in
experimental generations of entangled photons from trapped atoms [9], spontaneous
parametric down-conversion (SPDC) [10], and quantum dots [11] etc. A checklist of
relevant parameters for an entangled-photon pair source include [12]:
A. Entanglement fidelity. The produced two photons should be in a state close to a
maximally entangled Bell state;
B. On-demand generation. The source should, at a certain time, emit one and only
one pair of entangled photons;
C. Collection efficiency. The photons should be extracted out from the source and
collected with a high efficiency;
D. Indistinguishability. The photons emitted from different trials should be exactly
identical in all degrees of freedom.
The past decades witnessed increasingly more sophisticated Bell tests and advanced
photonic quantum information technologies enabled by developments of the photon
entanglement source striving to fulfill the four criteria. For example, by combining A
and C, the SPDC photons allowed for Bell tests closing both the locality and detection
loopholes simultaneously [13, 14]. Very recently, ultrafast pulsed SPDC satisfied A, C,
and D and was exploited to demonstrate 12-photon entanglement and scattershot boson
sampling [15]. However, the item B remains an intrinsic problem for the SPDC where
the photon pairs are generated probabilistically, and inevitably accompanied with
undesirable multi-pair emissions.
An alternative route to generate entangled photons is through radiative cascades in
single quantum emitters such as quantum dots which can have a near-unity quantum
efficiency [11], therefore meeting the item B. However, the solid-state artificial atom
system has its own challenges, including the structural symmetry, extraction efficiency,
and dephasings. To this end, tremendous progress has been reported in eliminating the
fine structure splitting of neutral excitons [16-18], improving the extraction efficiency
using double-micropillar structures [19] or broadband antennas [20-22], and enhancing
the entanglement fidelity and photon indistinguishability using resonant excitation [23,
24]. Encouragingly, the entanglement fidelity (A) and the photon indistinguishability
(D) (for 2 ns separation) has reached 0.978(5) and 0.93(7), respectively [18, 24]. Very
recently, the entanglement fidelity of 0.9 (A) was combined with a record-high pair
extraction efficiency of 0.37 per pulse (C) on the same device [22].
Despite these progress, it remained an outstanding challenge to simultaneously fulfill
all the criteria A-D, which is crucial for the photon entanglement source to be useful
for many applications such as quantum repeaters [25] and optical quantum computing
[26]. For example, efficiently “fusing” entangled photon pairs into large-scale cluster
states relies on high entanglement fidelity, quantum interference visibility and heralding
efficiency all together [27].
In this Letter, we report a near-perfect entangled-photon source that for the first time
fulfills A-D. By coherently driving a single InGaAs quantum dot coupled to a bullseye
microcavity with broadband Purcell enhancement, we create entangled photons with a
fidelity of 0.90(1), extraction efficiency of 0.79(1), and photon indistinguishability up
to 0.93(1) simultaneously.
While polarized single-photon sources from quantum dot-micropillars with both high
efficiency and photon indistinguishability have been demonstrated very recently [28],
the creation of near-perfect entangled photon pairs posed additional challenges. First,
the fine structure splitting should be smaller than the radiative linewidth of the single
photons, leaving no room for leaking which-path information. Second, as the two single
photons from the biexciton-exciton (XX-X) radiative cascaded emission have different
wavelengths, broadband Purcell-cavities should be used to enhance both the XX and X
photons. The Purcell factor that can accelerate the radiative decay rate, together with
resonant excitation without inducing dephasing and emission time jitter, is desirable
both for improving the two-photon entanglement fidelity and indistinguishability.
We choose self-assembled InGaAs quantum dots as single quantum emitters which
can have near-unity quantum efficiencies [29]—a prerequisite for the criteria B—and
near-transform-limited emission linewidth [30]. For a broadband high-Purcell cavity,
we adopt circular Bragg grating (CBG) in a bullseye geometry [31] which features a
small effective mode volume and a relatively low Q factor (~150). The CBGs have been
previously employed to enhance the single-photon collection from quantum dots [32]
and nitrogen vacancy centers in diamond [33]. A scanning electron microscope image
of our CBG device is shown in Fig. 1a. We design the parameters of the CBG as detailed
in Fig. 1b in order to align its resonance with a moderate spectral range of ~5 nm to the
center of the wavelength of the photon pairs (see the caption of Fig. 1 and supplemental
materials for more details).
