Single photon interference between bidirectionally extracted photons originating from semiconductor quantum dots

We report the experimental demonstration of the single-photon interference of bidirectionally extracted photons from epitaxially grown semiconductor quantum dots. The quantum dots were directly connected to single-mode optical fibers. Single-photon nature between transmission and reflection directions was confirmed through detection of antibunching in second-order photon correlation measurements. A Mach–Zehnder interferometer that was naturally formed by introducing the two outputs into a 2 x 2-fiber coupler was used to perform first-order photon correlation measurements.

E pitaxially grown semiconductor III-V quantum dots (QDs) generate bright, indistinguishable and entangled photons [1][2][3][4] with long-term stability and wavelength tunability. Various efforts have been made to integrate a nanoscale photon source such as a QD into a single mode fiber (SMF) from the perspective of consistency with existing optical fiber infrastructures. [5][6][7][8] Recently, we reported the detection of bidirectional single photons using an epitaxially grown InAs QD sandwiched by SMFs. 9) This QD-in-fiber (QDinF) showed long-term stability in terms of emitted photon energy and number, which is one of the most important properties for a fiber-based nanoscale photon emitter from a scientific and engineering viewpoint.
In this paper, we present fiber-based bidirectional singlephoton extraction from epitaxially grown In 0.8 Al 0.2 As QDs. The photons emitted from the single InAlAs QDs were extracted from both sides of the SMFs. Clear antibunching between the two outputs of two SMF patch cables was observed in second-order photon correlation measurements. To confirm bidirectional single-photon extraction, we performed first-order auto-correlation measurements between the two outputs of the SMFs under single-photon emission. Moreover, we discuss whether the QDinF structure has the possibility to work for a well-known dual-rail photon qubit device. 10,11) In 0.8 Al 0.2 As QDs were grown to a density of approximately 2.5 × 10 10 cm −2 on a 600-nm-thick Al 0.35 Ga 0.65 As barrier layer on a non-doped GaAs(001) substrate using molecular-beam epitaxy (RIBER MBE32P). To bidirectionally extract the photons originating from QDs in both directions, the GaAs substrate and an 800-nm-thick Al 0.8 Ga 0.2 As were removed from the 150 nm AlGaAs=InAlAs-QDs= 600 nm AlGaAs structure by chemical etching (HF), and the resulting emitting layer (H 0.75 µm × W 20 µm × L 40 µm) was sandwiched between two FC=PC SMF patch cables (Thorlabs SM600) with a ϕ900 µm jacket. This QDinF device was set in a liquid 4 He reservoir at 4.2 K.
We used a fiber-pigtailed 637-nm laser diode (Throlabs LP637-SF70) as an excitation source. To suppress the laser spectral noise, a bandpass filter (Edmund Optics #65-106) was inserted. To spatially separate the emissions in the reflection direction, a dichroic beam combiner (Edmund Optics #86-402) was used [ Fig. 1(a)]. Figure 1(b) shows the timeintegrated photoluminescence (PL) spectra of transmission (TO) and reflection (RO) configurations under barrier excitation at a power density of 6.6 W=cm 2 . The emission was dispersed by a monochrometer (HORIBA SPEX500m with 1800 g=mm) and detected with an Si-charge coupled device (Princeton Instruments PIXIS256E). The typical exposure time was 1 s to obtain a PL spectrum with a high signal-tonoise ratio. The emission X was centered at 791.6 nm with a full width at half maximum of 174.47 µeV obtained by the spectra fitting with a Lorentzian function. The observed X-shape was exactly identical between TO and RO, whereas the PL intensity was different because of the difference in the thickness of the QD-sandwiched AlGaAs barrier layer.
