Weak-Light Nonlinearity Using a Dark State in Coupled Quantum Dots

We present a proposal for deterministic remote preparation of electrons states in a semiconductor nanostructure consisting of a single and a double quantum dot. We show that deterministic remote preparation requires a minimum of only one controlled-Not gate plus one Hadamard gate for the basis transformation, and one Hadamard gate and one single-spin rotation for the reconstruction procedure. Picosecond-scale pulses allow for ultra-short total duration of the protocol, which implies a high remote preparation fidelity.

Electronic states in coupled quantum dots are studied numerically and qualitatively in this article. A second-order finite volume scheme based on uniform meshes is first developed to solve the three-dimensional Schrödinger equation. The scheme is used to solve the eigenvalue problem with more than 12 million unknowns. Using these efficient numerical tools, we study quantum structure induced interactions, with emphases on the effects of dot size and space layer thickness. The numerical experiments have predicted the phenomena that envelope functions become delocalized over two QDs and the energy levels show anticrossing behavior.

Electronic states in coupled quantum dots are studied numerically and qualitatively in this article. A second-order finite volume scheme based on uniform meshes is first developed to solve the three-dimensional Schrödinger equation. The scheme is used to solve the eigenvalue problem with more than 12million unknowns. Using these efficient numerical tools, we study quantum structure induced interactions, with emphases on the effects of dot size and space layer thickness. The numerical experiments have predicted the phenomena that envelope functions become delocalized over two QDs and the energy levels show anticrossing behavior.

We investigate the generation of entanglement of coherent excitonic states in coupled quantum dots placed in a cavity by meaning of the state preparation fidelity [Nature (London) 404 (2002) 256; Phys. Rev. A 65 (2002) 012107; J. Uffink, Phys. Rev. Lett. 88 (2002) 230406.] The effect of the number of excitons and the coherent intensity |α| of the cavity field on the entanglement is also studied.

Potential applications of quantum dots (QDs) have driven extensive efforts to grow high-quality QDs on semiconductor substrates by using various techniques [1]. Optoelectronic quantum devices utilizing QDs can be fabricated because QDs have discrete artificial atomic energy levels [2]. Thus, the microstructural and the optical properties of self-assembled QD systems have been particularly attractive for many years because of the potential application of QDs to optoelectronic devices [3–8]. In particular, the optical properties of QDs have been widely investigated because of interests in both fundamental physical properties and promising applications, such as QD lasers [9, 10], QD infrared photodetectors [11, 12], and QD memory devices [13] operating at lower current and at higher temperature. Among the many quantum dot structures, coupled quantum dot structures consisting of two smaller band-gap wells, which are different in band-gap energy and are separated by a thin embedded barrier, are currently receiving considerable attention for promising applications in electronic and optoelectronic devices [14–18]. Since the microstructural and the optical properties of coupled QDs are very important for optoelectronic devices based on QD structures, studies concerning the physical properties are still necessary in order to fabricate high-efficiency coupled QD devices. Many works on the formation and the physical properties of InAs/GaAs QDs grown by using the Stranski–Krastanov (S–K) growth mode have been performed. Even though some works on the sizes and the shapes of vertically stacked self-assembled QDs grown by using an indium-flush procedure have been performed [19–21], studies concerning the dependence of the microstructural and the optical properties on the GaAs spacer thickness in InAs/GaAs closely coupled double QDs grown by using the indium-flush method have not yet been reported. While the size of the upper QD in a coupled double QD grown by using the S–K mode is larger than that of the lower QD due to a strain field [22], the sizes of the two QDs in the coupled QDs grown by using the S–K mode, together with an indium-flush procedure, are almost the same. Since the top and the bottom dots of a double QD having similar sizes and shapes is important for investigating the coupling effects of double QDs and their promising applications in electronic and optoelectronic devices, the indium-flush method, which is an effective way to control precisely the sizes and the thicknesses of the QDs, should be very useful for investigating the coupling behavior in double QDs [19]. Furthermore, very few works on the dependence of the activation energy of double QDs on the spacer thickness have been done. This letter reports the dependences of the microstructural and the optical properties on the GaAs spacer thickness in InAs/GaAs double QDs with different GaAs spacer layers grown by using molecular beam epitaxy (MBE) with an indium-flush method. Transmission electron microscopy (TEM) measurements were performed to characterize the microstructural properties of the InAs/GaAs double QDs, and photoluminescence (PL) measurements were carried out in order to investigate the dependences of the full width at half maximum (FWHM), the peak position of the interband transitions, and the activation energy on the I. Y. Jung AE Y. M. Park AE Y. J. Park AE J. I. Lee Nano-Device Research Center, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, Korea

We report on exciton-acoustic-phonon coupling effects on the generation of exciton maximally entangled states in N=2 and 3 quantum dot systems. In particular, we address the question of the combined effect of laser pulses, appropriate for generating Bell and Greenberger-Horne-Zeilinger entangled states, together with decoherence mechanisms as provided by a phonon reservoir. By solving numerically the master equation for the optically driven exciton-phonon kinetics, we show that the generation of maximally entangled exciton states is preserved over a reasonable parameter window.

