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# Quantum interference of identical photons from remote GaAs quantum dots

## Abstract

Photonic quantum technology provides a viable route to quantum communication1,2, quantum simulation3 and quantum information processing4. Recent progress has seen the realization of boson sampling using 20 single photons3 and quantum key distribution over hundreds of kilometres2. Scaling the complexity requires architectures containing multiple photon sources, photon counters and a large number of indistinguishable single photons. Semiconductor quantum dots are bright and fast sources of coherent single photons5,6,7,8,9. For applications, a roadblock is the poor quantum coherence on interfering single photons created by independent quantum dots10,11. Here we demonstrate two-photon interference with near-unity visibility (93.0 ± 0.8)% using photons from two completely separate GaAs quantum dots. The experiment retains all the emission into the zero phonon line—only the weak phonon sideband is rejected; temporal post-selection is not employed. By exploiting quantum interference, we demonstrate a photonic controlled-not circuit and an entanglement with fidelity of (85.0 ± 1.0)% between photons of different origins. The two-photon interference visibility is high enough that the entanglement fidelity is well above the classical threshold. The high mutual coherence of the photons stems from high-quality materials, diode structure and relatively large quantum dot size. Our results establish a platform—GaAs quantum dots—for creating coherent single photons in a scalable way.

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## Data availability

The raw data that support the findings of this study are available at https://doi.org/10.5281/zenodo.6371310 and from the corresponding author upon reasonable request.

## Code availability

The codes that have been used for this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank P. Lodahl, D. Reiter, P. Treutlein and R. Uppu for the stimulating discussions. The work was supported by NCCR QSIT and SNF project nos. 200020_175748 and 200020_204069. L.Z., G.N.N. and A.J. received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 721394 (4PHOTON), no. 861097 (QUDOT-TECH) and no. 840453 (HiFig), respectively. J.R., A.D.W. and A.L. acknowledge financial support from the grants DFH/UFA CDFA05-06, DFG TRR160, DFG project 383065199 and BMBF QR.X Project 16KISQ009.

## Author information

Authors

### Contributions

L.Z., G.N.N., C.S. and A.J. carried out the experiments. J.R., L.Z., M.C.L., A.D.W. and A.L. designed and grew the sample. C.S., G.N.N. and L.Z. fabricated the sample. L.Z., G.N.N., C.S., A.J., M.C.L. and R.J.W. analysed the data. L.Z., G.N.N., C.S. and R.J.W. wrote the manuscript with input from all the authors.

### Corresponding author

Correspondence to Liang Zhai.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Photoluminescence and resonance fluorescence charge plateaus.

a, Photoluminescence from QD2 as a function of the externally applied gate voltage, Vg. The three excitons which can be resonantly excited are labelled: the positive trion X+, the neutral exciton X0 and the negative trion X. b, Resonance fluorescence on X from QD2. Resonance fluorescence is mapped out by scanning both the laser frequency and the gate voltage. The dashed line indicates the frequency at which all the experiments on QD2 are performed. c, Resonance fluorescence on X from QD1. The dashed line represents the same frequency as in b.

### Extended Data Fig. 2 Lifetimes and linewidths of the X− in three quantum dots.

a–c, Time-resolved resonance fluorescence from QD 1–3 under resonant pulsed excitation. The resonance fluorescence intensity of each QD follows an exponential decay. From the fits (black curves), the radiative decay rates are extracted as Γ1 = 3.75 GHz, Γ2 = 3.91 GHz and Γ3 = 3.54 GHz. The corresponding lifetimes are displayed next to the exponential fits. The radiative lifetime of GaAs QDs is typically41 around 250 ps. In our sample, the average lifetime is around 300 ps – there is no Purcell enhancement. d–f, Spectrum of the resonance fluorescence obtained by slowly scanning a narrow-bandwidth continuous-wave (CW) laser across the X. The typical measurement time is 5–10 minutes: the linewidth probes the noise over a huge frequency bandwidth. The measured linewidths (values are displayed next to the fits) are very close to the lifetime limits.

### Extended Data Fig. 3 The noise in GaAs quantum dots.

a, Auto-correlation measurements of X in a GaAs QD in the diode heterostructure under continuous-wave (CW) excitation. The CW laser excites the QD resonantly. The auto-correlation g(2) is normalized by the mathematical expectation22 based on the photon count rates and the integration time. The g(2) is flat, a feature showing the absence of the blinking. b, Noise spectrum of a GaAs QD under resonant excitation. Like a, a narrow-bandwidth laser is placed at the exact resonance of X. The noise is resolved as a function of frequency f. The black curve represents a Lorentzian fit to the noise profile. The orange dashed line represents the shot-noise level. The bandwidth of the Lorentzian is extracted to be 19 Hz (half-width-at-half-maximum), showing that the environmental noise is concentrated at lower frequencies. The noise spectrum at higher frequencies, for example 104–106 Hz, remains small and mostly flat. c, Noise spectrum of a GaAs QD when the sensitivity of either charge noise or spin noise is increased. The light-blue curve represents the condition when the laser is detuned by half of the QD linewidth, Δ = Γ/2. In this case, low-frequency ( < 102 Hz) charge noise is enhanced compared to b. The orange curve represents the condition where the QD is placed in a small magnetic field B = 50 mT, and the laser frequency is placed in the centre of two Zeeman-split peaks. The low-frequency noise becomes less, but the noise within 102–104 Hz range is enhanced, which is likely the spin noise.