Both outputs of the QDinF were filtered with a 0.5-nmwide band-pass filter (Optoquest custom-made product) to select the X, and two band-pass filters (Edmund Optics #86-  956) were used to suppress background photons, i.e., reflection and transmission of the excitation laser at the interface of both the SMF patch cables and unwanted emissions originating from other QDs. The two outputs of QDinF were sent to a single photon counting module (SPCM; Perkinelmer SPCM-AQR). Figure 1(c) shows the excitation power dependence of the photon count rates of PL that was spectrally selected by band-pass filters. As the excitation power increased, the detected photon count rates of each SPCM monotonically increased and saturated at approximately 4 W=cm 2 , suggesting that observed X was PL originating from a single exciton state confined in the QDs.
To confirm the single photon nature of QDinF, the coincidence between TO and RO of QDinF was recorded by a time-amplitude converter (TAC) board (Becker & Hickl SPC-130E). The second-order correlation curves were measured under continuous wave and Al 0.35 Ga 0.65 As barrier excitation. The detected total single count rate at SPCMs was approximately 14.1 kHz with an excitation power of 1.6 W=cm 2 . A histogram of the normalized coincidence counts with time bins of 19.5 ps and an integration time of 11.9 h is shown in Fig. 2(a). The data exhibited the well-known antibunching dip at zero time delay. The measured coincidence (g ð2Þ m ) was the covolution of the ideal response (g ð2Þ b ) 12) with the instrumental response ( f ), where ρ [= S=(S + B)] is related to the signal-to-noise ratio and τ rise [= τ r τ p =(τ r + τ p )], where τ r is the lifetime of X and τ p is the inverse pumping rate. 13) The instrumental response time deduced from the fitted FWHM was 439 ps according to a Gaussian function. The measured data (circles) were fitted with the convolution of Eqs. (1) and (2). The solid (red) and (blue) curves are fitting results of g ð2Þ m and g ð2Þ b , respectively. Here B (= 150 Hz) is fixed by the dark counts of the SPCM. Figure 2(b) shows the excitation power dependence of g (2) (0) and τ rise . With increasing excitation power, τ rise gradually narrowed from approximately 1 ns, which is longer than τ r (∼ 0.7 ns) measured by cross-correlation under pulsed photoexcitation using a ps mode-locked Ti:Sapphire laser with a center wavelength 720 nm for InAlAs WL excitation. This discrepancy is attributed to the elongation of the effective lifetime caused by the excess charge diffusion in the AlGaAs barrier layer under cw excitation. However, in the high-excitation power region, the lack of time resolution limited by the instrument response prevented us from determining τ rise and g (2) (0); therefore, we imposed a restriction of τ rise > 439 ps during the fitting process. The averaged g (2) (0) = 0.39 (± 0.02) was lower than 0.5, which was the quantum limit in the measured excitation power range; however, an accidental coincidence remained because of the background photons originating from a large number of QDs weakly coupled with SMFs, as shown in Fig. 1(b).
To confirm the bidirectional extraction of a single photon originating from the QD, the coherence properties of X were investigated by a type of time-domain spectroscopy called single-photon Fourier spectroscopy. 14) The two outputs (TO and RO) of QDinF sent photons to SPCMs through a 2 × 2fiber coupler (Thorlabs FC780-50B-FC), with an optical delay line inserted into the transmission configuration, as shown in Fig. 3(a). All fiber components were mechanically fixed and installed in an isolated small darkroom in order to prevent environmental fluctuations. Rotating a thin glass plate in the optical delay line enabled fine-tuning of the relative phase θ (approximately 0.2 fs) between the two outputs, and an interference fringe could be observed, indicating that a Mach-Zehnder (MZ) interferometer configu- ration was naturally formed. Here the interference fringe was as follows: where PN 1 (2) and d are the photon numbers detected by each SPCM and the averaged dark count of both SPCMs, respectively. By varying the temporal delay τ and θ, Vð; Þ was recorded, as shown in Fig. 3(b). The detected photon number evolution of each SPCM as a function of τ was as follows: where PN 12 , E 0 , and V 0 ðÞ ¼ maxfjVð; Þj; ¼ 0; . . . ; 2g are the total photon number of both SPCMs, the center selected photon energy, and the visibility (interference fringe contrast), respectively. Figure 3(c) shows V A(τ) as a function of the time delay τ between TO and RO. The visibility of the interference fringes decayed almost with an a simple exponential function (solid line) V 0 ð0Þe À=T 2 , implying that the spectrally selected line had a Lorenztian shape. The obtained dephasing time T 2 of 8.3 (± 0.3) ps was longer than the 1.3 ps deduced by the spectral window of the 0.5-nmwide band-pass filter, corresponding to FWHM of the X of 2ħ=T 2 $ 157:2 µeV [ Fig. 1(a)]. The observed value of T 2 is more than a few order of magnitude shorter under resonant excitation using various different experimental methods and materials. 13,[15][16][17] This short T 2 is attribute to fluctuations of environmental excess charges in InAlAl WL and comparable to the neutral exciton spin relaxation time under non-resonant excitation. 18) This meant that the single photon state |φ〉 generated by the QD was directly spatially separated and extracted to TO and RO via bidirectionally located SMFs in the QD; j0i TO j1i RO þ j1i TO j0i RO , which is similar to the well-known dual rail photon qubit state. In the case of jj 2 ¼ jj 2 ¼ 0:5, the visibility at zero delay time V A(0) = 1 (ideal) is larger than the observed value of 0.316 (± 0.005) due to the unbalanced optical coupling between the QD and the edge faces of the SMFs and the throughputs of the free space modules such as temporal delay and spectral filtering [ Fig. 1(b)]. To attain a balance between α and β, a variable attenuator was inserted before the 2 × 2-fiber coupler. Figure 3(d) shows the time-averaged photon-number ratio is the total photon number of TO=RO detected by both SPCMs. We obtained V A(0) values in the R-range of 0.01 to 4, corresponding to the input ratio for the 2 × 2-fiber coupler. The measured V A(0) attained a maximum value under a condition of R = 1 and recovered from 0.20 up to 0.62. This maximum value was still lower than the expected ideal value of 1.0 mainly because of the polarization mismatch at the 2 × 2-fiber coupler caused by the incomplete optical coupling between the QD and SMF and the cross-polarization coupling inside the SMF.
Here we discuss the deviation of V A(0) by the assumption that all optical loss mechanisms are equivalent to inserting beam splitters into the optical paths [inset of Fig. 3(d)]. Initially, we assume that a single photon state originating from the QD is split into spatially separated components by a 50=50 beam splitter, and j'i ¼ 1= ffiffiffi 2 p ðj1i TO j0i RO þ ij0i TO j1i RO Þ, which corresponds to an ideal QDinF situation. After passing through the unbalanced TO and RO arms with optical losses including incompletion of optical coupling at the interface between the QD and the edge faces of the SMFs and free space modules, the single photon state transforms to 1= where Γ TO=RO is the reflectance of a hypothetically inserted beam splitter, corresponding to the total optical losses in the TO=RO arm. Combining with a 2 × 2-fiber coupler, the single photon state transforms to The measured V A(0) can be reproduced (black curve) as follows: where γ [= 0.64 (± 0.01)] is a fitting parameter related to the degree of polarization mismatch. This fact provides evidence that a single photon in the modes of two optical paths (TO and RO) can serve as the basis of a dual-rail qubit and that α=β can be encoded from 0.2 to 4.
In summary, we have demonstrated single-photon extraction from epitaxially grown InAlAs QDs sandwiched by single-mode fibers. The photon antibunching behavior was confirmed by second-order photon correlation measurements. The first-order autocorrelation function was measured between bidirectional outputs of a SMF. These experimental results suggest that the single photon state generated by the QD was directly spatially separated and extracted via bidirectionally located SMFs in the QD, signifying that the QDinF structure can naturally form a dual-rail photon qubit without any additonal passive fiber components. Moreover, in the naturally formed MZ interferomter, the visibility at zero delay time could be improved nearly three times by the control of the throughput ratio between the two arms. Our results suggest that QDinF devices have significant potential as photon sources and qubits that can be operated at cost with high durability on a maintenance-free basis over a long period for the inspection and development of quantum information protocols.