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arXiv:1706.02486 · Physical Review A

Protocol for generating multiphoton entangled states from quantum dots in the presence of nuclear spin fluctuations

Emil V. Denning, Jake Iles-Smith, Dara P. S. McCutcheon, Jesper Mørk

Published Dec 26, 2017• 7 citations
arXivHTMLPDF

Abstract

Multiphoton entangled states are a crucial resource for many applications in quantum information science. Semiconductor quantum dots offer a promising route to generate such states by mediating photon-photon correlations via a confined electron spin, but dephasing caused by the host nuclear spin environment typically limits coherence (and hence entanglement) between photons to the spin ${T}_{2}^{*}$ time of a few nanoseconds. We propose a protocol for the deterministic generation of multiphoton entangled states that is inherently robust against the dominating slow nuclear spin environment fluctuations, meaning that coherence and entanglement is instead limited only by the much longer spin ${T}_{2}$ time of microseconds. Unlike previous protocols, the present scheme allows for the generation of very low error probability polarization encoded three-photon GHZ states and larger entangled states, without the need for spin echo or nuclear spin calming techniques.

DOI
10.1103/physreva.96.062329

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Multiphoton entangled states are a crucial resource for many applications in quantum information science. Semiconductor quantum dots offer a promising route to generate such states by mediating photon-photon correlations via a confined electron spin, but dephasing caused by the host nuclear spin environment typically limits coherence (and hence entanglement) between photons to the spin T2∗{T}_{2}^{*}T2∗​ time of a few nanoseconds. We propose a protocol for the deterministic generation of multiphoton entangled states that is inherently robust against the dominating slow nuclear spin environment fluctuations, meaning that coherence and entanglement is instead limited only by the much longer spin T2{T}_{2}T2​ time of microseconds. Unlike previous protocols, the present scheme allows for the generation of very low error probability polarization encoded three-photon GHZ states and larger entangled states, without the need for spin echo or nuclear spin calming techniques.
Deterministic photon sources allow long-term advancements in quantum optics. A single quantum emitter embedded in a photonic resonator or waveguide may be triggered to emit one photon at a time into a desired optical mode. By coherently controlling a single spin in the emitter, multi-photon entanglement can be realized. We demonstrate a deterministic source of three-qubit entanglement based on a single electron spin trapped in a quantum dot embedded in a planar nanophotonic waveguide. We implement nuclear spin narrowing to increase the spin dephasing time to T2∗≃33{T}_{2}^{*}\simeq 33T2∗​≃33 ns, which enables high-fidelity coherent optical spin rotations, and realize a spin-echo pulse sequence for sequential generation of spin-photon and spin-photon-photon entanglement. The emitted photons are highly indistinguishable, which is a key requirement for scalability and enables subsequent photon fusions to realize larger entangled states. This work presents a scalable deterministic source of multi-photon entanglement with a clear pathway for further improvements, offering promising applications in photonic quantum computing or quantum networks. Entanglement between single photons and solid-state emitters is a key component for photonic quantum computing and networks. Here, using a single electron spin in a quantum dot, the authors present a deterministic photon source achieving three-qubit entanglement of one electron spin and two photons.
We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.
Semiconductor quantum dots can be used as sources of entangled single photons, which constitute a crucial resource for optical quantum computing. We present theoretical research on entanglement verification and nuclear spin physics, leading to results that are relevant to both experimental work and the theory of quantum optics and mesoscopic quantum systems. Optical quantum computing requires large entangled photonic states, yet characterizing even few-photon states is a challenge in current experiments due to low photon detection efficiencies. We present a lower bound on a measure of computational usefulness of a potentially large quantum state that requires only measured values of three-photon correlations. Hence this bound provides a simple and applicable benchmarking method for quantum dot experiments. We then turn to the critical issue of the interaction between electron and nuclear spins in quantum dots. This interaction gives rise to decoherence that stands in the way of generating entangled photons as well as nuclear phenomena that might help to overcome this challenge. We formulate a quantum mechanical model of the nuclear spin system in a quantum dot driven by continuous-wave laser light. Based on the analytical steady state solution of this model we predict a novel nuclear spin effect, giving rise to nuclear spin polarization that counteracts the effect of an external magnetic field. Beyond the decoherence problem nuclear spins give rise to randomly time-varying transition energies. A quantum mechanical model of this noise as well as the effect of photon scattering is developed, leading to the insight that optical driving can continuously probe the electron transition energy and thereby prevent it from changing.