### Extended Data Fig. 4 Remote interference visibility as a function of evaluation time-window.

a, A sketch showing the evaluation time-binning window in the HOM data analysis. The pulsed excitation laser has a repetition period of Tperiod = 13 ns, which corresponds to ~ 50τr. Every Tperiod contains one HOM peak, and the time-binning window (with a width of Tbin) is centred around each HOM peak. In b,c we reduce the width of the time-window Tbin from Tperiod to close to zero, and calculate/extract the theoretical/measured value of the two-QD HOM visibility. In b, we apply the time-binning window to a theoretical delay dependence two-photon interference $${{{{\mathcal{G}}}}}^{(2)}(\tau )$$. This $${{{{\mathcal{G}}}}}^{(2)}(\tau )$$ is calculated using equation (19) in Supplementary Information, with parameters Γ1 = 3.75 GHz, Γ2 = 3.91 GHz, Γ* = 34 MHz, Ξ = 2 × 34 MHz, δt = 0 and Δ = 0. The calculated two-QD HOM visibility $${{{{\mathcal{V}}}}}_{{{{\rm{cal}}}}}$$ drops to 93% at Tbin = 20τr and levels off. In c, the measured two-QD HOM visibility (QD1 and QD2, δt = 0, Δ = 0) is shown as a function of the normalized width of the time-window. The visibility can be effectively increased to $${{{{\mathcal{V}}}}}_{\exp } \sim 98 \%$$ when Tbin is comparable with the QD lifetime. At large time-windows (Tbin → Tperiod), we determine the real two-QD HOM visibility, $${{{\mathcal{V}}}}=93 \%$$: in this limit, no temporal post-selection is included.

### Extended Data Fig. 5 Effects of spectral filtering and temporal post-selection on two-photon interference from remote quantum dots.

a, The effect of spectral filtering as a function of the filter bandwidth Δvfil. We study here a filter with a narrow bandwidth and assume a Lorentzian transmission function (for example, an etalon). Δvfil is normalized by the QD’s radiative rate 1/(2πτr) (assuming identical QDs). $${{{{\mathcal{A}}}}}_{{{{\rm{noise}}}}}$$ is an indicator of the spectral filtering effect. It is defined as the ratio between the noise-related linewidth broadening and the QD’s intrinsic linewidth. Different coloured lines represent different levels of noise, characterized by ($${{{\varGamma }}}_{{{{\rm{sum}}}}}^{* }+{{\varXi }}\pi$$)/Γ. Both the intrinsic and the noise part of the QD spectrum experience spectral filtering effect, but their ratio $${{{{\mathcal{A}}}}}_{{{{\rm{noise}}}}}$$ decreases as the filter narrows. However, this reduction in $${{{{\mathcal{A}}}}}_{{{{\rm{noise}}}}}$$ only becomes apparent when the filter is narrow, for example Δvfil(2πτr) < 5. b, The effect of spectral filtering on the photon counts. ηfil represents the percentage of photons exiting a spectral filter compared to the photons before filtering. Here, the peak transmission of the filter is set to unity and the filter is exactly centred at the QD resonance, an idealized situation. c, The effect of temporal post-selection on two-QD HOM interference as a function of the width of evaluation time-window Tbin. Performing temporal post-selection with a narrow Tbin leads to an increase in two-QD HOM visibility $${{{{\mathcal{V}}}}}_{{{{\rm{post}}}}}$$ at the expense of coincidence count rates. Here, the line colours again represent the different noise conditions. Similar to spectral filtering, the effect of post-selection only becomes prominent at small Tbin. d, The effect of temporal post-selection on coincidence counts. ηpost is defined as the ratio between the total coincidence events after temporal post-selection compared to the no post-selection case.

### Extended Data Fig. 6 Projection outcomes of $${\left|{{\Psi }}\right\rangle }^{-}$$ in quantum state tomography.

The probabilities Sν are calculated by adding up the coincidence counts in the central peak and normalizing the sum to the overall counts in each set of four coincidence measurements. Here, 36 possible ν-states are listed in the x-axis. The two dashed lines indicate the Sν = 0.25 and Sν = 0.5 levels. The light grey background represents the projection probabilities for the ideal $$\left|{{{\Psi }}}^{-}\right\rangle$$ state.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–11, Table 1 and Notes 1–3.

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Zhai, L., Nguyen, G.N., Spinnler, C. et al. Quantum interference of identical photons from remote GaAs quantum dots. Nat. Nanotechnol. 17, 829–833 (2022). https://doi.org/10.1038/s41565-022-01131-2

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• DOI: https://doi.org/10.1038/s41565-022-01131-2