## Periodic Reporting for period 4 - DG-PESP-CS (Deterministic Generation of Polarization Entangled single Photons Cluster States)

Reporting period: 2020-12-01 to 2021-05-31

Despite the fact that quantum optics is a mature field with an impressive toolkit of devices for handling photonic qubits, photons are unlikely to be the medium of choice for tasks that rely on localization and interactions between photons such as 2-qubit gates . As a consequence, entangled states with only a limited number of photons have been demonstrated prior to our project and only in a probabilistic manner. We overcame this problem using confined electronic spin in a semiconductor quantum dot. In these nanostructures the electronic spin strongly interacts with light, via the spin orbit interaction. Due to this interaction the spin can act as a needle in a knitting machine entangling the polarization states of sequentially emitted single photons resulting from timed periodic optical excitation of the spin.

The overall objective of our proposal was to demonstrate prototype devices, capable of deterministic generation of cluster states of polarization entangled photons in one and more dimensions.

Such clusters are invaluable resources for quantum communication and entanglement distribution between remote nodes.

The overall objective of our proposal was to demonstrate prototype devices, capable of deterministic generation of cluster states of polarization entangled photons in one and more dimensions.

Such clusters are invaluable resources for quantum communication and entanglement distribution between remote nodes.

We made a major breakthrough, which gained worldwide recognition, resulting in high impact publications, press releases and many invitations for conferences and workshops. The breakthrough was the first demonstration of a prototype device capable of generating a one-dimensional cluster state of polarization entangled photons [1]. Following this breakthrough, we proceeded by devoting major efforts into constructing and building a state-of-the-art experimental system for capitalizing on our success and achieving the ambitious goals of our proposal.

Our efforts resulted so far in 8 publications and over 35 invited conferences and workshops presentations:

1) We demonstrated experimentally that the biexciton-exciton radiative cascade in semiconductor quantum dots is an excellent deterministic source of maximally polarization entangled photon pairs. We showed that (a) the polarization states of the emitted two photons are maximally entangled during the whole radiative decay, and (b) the measured degree of entanglement between the polarization states of the two photons depends only on the temporal resolution by which the time difference between the two photon emissions is determined [2].

2) Precision measurements of optical phases have many applications in science and technology. Entangled multiphoton states can perform such measurements with precision that significantly surpasses the shot-noise limit.

We generate entangled multiphoton states on demand and used the resulting multiphoton state to demonstrate super-resolved optical phase measurement. Our results open up a scalable way for realizing genuine quantum enhanced supersensitive measurements [3].

3) We investigated experimentally and theoretically the depolarization dynamics of five different electronic spin configurations confined in the same semiconductor quantum dot. We showed that the measured temporal spin polarization is well described by a central spin model which attributes the depolarization to the hyperfine interaction between the spin and the nuclear spin bath of the quantum dot atoms [4].

4) While full tomography of photons is straightforward, matter spin tomography is a challenging task. We developed a method for full tomography of confined spins. We excite the spin qubit using a short, resonantly tuned, polarized optical pulse, coherently converting the qubit to an excited qubit that decays by emitting a polarized photon. The measured time-resolved circular polarization degree of the emitted light provides full tomography of the matter spin qubit before its excitation [5].

5) Using the methods developed in Refs. [4-5] we investigated the temporal evolution of the spin purity of the conduction band electron and that of the valence band hole. In the limit of weak externally applied magnetic field comparable in strength to the Overhauser field due to fluctuations in the surrounding nuclei spins, we found that the spin purity performs oscillations which we quantitatively modeled. Our studies are essential for the design and optimization of quantum-dot-based entangled multi-photon sources, which set stringent limitations on the magnitude of the external field [6].

6) We developed a novel method for quantum tomography of multi-qubit states. The method is applied to spin-multiphoton states produced by periodic excitation of a confined spin every 1/4 of its precession period leading to deterministic generation of entangled photons in a cluster state. We characterize the periodic process map which produce the photonic cluster. From this map we quantify the robustness of the entanglement in the cluster. The 3-fold enhanced generation rate over that of Ref. [1], reduces the spin decoherence and improves the robustness of the entanglement in the multi -photon state [7].

7) Measurement-based quantum communication relies on the availability of highly entangled multi-photon states. The inbuilt redundancy in the cluster allows communication between remote nodes using repeated local measurements, compensating for photon losses and probabilistic Bell-measurements. Applications require that the cluster generation be fast, deterministic and its photons - indistinguishable. We developed a novel source based on a confined heavy-hole. The hole precesses in a finely tuned external weak magnetic field, while being periodically excited by optical pulses. Consequently, the dot emits indistinguishable entangled photons. The entanglement is optimized by the field strength. We demonstrated Gigahertz rate deterministic generation of > 85% indistinguishable photons in a cluster with characteristic entanglement-length of more than 10 photons [8].

Our efforts resulted so far in 8 publications and over 35 invited conferences and workshops presentations:

1) We demonstrated experimentally that the biexciton-exciton radiative cascade in semiconductor quantum dots is an excellent deterministic source of maximally polarization entangled photon pairs. We showed that (a) the polarization states of the emitted two photons are maximally entangled during the whole radiative decay, and (b) the measured degree of entanglement between the polarization states of the two photons depends only on the temporal resolution by which the time difference between the two photon emissions is determined [2].

2) Precision measurements of optical phases have many applications in science and technology. Entangled multiphoton states can perform such measurements with precision that significantly surpasses the shot-noise limit.

We generate entangled multiphoton states on demand and used the resulting multiphoton state to demonstrate super-resolved optical phase measurement. Our results open up a scalable way for realizing genuine quantum enhanced supersensitive measurements [3].