To redirect the single photon emission from downward back to upward, a gold mirror
is fabricated at the bottom of the quantum dot. The idea of backside metallic broadband
mirror has been used in quantum dots membranes and embedded in nanowire [34], solid
immersion lens and antennas [22, 35], etc. A 360 nm thick SiO
2
is sandwiched between
the GaAs membrane and the gold mirror, forming a constructive interference between
the downward and upward light. Our numerical simulation in Fig. 1c shows that for our
chosen parameters, a Purcell factor of ~20 and an extraction efficiency (defined as the
ratio of single photons escaped from bulk GaAs and collected into the first lens) up to
90% can be achieved for both the X and XX photons. Another key issue to check is that
whether the emitted photons can be efficiently collected into a single-mode fiber. We
simulate the far field intensity distribution using finite-different time-domain method.
The numerical results (see in Fig. 1d) shows that the single-photon emission is highly
directional and slightly elliptical. An objective lens with a numerical aperture (NA) of
0.65 is capable of collecting ~90% of the emitted photons.
As illustrated in the inset of Fig. 2a, our scheme to generate entangled photons is via
XX-X cascade radiative decay in an InGaAs quantum dot. The polarization of emitted
photons is determined by the spin of the intermediate exciton states. In our sample, ~
3% of the quantum dots show fine structure splitting below 2.5 µeV. We pick a quantum
dot with a small fine structure splitting of <1.2 µeV, which is limited by the resolution
of the spectrometer. We use coherent two-photon excitation scheme [23] to pump the
quantum dot to the XX state. The energy of the pump pulsed laser is set at the average
energy of the XX and X photons. We observe a clean photon pair emission spectrum as
shown in Fig. 2a, where the X and XX lines are separated by ~1.6 nm.
We vary the average power of the laser and record the photon counts with a nanowire
superconducting single-photon detector. The data for both XX and X photons are shown
in Fig. 2b, where we observe clear Rabi oscillations due to a coherent control of the
quantum dot biexcitonic system [23]. The XX and X photon count rates reach their first
maxima at π pulses under a pumping laser power of ~16 nW. Such a power is ~ 3 orders
of magnitudes lower than in non-resonant excitations where the photon counts usually
grow asymptotically with pump power [16, 19]. The efficient excitation requiring only
very low pump power is important for eliminating the undesired multiexciton states and
fluctuating electrical noise in the vicinity of the quantum dot.
Under a pumping rate of 76 MHz and at π pulse, the final count rates observed in our
experimental set-up are
6
4.41 10 / s×
and
6
4.34 10 / s×
for the XX and X photons,
respectively. By bookkeeping independently calibrated single-photon detection
efficiency (~76%), optical path transmission rate (~25%, including optical window,
grating, two beam splitters and fiber connectors), and single-mode fiber coupling
efficiency (~65%), XX excited-state preparation efficiency at π pulse and radiation
efficiency (~70%), blinking (~84%), we estimate that 79.5% (78.2%) of the generated
XX (X) single photons are collected into the first objective lens (NA=0.68). Thus the
photon pair extraction efficiency is 62.2% (criteria C).
The record high photon counts observed in Fig. 2b suggest a strong Purcell coupling
with single quantum emitters. To quantify the Purcell factor, we perform time-resolved
resonance fluorescence measurements under the two-photon excitation to extract the
radiative lifetimes of the XX and X photons (Fig. 2c), which are 66.4(1) ps and 126.7(4)
ps, respectively, shortened by a factor of 11.3 and 8.7 compared to the quantum dot in
bulk GaAs. The Purcell factor of the XX photon is higher than that of the X photon,