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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Extension of electron spin coherence in a quantum dot via CPT-locking of the Overhauser field

Dorian A. Gangloff, G. Éthier-Majcher, Robert Stockill, Claire Le Gall, Mete Atatüre

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Summary form only given. Semiconductor quantum dots (QD) offer the current state-of-the-art in intensity and coherence for single photon generation, as well as serving as a testbed for various novel approaches to quantum networking. Their high brightness provides a means to produce high-bandwidth spin-photon entanglement [1]. However, the purity and usefulness of the generated entangled state is severely limited by the coherence time of the QD charge carrier spin, typically on the order of 2ns for electrons in a self-assembled InGaAs QD. This limit is imposed by low-frequency fluctuations of the Overhauser field generated by host nuclear spins, affecting the electron spin resonance frequency.Here, we measure an extension of T2 by over an order of magnitude, enabled by prior preparation of the surrounding nuclear spin bath. The interplay of dynamic nuclear polarization and coherent population trapping (CPT) can lead to a controllable mechanism that locks the nuclear spins, and thereby reduces the Overhauser field fluctuations [2,3]. We use the lambda-scheme formed by an optical transition between bound electron and negatively-charged exciton in Voigt geometry at a field of 5T. There, we use the CPT dark-state resonance as a means to lock the polarization state of the nuclear spins surrounding the electron spin. Using ultrafast optical spin rotations, we perform a Ramsey sequence following a CPT preparation of the nuclear spins, to measure the Free Induction Decay of the electron spin coherence [4]. With a pulse sequence composed of 70μs of CPT preparation, followed by 70μs of repeated Ramsey measurements, as shown in Fig. 1a, we observe coherent electron spin oscillations at a Ramsey delay of 29ns, as shown in Fig. 1b. The oscillations are free of the deleterious effects of nuclear polarization typical in such measurements [5], indicating the stabilization of the mean Overhauser field to a fixed value. The measured T2 of 39ns is over an order of magnitude longer than the Ti of 3ns measured on the system with unprepared nuclear spins, as shown in Fig. 1c.