3) We investigated experimentally and theoretically the depolarization dynamics of five different electronic spin configurations confined in the same semiconductor quantum dot. We showed that the measured temporal spin polarization is well described by a central spin model which attributes the depolarization to the hyperfine interaction between the spin and the nuclear spin bath of the quantum dot atoms [4].

4) While full tomography of photons is straightforward, matter spin tomography is a challenging task. We developed a method for full tomography of confined spins. We excite the spin qubit using a short, resonantly tuned, polarized optical pulse, coherently converting the qubit to an excited qubit that decays by emitting a polarized photon. The measured time-resolved circular polarization degree of the emitted light provides full tomography of the matter spin qubit before its excitation [5].

5) Using the methods developed in Refs. [4-5] we investigated the temporal evolution of the spin purity of the conduction band electron and that of the valence band hole. In the limit of weak externally applied magnetic field comparable in strength to the Overhauser field due to fluctuations in the surrounding nuclei spins, we found that the spin purity performs oscillations which we quantitatively modeled. Our studies are essential for the design and optimization of quantum-dot-based entangled multi-photon sources, which set stringent limitations on the magnitude of the external field [6].

6) We developed a novel method for quantum tomography of multi-qubit states. The method is applied to spin-multiphoton states produced by periodic excitation of a confined spin every 1/4 of its precession period leading to deterministic generation of entangled photons in a cluster state. We characterize the periodic process map which produce the photonic cluster. From this map we quantify the robustness of the entanglement in the cluster. The 3-fold enhanced generation rate over that of Ref. [1], reduces the spin decoherence and improves the robustness of the entanglement in the multi -photon state [7].

7) Measurement-based quantum communication relies on the availability of highly entangled multi-photon states. The inbuilt redundancy in the cluster allows communication between remote nodes using repeated local measurements, compensating for photon losses and probabilistic Bell-measurements. Applications require that the cluster generation be fast, deterministic and its photons - indistinguishable. We developed a novel source based on a confined heavy-hole. The hole precesses in a finely tuned external weak magnetic field, while being periodically excited by optical pulses. Consequently, the dot emits indistinguishable entangled photons. The entanglement is optimized by the field strength. We demonstrated Gigahertz rate deterministic generation of > 85% indistinguishable photons in a cluster with characteristic entanglement-length of more than 10 photons [8].

In Ref. [8] we achieved an important milestone by demonstrating characteristic entanglement-length and photon indistinguishability which are 3 and 4 times better, respectively than in Ref. [1]. We believe that further feasible optimizations will result in widespread implementations of quantum communication. We keep working towards that end.

References:

[1] I. Schwartz, D. Cogan, D. Gershoni et al. “Deterministic generation of a cluster state of entangled photons.” Science, 354, 434 (2016)

[2] R. Winik, D. Cogan, D. Gershoni, et al, “On-demand source of maximally entangled photon pairs using the biexciton-exciton radiative cascade.” Phys. Rev. B 95, 235435 (2017)

[3] G. Peniakov , Z.-E. Su, D. Gershoni et al, “Towards supersensitive optical phase measurement using a deterministic source of entangled multiphoton states“. Phys. Rev. B 101, 245406 (2020). Editors’ Suggestion

[4] D. Cogan, O. Kenneth, N. H. Lindner, D. Gershoni, et al, “Depolarization of Electronic Spin Qubits Confined in Semiconductor Quantum Dots“. Phys. Rev. X 8, 041050 (2018)

[5] D. Cogan, G. Peniakov, Z.-E. Su, and D. Gershoni. “Complete state tomography of a quantum dot spin qubit“. Phys. Rev. B 101, 035424 (2020). Editors’ Suggestion

[6] D. Cogan, Z-E Su, O. Kenneth and D. Gershoni “The coherence of quantum dot confined electron- and hole-spin in low external magnetic field” arXiv:2108.05173

[7] D. Cogan, G. Peniakov, O. Kenneth, Y. Don and D. Gershoni “Quantum tomography of entangled spin-multi-photon states” arXiv:2108.05919

[8] D. Cogan, Z-E Su, O. Kenneth, Y. Don and D. Gershoni “A deterministic source of indistinguishable photons in a cluster state” in preparation.

References:

[1] I. Schwartz, D. Cogan, D. Gershoni et al. “Deterministic generation of a cluster state of entangled photons.” Science, 354, 434 (2016)

[2] R. Winik, D. Cogan, D. Gershoni, et al, “On-demand source of maximally entangled photon pairs using the biexciton-exciton radiative cascade.” Phys. Rev. B 95, 235435 (2017)

[3] G. Peniakov , Z.-E. Su, D. Gershoni et al, “Towards supersensitive optical phase measurement using a deterministic source of entangled multiphoton states“. Phys. Rev. B 101, 245406 (2020). Editors’ Suggestion

[4] D. Cogan, O. Kenneth, N. H. Lindner, D. Gershoni, et al, “Depolarization of Electronic Spin Qubits Confined in Semiconductor Quantum Dots“. Phys. Rev. X 8, 041050 (2018)

[5] D. Cogan, G. Peniakov, Z.-E. Su, and D. Gershoni. “Complete state tomography of a quantum dot spin qubit“. Phys. Rev. B 101, 035424 (2020). Editors’ Suggestion

[6] D. Cogan, Z-E Su, O. Kenneth and D. Gershoni “The coherence of quantum dot confined electron- and hole-spin in low external magnetic field” arXiv:2108.05173

[7] D. Cogan, G. Peniakov, O. Kenneth, Y. Don and D. Gershoni “Quantum tomography of entangled spin-multi-photon states” arXiv:2108.05919

[8] D. Cogan, Z-E Su, O. Kenneth, Y. Don and D. Gershoni “A deterministic source of indistinguishable photons in a cluster state” in preparation.