We demonstrate an entirely new method to probe quantum measurement phenomena in semiconductor quantum dot (QD) spin qubits [1]. In addition to providing direct evidence for the quantum nature of solid state qubits, we show that our method has practical importance since it provides a completely alternative route for measuring ensemble and quantum dephasing times, T2* and T2, using only repeated projective measurements and without the need for coherent spin control. Our approach is based on measuring time-correlators of a spin qubit in an optically active QD beyond the second order. We utilize a quantum dot spin-storage structure to initialize a single electron spin in a quantum dot subject to a magnetic field applied in Voigt geometry through tunnel ionization and perform repeated projective measurements of the spin at times t1 and t2. This measurement is repeated, corresponding to ensemble averaging, and the resulting third-order time correlations reveals rich physics: For times t1 or t2 < T2* Larmor precession is observed which reveals the ensemble dephasing time T2*. Importantly, even though the time-correlators were obtained through averaging many measurements for times t1 and t2 > T2* oscillations are observed that decay with the dephasing time T2 and allow its determination even without the need for coherent spin control. Finally, combining the third-order time correlator with the second-order time correlator allows to demonstrate a violation of Leggett-Garg type inequalities for certain times providing clear evidence for the quantum nature of the quantum dot spin. [1] A. Bechtold et al. Phys. Rev. Lett. 117, 027402 (2016)
We demonstrate an entirely new method to probe quantum measurement phenomena in semiconductor quantum dot (QD) spin qubits [1]. In addition to providing direct evidence for the quantum nature of solid state qubits, we show that our method has practical importance since it provides a completely alternative route for measuring ensemble and quantum dephasing times, T2* and T2, using only repeated projective measurements and without the need for coherent spin control. Our approach is based on measuring time-correlators of a spin qubit in an optically active QD beyond the second order. We utilize a quantum dot spin-storage structure to initialize a single electron spin in a quantum dot subject to a magnetic field applied in Voigt geometry through tunnel ionization and perform repeated projective measurements of the spin at times t1 and t2. This measurement is repeated, corresponding to ensemble averaging, and the resulting third-order time correlations reveals rich physics: For times t1 or t2 < T2* Larmor precession is observed which reveals the ensemble dephasing time T2*. Importantly, even though the time-correlators were obtained through averaging many measurements for times t1 and t2 > T2* oscillations are observed that decay with the dephasing time T2 and allow its determination even without the need for coherent spin control. Finally, combining the third-order time correlator with the second-order time correlator allows to demonstrate a violation of Leggett-Garg type inequalities for certain times providing clear evidence for the quantum nature of the quantum dot spin. [1] A. Bechtold et al. Phys. Rev. Lett. 117, 027402 (2016)
We measure time correlators of a spin qubit in an optically active quantum dot beyond the second order. Such higher-order correlators are shown to be directly sensitive to pure quantum effects that cannot be explained within the classical framework. They allow direct determination of ensemble and quantum dephasing times, T_{2}^{*} and T_{2}, using only repeated projective measurements and without the need for coherent spin control. Our method enables studies of purely quantum behavior in solid state systems, including tests of the Leggett-Garg type of inequalities that rule out local hidden variable interpretation of the quantum-dot spin dynamics.
Self-assembled quantum dots (QDs) containing a single electron are one of the leading candidate systems for the realization of a quantum computer. The spin states of charges confined in these dots have been shown to possess a number of qualities that are attractive for use as the quantum bits (qubits) in quantum computing implementations, particularly their long lifetimes and coherence times. In addition, these spin qubits may be controlled optically, offering the prospect of ultrafast qubit gate operations, a crucial necessity for the execution of quantum algorithms. Due to the weak interaction of self-assembled QDs with light, however, the coherent optical control and read-out of the spin states of charged self-assembled QDs has proven to be a considerable challenge. This thesis presents two sets of experiments demonstrating the coherent optical control and read-out of the quantum states of a self-assembled InAs QD containing a single electron. The first utilizes mode-locked picosecond optical pulses to control the optical transitions in the dot and to detect QD level occupations. These capabilities are used to observe transient phenomena in a singly charged InAs QD such as the generation and decay of excited state population and spin precession. Further, Rabi oscillations between the electron and the lowest-lying excited state are observed, demonstrating the ability to coherently control the optical transitions of the QD, a prerequisite for spin control. These results are built upon in the second set of experiments, in which a combination of optical pulses, an externally applied DC magnetic field and a continuous-wave (CW) optical field are employed to initialize and completely control the states of a QD confined electron spin. Spin control by the use of pulse-driven two-photon Raman processes, spin precession about the external magnetic field and geometric phases generated by CW-driven cyclic evolutions in the dot is demonstrated. A number of spin qubit gate operations are shown for these spin control mechanisms, forming a foundational set of single qubit gates required for the implementation of quantum computing with singly charged self-assembled QDs.