DOI
10.1109/cleoe-eqec.2017.8087611

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Summary form only given. Semiconductor quantum dots (QD) offer the current state-of-the-art in intensity and coherence for single photon generation, as well as serving as a testbed for various novel approaches to quantum networking. Their high brightness provides a means to produce high-bandwidth spin-photon entanglement [1]. However, the purity and usefulness of the generated entangled state is severely limited by the coherence time of the QD charge carrier spin, typically on the order of 2ns for electrons in a self-assembled InGaAs QD. This limit is imposed by low-frequency fluctuations of the Overhauser field generated by host nuclear spins, affecting the electron spin resonance frequency.Here, we measure an extension of T2 by over an order of magnitude, enabled by prior preparation of the surrounding nuclear spin bath. The interplay of dynamic nuclear polarization and coherent population trapping (CPT) can lead to a controllable mechanism that locks the nuclear spins, and thereby reduces the Overhauser field fluctuations [2,3]. We use the lambda-scheme formed by an optical transition between bound electron and negatively-charged exciton in Voigt geometry at a field of 5T. There, we use the CPT dark-state resonance as a means to lock the polarization state of the nuclear spins surrounding the electron spin. Using ultrafast optical spin rotations, we perform a Ramsey sequence following a CPT preparation of the nuclear spins, to measure the Free Induction Decay of the electron spin coherence [4]. With a pulse sequence composed of 70μs of CPT preparation, followed by 70μs of repeated Ramsey measurements, as shown in Fig. 1a, we observe coherent electron spin oscillations at a Ramsey delay of 29ns, as shown in Fig. 1b. The oscillations are free of the deleterious effects of nuclear polarization typical in such measurements [5], indicating the stabilization of the mean Overhauser field to a fixed value. The measured T2 of 39ns is over an order of magnitude longer than the Ti of 3ns measured on the system with unprepared nuclear spins, as shown in Fig. 1c.
We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.
Hyperfine interaction between electron spin and randomly oriented nuclear spins is a key issue of electron coherence for quantum information/computation. We propose an efficient way to establish high polarization of nuclear spins and reduce the intrinsic nuclear spin fluctuations. Here, we polarize the nuclear spins in semiconductor quantum dot (QD) by the coherent population trapping (CPT) and the electric dipole spin resonance (EDSR) induced by optical fields and ac electric fields. By tuning the optical fields, we can obtain a powerful cooling background based on CPT for nuclear spin polarization. The EDSR can enhance the spin flip–flop rate which may increase the cooling efficiency. With the help of CPT and EDSR, an enhancement of 1300 times of the electron coherence time can be obtained after a 10-ns preparation time.
We demonstrate the extension of coherence between all four two-electron spin ground states of an InAs quantum dot molecule (QDM) via nonlocal suppression of nuclear spin fluctuations in two vertically stacked quantum dots (QDs), while optically addressing only the top QD transitions. Long coherence times are revealed through dark-state spectroscopy as resulting from nuclear spin locking mediated by the exchange interaction between the QDs. Line shape analysis provides the first measurement of the quieting of the Overhauser field distribution correlating with reduced nuclear spin fluctuations.
A single spin confined to a semiconductor quantum dot is a system of significant interest for quantum information science, as a potential optically-addressable qubit. In many respects, a quantum dot behaves like a single atom with high quality single photon emission. By controlling the light-matter coupling in such a system, it is possible to generate highly non-classical states of light and coherently control a single spin confined to the quantum dot. A departure from the ideal atomic picture appears once we consider the mesoscopic environment with which the quantum dot interacts. Charge fluctuations in the surroundings of the quantum dot affect the photon emission frequency leading to inhomogeneous broadening. Further broadening of the emission is caused by coupling to phonon modes of the host semiconductor material. Finally, coupling between the spin of a confined electron and a large bath of nuclear spins residing in the quantum dot leads to fast dephasing of the electron spin. All of these effects are typically considered detrimental to the potential use of quantum dots for quantum technologies. In this thesis, we develop the environmental coupling of a negatively charged quantum dot as a resource for quantum optics and spin control. First, the phonon-assisted fluorescence is shown to be a useful independent channel for feedback stabilisation of the quantum dot emission frequency, without requiring a measurement of the indistinguishable zero-phonon line. With stabilisation, the corresponding frequency broadening is drastically improved, and the sub-Hz frequency fluctuations are no longer resolved. Next, we show low-power resonance fluorescence emission spectra of the negatively charged trion transition. In the low power regime of resonance fluorescence, the excited state is not populated and most of the emission is coherent. In addition to elastic Rayleigh scattering, we observe coherent Raman sidebands, linked to an effective magnetic field created by the hyperfine interaction, the Overhauser field. This fluctuating effective field lifts the electron spin degeneracy in the absence of a magnetic field, and dictates the optical selection rules of the trion system. These spectra therefore allow for a measurement of the time-averaged distributions of in-plane and out-of-plane Overhauser field components. In the final part of the thesis, we use this hyperfine-generated Λ -scheme to optically create electron spin superpositions through two-colour excitation and coherent population trapping. We then show that rapid shifts in the relative phase of the lasers lead to initialisation of the electron spin into a rotated dark state.
Recent studies in self-assembled InAs quantum dots (QDs) for applications in quantum information processing have demonstrated initialization, readout and long decoherence time of an electron spin confined in a single QD. These arguably fulfill three out of the five DiVincenzo criteria for the physical implementation of quantum computation. Based on recent developments self-assembled InAs quantum dot molecules (QDMs), several advancements in the optical manipulation of two-electron spin states have been made. As a continuation of these studies towards a full two-qubit system, this thesis addresses one of the remaining criteria concerning a universal set of quantum gates. The physical platform for two-qubit gates is provided by two electrons confined in the QDM where the Coulomb exchange interaction gives rise to the singlet and triplet manifolds. In a transverse magnetic field, an eight-level system consisting of four singlet-triplet spin states, four optical excited states and twelve dipole allowed transitions arises. Spin initialization via multi-laser optical pumping is demonstrated with near unity fidelity for three of the spin states, while the remaining one can, in principle, be achieved by coherent optical pumping using four CW lasers. The effects of dynamic nuclear spin polarization, arising from the coupling between the electrons and the surrounding nuclei, is evident in the frequency pulling and pushing lineshapes in absorption profiles. This thesis shows that the optical nuclear spin locking that was demonstrated in a single QD earlier is effective in QDMs, yielding a long spin decoherence time of about 1 microsecond. Spectroscopic evidence suggests that this is accompanied by the first evidence of a narrowing in the Overhauser field distribution. The results reveal that stabilization of nuclear spin polarization in both QDs is achieved by optical manipulations in the top QD, demonstrating the effect of non-local nuclear spin locking. Finally, it is shown theoretically that pulsed excitation results in single spin rotations and in conjunction with the Coulomb exchange interaction, provides the ingredients for a universal two-qubit gate. A feasible experimental demonstration of the two-qubit gate is proposed, along with the methodology for the population readout of individual spin states.
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of decoherence also leads to a method of coherence recovery of the electron by disentanglement, realized through maneuvering the nuclear bath evolution by control of the electron spin-flip. The studies form the basis to outline the construction of a solid-state quantum network for scalable and distributed processing of quantum information