Self-assembled quantum dots can act as an interface between single spins and photons. They combine the flexibility and scalability of semiconductor systems with near-perfect two level systems, emitting highly coherent single photons. In potential quantum information processing architectures based upon optical networks, quantum dots permit light-matter coupling between matter qubits and photonic links. Single trapped charge carriers in quantum dots can be addressed optically, generating spin-photon entanglement between the matter qubits and \lq flying' photon qubits, a key first step in creation of a network. Such an optically linked network of spins in quantum dots has yet to be realized. The semiconductor environment presents a key challenge; it broadens the spectrum of the emitted light, which reduces the fidelity of schemes based upon photon exchange or interference. In addition, these quantum dots are subject to hyperfine coupling to a bath of >>> 105^{5}5 nuclear spins. While this presents an opportunity to study the physics of a central spin in a spin bath, it degrades the spin coherence of a trapped electron or hole. The suggested gate operations to generate entanglement, and the spin measurements to verify a created state, rely upon photon detection. Thus a second limitation occurs due to low efficiency of detectors and photon collection probability. Recent developments in detector technology have enabled us to bring generation and verification of entangled states with quantum dots into the realm of possibility. This dissertation begins with a detailed study of the interaction of a single electron spin with the solid state environment of the quantum dot, analysing the intensity noise of scattered light under resonant excitation to uncover the timescales and relative amplitudes of identified noise sources. A technique for rapid characterization of samples is presented, focusing in particular upon comparison of spectral broadening of the optical transitions relevant to a spin-photon interface. Having identified the extent of environmental factors acting upon the quantum dots, we turn to a demonstration of photon-mediated entanglement between two distant electron spins using a probabilistic scheme. We are able to generate entangled states at 7 kHz, the fastest yet reported for photon-mediated protocols. The average state fidelity of the created Bell states is 63.5 ±\pm± 3.0 \%., violating the classical limit by over 4 standard deviations of the mean. In addition, we demonstrate full optical phase tuning of the Bell state ∣Ψ=12(∣↑∣↓+eiϕ∣↓∣↑)|{\Psi} = \frac{1}{\sqrt{2}}\left(|{\uparrow}|{\downarrow} + e^{i\phi}|{\downarrow}|{\uparrow} \right)∣Ψ=2​1​(∣↑∣↓+eiϕ∣↓∣↑). This is a proof of principle experiment, and sets a fidelity benchmark upon which gains can be made by mitigation of environmental dynamics.
Spins in a solid-state environment and photons are both promising physical systems regarding the implementation of qubits. Whereas electron and nuclear spins act very well as localized qubits that are able to store and process quantum information, photons are the primary candidates to transmit quantum information between distant locations. Entanglement, on the other hand, is a fundamental resource of quantum information processing enabling, e.g., secure communication over long distances. The generation and manipulation of entanglement are thus fundamental steps in order to leverage the benefits of quantum information processing. The aim of this dissertation is therefore to theoretically investigate entangling mechanisms for various physical systems. A functioning source of entangled photons is a basic hardware component required for quantum communication. To this end, we study a system composed of semiconductor quantum wells inside a microcavity, known as intersubband cavity system, in which the interaction of the electronic system with the cavity field can reach the ultrastrong coupling regime. The ground state contains a finite number of photons, and we find that these photons are entangled. The amount of entanglement is quantified analytically, and maximal entanglement is found to be possible. The technique of entanglement purification allows to restore maximal entanglement that has decreased, e.g. due to decoherence. Purification requires quantum memory, a role for which electron spins in electrically-defined quantum dots are well suited. However, existing purification protocols are rather unpractical in this case. Here, the concept of asymmetric bilateral two-qubit operations is introduced to purify spin entanglement by harnessing the typical interaction between electrons in neighboring quantum dots. As it turns out, this concept can be applied to a variety of qubit systems, e.g. superconducting qubits or spins in nitrogen-vacancy centers in diamond. The latter example offers several possibilities to implement a qubit, of which the intrinsic nitro- gen nuclear spin has proven its viability in many ways. We develop a scheme to deterministically couple two nuclear spin qubits, in which the interaction is mediated by an optical cavity. It is found that an entangling two-qubit gate, also required for universal quantum computation, can be implemented with operation times below 100 nanoseconds, i.e. several orders of magnitude faster compared to the decoherence time of the nuclear spin. The verification of entanglement, which is required e.g. in entanglement-based quantum com- munication to detect an eavesdropping attack, typically involves a measurement of qubit states. Using the input-output formalism, we derive a fully quantum-mechanical model of an optical readout scheme to measure the spin state of an electron in a self-assembled quantum dot.
Photonic graph states are key resource states for measurement based quantum information processing. As semiconductor quantum dots are excellent deterministic photon emitters, several protocols using them for the generation of linear cluster states have been proposed, either based on constant precession of a hole or electron spin in a weak magnetic field, or based on optical spin control, in a stronger magnetic field. We theoretically compare four such schemes, using polarization or time-bin encoding, respectively, for a range of cavity environments and spin coherence times. In particular we study how different error mechanisms affect the different schemes, using a microscopic model of the spin control, the excitation and emission dynamics, and of the phonon bath. We find the spin-precession based schemes to scale well with strong cavity enhancement and to be naturally robust against phonon-induced decoherence, while the schemes using optical spin control can perform well for lower spin coherence times and are strongly dependent on the cooperativity of the cavity induced cycling transition. Our results provide a regime map for choosing between magnetic-field-driven and optically controlled protocols depending on spin coherence time, Purcell enhancement, and suppression of unwanted decay channels.