Long spin coherence times of carriers are essential for implementing quantum technologies using semiconductor devices for which, however, a possible obstacle is spin relaxation. For the spin dynamics, decisive features are the band structure, crystal symmetry, and quantum confinement. Perovskite semiconductors recently have come into focus of studies of their spin states, notivated by efficient optical access and potentially long-living coherence. Here, we report an electron spin coherence time T2 of the order of 1 ms, measured for a bulk FA0.95Cs0.05PbI3 lead halide perovskite crystal. Using periodic laser pulses, we synchronize the electron spin Larmor precession about an external magnetic field in an inhomogeneous ensemble, the effect known as spin mode locking. It appears as a decay of the optically created ensemble spin polarization within the dephasing time T2∗ of up to 20 ns and its revival during the spin coherence time T2 reaching the millisecond range. This exceptionally long spin coherence time in a bulk crystal is complemented by millisecond-long longitudinal spin relaxation times T1 for electrons and holes, measured by optically-detected magnetic resonance. These long-lasting spin dynamics highlight perovskites as promising platform for the quantum devices with all-optical control.
In this work, we study the resonant nonlinear optical response obtained when optical fields are used to excite charged semiconductor quantum dots (QDs). The basic physics of charged excitons (trions) created by optical excitation of charged QDs is of interest from the point of view of optically driven spin based quantum computing (QC). Stimulated Raman excitation, resonantly enhanced by the optical dipole coupling to the trion state, was used to optically generate electron spin coherence in the ground state of charged QDs. The evolution of the spin coherence was monitored through quantum beats in the phase-sensitively detected four wave mixing signal. The decay of the beats is a measure of the spin coherence time, which was found to be at least an order of magnitude greater than either the trion dipole coherence, or the Raman coherence time between excitons in a single neutral QD. A fascinating outcome of the experiment was the first observation of a contribution to the spin coherence induced by the vacuum field, which is also responsible for spontaneous emission from the trion state, known as spontaneously generated coherence (SGC). QC demands that coherent optical manipulations should be performed within the spin coherence time. We performed coherent optical control experiments, with a pair of phase-locked pump pulses, that showed the quantum nature of the coherence through interference of different quantum mechanical pathways. We showed both in experiment and theory that we can manipulate the spin coherence on the time scale of the Larmor frequency, as well as on an ultrafast femtosecond time scale, corresponding to the optical frequency of the trion state. Finally, resonant optical excitation of both the bright and nominally forbidden transitions from a single electron spin in a QD to the trion state were demonstrated. This allows for direct optical access to all the transitions required for optically driven QC with QD electron spins. We used frequency-domain nonlinear spectroscopy measurements on single QD trions to obtain the trion dipole decoherence and decay rates. Further, we demonstrated that the single electron spin coherence could be generated and detected optically, and found that the spin coherence time was significantly greater than in ensemble measurements at the same magnetic field.
InAs quantum dots (QDs) can be used as optically coupled quantum storage devices for quantum information applications. The QD can be charged with a single electron, where the spin state (up or down) provides a long lived quantum bit (qubit). The QD's optically excited states are used to initialize, manipulate, and read out the electron spin state with laser pulses. However, most practical quantum information applications require many interacting qubits, forming a quantum network. Since QDs are based on semiconductor technology, and are compatible with standard nano-fabrication processing, there is promise that they can provide a solid state platform where a scalable quantum information architecture is realizable. We focus on scaling the QD system to multiple qubits using intermediate spin-photon entangled states. In this work, experimental and theoretical techniques are developed to study the QD-light matter interaction at the single photon level. Resonance fluorescence from a single QD is experimentally realized, and the single photon nature of the scattered radiation is verified through intensity correlation experiments. Transient fluorescence measurements on resonantly excited QDs are performed using time correlated single photon counting techniques to measure the excited state lifetime. High speed electro-optic modulators are used to time gate narrow bandwidth lasers, so that a QD can be driven under step-wise excitation, allowing for the direct observation of time-dependent optical Rabi oscillations. From these measurements, we are able to extract a decoherence rate which is consistent with the lifetime limit, indicating that pure dephasing is negligible in this system. These techniques are applied to the QD spin system to demonstrate a spin-photon entangled state, by performing correlation measurements on the spin and photon state in two bases. A lower bound on the entanglement fidelity of 0.59(4) is achieved, which exceeds the classical limit of 0.5 by more than two standard deviations. The entanglement fidelity is limited primarily by the finite timing resolution of available single photon detectors. Taking this into account, we achieve 84% of the apparatus limited fidelity. These spin-entangled photons can be used to mediate entanglement between distant QD spins, providing the basis of an optically coupled QD spin network.
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.