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Physical Review B

Creation of entangled spin qubits between distant quantum dots

Nobuhiko Yokoshi, Hiroshi Imamura, Hideo Kosaka

Published Oct 25, 2013• 10 citations
Publisher

Abstract

We theoretically show that an entangled state can be prepared between distant heavy-hole spin qubits by using III--V semiconductor quantum dots (QDs) in cascaded cavities. In this scheme, using quantum state transfer between photons and carrier spins, the local spin-singlet state in a virtually excited trion is stretched into the two separated QDs via a single-photon transmission. We calculate the effective Liouville equation and determine the optimal conditions for entanglement creation. We also discuss the possibility of distributing entangled electron spins in the same manner.

DOI
10.1103/physrevb.88.155321

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We theoretically show that an entangled state can be prepared between distant heavy-hole spin qubits by using III--V semiconductor quantum dots (QDs) in cascaded cavities. In this scheme, using quantum state transfer between photons and carrier spins, the local spin-singlet state in a virtually excited trion is stretched into the two separated QDs via a single-photon transmission. We calculate the effective Liouville equation and determine the optimal conditions for entanglement creation. We also discuss the possibility of distributing entangled electron spins in the same manner.
A scheme for probabilistic entanglement generation between two distant single electron doped quantum dots, each placed in a high-QQQ microcavity, by detecting strong coherent light which has interacted dispersively with both subsystems and experienced Faraday rotation due to the spin selective trion transitions is discussed. In order to assess the applicability of the scheme for distant entanglement generation between atomic qubits proposed by T. D. Ladd et al. [New J. Phys. 8, 184 (2006)] to two distant quantum dots, one needs to understand the limitations imposed by hyperfine interactions of the quantum dot spin with the nuclear spins of the material and by nonidentical quantum dots. Feasibility is displayed by calculating the fidelity for Bell state generation analytically within an approximate framework. The fidelity is evaluated for a wide range of parameters and different pulse lengths, yielding a trade-off between signal and decoherence, as well as a set of optimal parameters. Strategies to overcome the effect of nonidentical quantum dots on the fidelity are examined and the time scales imposed by the nuclear spins are discussed, showing that efficient entanglement generation is possible with distant quantum dots. In this context, effects due to light hole transitions become important and have to be included. The scheme is discussed for one- as well as for two-sided cavities, where one must be careful with reflected light which carries spin information. The validity of the approximate method is checked by a more elaborate semiclassical simulation which includes trion formation.
Quantum entanglement emerges naturally in interacting quantum systems and plays a central role in quantum information processing. Remarkably, it is possible to generate entanglement even in the absence of direct interactions: provided that which path information is erased, weak spin-state dependent light scattering can be used to project two distant spins onto a maximally entangled state upon detection of a single photon. Even though this approach is necessarily probabilistic, successful generation of entanglement is heralded by the photon detection event. Here, we demonstrate heralded quantum entanglement of two quantum dot heavy-hole spins separated by 5 meters using single-photon interference. Thanks to the long coherence time of hole spins and the efficient spin-photon interface provided by self-assembled quantum dots embedded in leaky microcavity structures, we generate 2300 entangled spin pairs per second, which represents an improvement approaching three orders of magnitude as compared to prior experiments. Delayed two-photon interference scheme we developed allows for efficient verification of quantum correlations. Our results lay the groundwork for the realization of quantum networks in semiconductor nanostructures. Combined with schemes for transferring quantum information to a long-lived memory qubit, fast entanglement generation we demonstrate could also impact quantum repeater architectures.
We study a simple, effective, and robust method for entangling two separate stationary quantum dot spin qubits with high fidelity using multiphoton Gaussian state. The fluorescence signals from the two dots interfere at a beam splitter. The bosonic nature of photons leads, in analogy with the Hong-Ou-Mandel effect, to selective pairing of photon holes (photon absences in the fluorescent signals). As a result, two odd photon number detections at the outgoing beams herald trion entanglement creation, and subsequent reduction of the trions to the spin ground states leads to spin-spin entanglement. The robustness of the Gaussian states is evidenced by the ability to compensate for photon absorption and noise by a moderate increase in the number of photons at the input. We calculate the entanglement generation rate in the ideal, nonideal, and near-ideal detector regimes and find substantial improvement over single-photon schemes in all three regimes. Fast and efficient spin-spin entanglement creation can form the basis for a scalable quantum dot quantum computing network. Our predictions can be tested using current experimental capabilities.
We investigate entanglement transfer from a system of two spin-entangled electron-hole pairs, each placed in a separate single mode cavity, to the photons emitted due to cavity leakage. Dipole selection rules and a splitting between the light hole and the heavy hole subbands are the crucial ingredients establishing a one-to-one correspondence between electron spins and circular photon polarizations. To account for the measurement of the photons as well as dephasing effects, we choose a stochastic Schrödinger equation and a conditional master equation approach, respectively. The influence of interactions with the environment as well as asymmetries in the coherent couplings on the photon entanglement is analysed for two concrete measurement schemes. The first one is designed to violate the Clauser-Horne-Shimony-Holt (CHSH) inequality, while the second one employs the visibility of interference fringes to prove the entanglement of the photons. Because of the spatial separation of the entangled electronic system over two quantum dots, a successful verification of entangled photons emitted by this system would imply the detection of nonlocal spin entanglement of massive particles in a solid state structure.
Dispersively coupled distant qubits in a shared cavity can become entangled through virtual photon exchange with energy-conserving phase evolution of their quantum states. This interaction can potentially be accelerated by operating on resonance, allowing for the exchange of real photons. In this theoretical study, we examine photon-mediated entanglement between two distant spins of electrons confined in double quantum dots formed in a Si/SiGe heterostructure. We calculate the dynamics of the combined system comprised of both spin qubits and the cavity, assuming that both spin qubits can be tuned into and out of resonance with the host cavity. We demonstrate that the exchange of real photons between the two spin qubits can result in rapid entanglement that is robust against decoherence. These results pave the way for the development of quantum gates on resonantly coupled distant semiconductor spin qubits.
We show that it is possible to employ reservoir engineering to turn two distant and relatively bad cavities into one good cavity with a tunable spontaneous decay rate. As a result, quantum computing schemes, which would otherwise require the shuttling of atomic qubits in and out of an optical resonator, can now be applied to distant quantum dots. To illustrate this we transform a recent proposal to entangle two qubits via the observation of macroscopic fluorescence signals [J. Metz et al., Phys. Rev. Lett. 97, 040503 (2006)] to the electron-spin states of two semiconductor quantum dots. Our scheme requires neither the coherent control of qubit-qubit interactions nor the detection of single photons. Moreover, the scheme is relatively robust against spin-bath couplings, parameter fluctuations, and the spontaneous emission of photons.