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# Entanglement in Quantum Dot Systems and Quantum Dot Molecules

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Experimental research over the last decade has established that solid-state spins allow for a faithful representation of quantum information over long timescales in integrated devices. Photons on the other hand, are ideal for transfer of quantum information. As a consequence, realization of a quantum interface between spins and photons has emerged as a promising direction for solid-state quantum information processing.

Entanglement plays a central role in fundamental tests of quantum mechanics as well as in the burgeoning field of quantum information processing. Particularly in the context of quantum networks and communication, some of the major challenges are the efficient generation of entanglement between stationary (spin) and propagating (photon) qubits, the transfer of information from flying to stationary qubits and the efficient generation of entanglement between distant stationary (spin) qubits. We have recently succeeded in demonstrating entanglement between the spin of a single quantum dot and a single emitted photon, teleportation from a photonic qubit to a spin qubit and generation of heralded entanglement between two distant hole spins. These results constitute the first steps towards the development of solid-state quantum networks.

**Spin-photon interface in quantum dots**

Our recent results demonstrate quantum entanglement between a semiconductor InGaAs quantum dot spin and the color of a propagating optical photon [1]; this observation was made possible by favorable selection rules for QDs in Voigt geometry (in-plane magnetic field), our record high photon collection efficiency from charge controlled QDs under resonant excitation, and the ability to perform time resolved resonance fluorescent measurements. The demonstration of entanglement relies on the use of fast single-photon detection which allows us to project the photon into a superposition of its two frequency components. Our results extend the previous demonstrations of single-spin photon entanglement in trapped ions, neutral atoms and nitrogen vacancy centers to the domain of artificial atoms in semiconductor nano-structures.

**Teleportation from a propagating photon to a spin qubit**

Based on this realization, we have then demonstrated the transfer of quantum information carried by a photonic qubit to a quantum dot spin using quantum teleportation [2]. Our realization is based on quantum interference of the photonic qubit to be teleported – which is generated by the neutral exciton radiative decay of a quantum dot – with the photonic part of a spin-photon entangled pair generated in another cryostat distant by five meters. The success of this experiment has been made possible by the high degree of indistinguishability of photons generated by distinct quantum dots, exceeding 80% interference visibility in a Hong-Ou-Mandel experiment. Detection of a coincidence after the beam splitter projects the state of the spin on the state of the photonic qubit prior to the protocol. Such an interface between dissimilar qubits has attracted considerable interest not only as a versatile quantum-state transfer method but also as a quantum computational primitive.

**Generation of heralded entanglement between distant quantum dot hole spins**

We have realized heralded entanglement between two semiconductor quantum dot hole spins separated by more than five meters [6]. The entanglement generation scheme relies on single photon interference of Raman scattered light from both dots under weak laser excitation; a single photon detection projects the system into a maximally entangled state. We developed a delayed two-photon interference scheme that allows for efficient verification of quantum correlations. Moreover the efficient spin-photon interface provided by self-assembled quantum dots allows us to reach an unprecedented rate of 2300 entangled spin pairs per second, which represents an improvement of four orders of magnitude as compared to prior experiments carried out in other systems. Our results extend previous demonstrations in single trapped ions or neutral atoms, in atom ensembles and nitrogen vacancy centers to the domain of artificial atoms in semiconductor nanostructures that allow for on-chip integration of electronic and photonic elements. This work lays the groundwork for the realization of quantum repeaters and quantum networks on a chip.

**Single-shot measurement of a quantum dot spin**

While Voigt geometry (i.e. external magnetic field perpendicular to the growth axis) realizes a lambda system that provides us an efficient spin-photon interface, the level scheme in Faraday geometry (i.e. external magnetic field parallel to the growth axis) presents cycling transitions that allow for efficient spin measurement. Although the probability of spin-flip during the measurement is not strictly zero due to heavy-light hole mixing, embedding the quantum dots into a lossy planar cavity allows sufficient extraction efficiency to have in average more than one detected photon when the spin is prepared in the measured state before it flips, allowing single shot spin measurement in a sub-microsecond time scale [3]. With this single-shot measurement ability it is then possible to perform a continuous measurement of the spin in the presence of a weak repumping mechanism and to observe the quantum jumps of the electron spin.

**Singlet-triplet qubit in quantum dot molecules**

In contrast to single quantum dots, the singlet triplet states of a quantum dot molecule allows us to obtain simultaneously a lambda system and a cycling transition. Moreover, while single trapped electrons coherence time is limited by hyperfine interaction with the nuclear spins and single holes coherence time is restricted by spin-orbit interaction coupling to charge fluctuations, in quantum dot molecules it is possible to decouple from both limiting interactions at the same time (to first order). We have shown that the coherence time T_{2}* can be prolonged by two orders of magnitude with respect to the electron spin T_{2}* when singlet-triplet states are employed, provided the quantum dot molecule is tuned to its “sweet-spot” [4].

**Quantum dot molecules: cycling transition readout of the pseudospin**

We have investigated the possibility to realize a cycling transition measurement of the pseudo-spin in a similar way to electron shelving technique in atomic physics: after preparing the state into either S or T_{0}, we realize an unconditional transfer from T_{0} to the T_{+} state using the T_{0} to R_{++} weakly allowed transition. We then drive the T_{+} to R_{++} cycling transition during a ~µs time; preparing the state T_{0} prior to the transfer pulse leads to scattering of an important number of photons, making a single-shot measurement of the pseudo-spin in principle possible.

Future prospects with these systems include demonstration of spin-photon interface and measurement of the coherence time under active stabilization of the charge fluctuations. We are also exploring prospects to utilize the long-range coherence properties of polariton condensates in microcavities to mediate interaction between spatially separate quantum dots and molecules. The high densities achievable in such condensates promise to allow the interaction strength to be tuned arbitrarily strong, while the short lifetimes would enable quick switching of the interaction.

- [1] Observation of entanglement between a quantum dot spin and a single photon W. B. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez & A. Imamoglu, Nature 491, 426–430 (2012)
- [2] Quantum teleportation from a propagating photon to a solid-state spin qubit W.B. Gao, P. Fallahi, E. Togan, A. Delteil, Y.S. Chin, J. Miguel-Sanchez, A. Imamoğlu , Nature Communications 4, 2744 (2013)
- [3] Observation of Quantum Jumps of a Single Quantum Dot Spin Using Submicrosecond Single-Shot Optical Readout A. Delteil, W. Gao, P. Fallahi, J. Miguel-Sanchez, A. Imamoğlu , Phys. Rev. Lett. 112, 116802
- [4] Coherent Two-Electron Spin Qubits in an Optically Active Pair of Coupled InGaAs Quantum Dots K. M. Weiss, J. M. Elzerman, Y. L. Delley, J. Miguel-Sanchez, and A. Imamoğlu, Phys. Rev. Lett. 109, 107401 (2012)
- [5] Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields. W. B. Gao, A. Imamoglu, H. Bernien and R. Hanson, Nature Photonics 9, 363-373 (2015)
- [6] Generation of heralded entanglement between distant hole spins A. Delteil, Z. Sun, W. B. Gao, E. Togan, S. Faelt, A. Imamoğlu, arXiv:1507.00465 (2015)
- [7] Spin measurement using cycling transitions of a two-electron quantum dot molecule Y. L. Delley, M. Kroner, S. Faelt, W. Wegscheider, A. İmamoğlu , arXiv:1509.04171 (2015)