Both multiple steady states and dark states have potential applications in the quantum information processing in the presence of dissipation. Here, we propose to implement multiple steady states and dark states in a double quantum dot (DQD) system using quantum reservoir engineering. By coupling the DQD to shared reservoirs, multiple steady states of both four- and two-fold degeneracy can be achieved for specific parameters. It is proved that the occurrence of such multiple steady states is attributed to the strong symmetry of the Lindblad master equation. The multiple steady states can be well revealed by the occupation number of the DQD, which exhibits a discontinuity at the strong-symmetric points and changes drastically in the vicinities of these points. In the regime of unique steady state, the system can be stabilized to a pure state, dubbed dark state, with intact coherence in spite of the dissipation. Our work shows that a variety of novel steady states can be implemented in the DQD system, which paves the way for engineering multiple steady states and dark states in the DQD system.

Chapter 6 - Microwave spectroscopy on quantum dots

We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots.

Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields (easy passages) and perpendicular magnetic fields (weak passages) are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear (spin hot spots reappear) if the double dot system loses symmetry by an xy-like perturbation.

The properties of electron transport through an effective closed three-level structure in anasymmetric double quantum dot system are studied. It is demonstrated that the relative phasebetween two laser fields can strongly modulate the current through the system, which is similarto the magnetic flux controlled coherent transport in an Aharnov–Bohm interferometer.Two different transport regimes are considered, one is the regime of the chemical potentialμR of the right lead between the ground stateε2 and the excited stateε3 of the right dot, theother is the regime of μR<ε2. In both regimes, the current can be tuned to zero by appropriately choosing the phases of thedriving lasers, which can be used as an optically controlled current switch. In the regime ofμR<ε2, the current peak approaches zero because the electron is nearly trappedinto the ground state of the left quantum dot. While in the regime ofε2<μR<ε3,I = 0 occurs when the electron is trapped in the dark state, a superposition of the two quantumdot ground states.

Semiconductor multiple-quantum-dot devices have been attracted as a single-electron pump and quantum bits (qubits) [1, 2]. In particular, silicon-based coupled-quantum-dot has been paid attentions for the applications as qubits in solid state quantum computers due to their long coherent time of electron spins [3]. In the previous reports, these devices have been demonstrated by the use of two-dimensional electron gas (2DEG) and multiple control gates, where many gates were used to form tunnel barriers. This device concept makes it difficult to integrate quantum dots (QDs) due to the interference of many gates. For the applications in quantum computing, development of coupled QDs with a smaller number of control gates is considered. We have already succeeded in the fabrication of serially coupled Si triple-quantum-dots (TQD) by pattern-dependent oxidation (PADOX) method [4] and additional oxidation of the silicon nanowire on a SOI wafer with three control gates [5, 6]. The formation of a Si TQD, where each QD is formed just under each control gate, was confirmed experimentally. The equivalent circuit of the fabricated TQD is shown in Fig. 1 (a). The device has nine gate capacitances and two inter-dot coupling capacitances. It is crucial to know these capacitances for controlling the potential and the number of electrons of each dot. It is well known that the nine gate capacitances can be evaluated from the stability diagram that consists of boundary of the charge transition in the QDs. If the distance between the three gates is relatively long enough to ignore the influence of non-adjacent QD, it is easy to get the stability diagrams of charges. However, when the TQD become compact in size, the outer QD cannot be ignored because the center gate strongly couples to all three QDs, i.e., C 23 or C 21 is comparable to C 22. The stability diagram of such TQD usually shows very complicated behavior because three boundaries of the charge transition lines of individual QDs are superimposed. Fig. 1(b) shows the stability diagram which is the contour plot of current of TQD at 10 K simulated as a function of the two gate voltages V 1 and V 2 by the use of Monte Carlo method. Green dotted lines in the figures are the boundaries of charge transition of QD3, which are difficult to determine from the diagram. In addition, the coupling capacitance between the QDs also makes the stability diagrams complicate. Figs. 1(c) and (d) show stability diagrams of the TQD when the coupling capacitances, C 2 and C 3, become larger. As shown in the figures, the current peaks (white regions) are split as coupling capacitance C 2 and C 3 increase.In this study, we propose a simple analyzing method to evaluate the TQD by defining the contributions from each QD in stability diagrams. In order to divide the complicated stability diagram of TQD into the diagram of each QD, we employ the simultaneous scanning of three gate voltages with different sweeping ratios [7]. The effectiveness of the method is also confirmed even when the inter-dot coupling capacitance is large as shown in Fig. 1(c) and (d). The analysis using this method was applied to a Si TQD device fabricated on SOI wafer and successfully achieved the nine gate capacitances of the TQD. Acknowledgement This work was partly supported by JSPS KAKENHI (nos. 25420279, 26630141, 15H01706, 16H04339 and 16K18073). References H. Pothier, et al.: “Single electron pump fabricated with ultrasmall normal tunnel junction,” Physica B, 169, 573 1991. W. G. van der Wiel, et al.: “Electron transport through double quantum dots,” Rev. Mod. Phys, 75, 1 2002. B. M. Maune, et al.: “Coherent singlet-triplet oscillations in a silicon-based double quantum dot,” Nature, 481, 344 2012. Y. Takahashi, et al.: “Fabrication technique for Si single-electron transistor operating at room temperature,” Electron. Lett. 31, 136 1995. T. Uchida, et al.: “Coupling capacitance between double quantum dots tunable by the number of electrons in Si quantum dots,” J. Appl. Phys. 117, 084316 2015. T. Uchida, et al.: “Fabrication and evaluation of series-triple quantum dots by thermal oxidation of silicon nanowire,” AIP Advances. 5, 117144 2015. T. Uchida, et al.: “Capacitance evaluation of compact silicon triple quantum dots by simultaneous gate voltage sweeping,” J. Appl. Phys. 120, 234502 2016. Figure 1

For two coupled identical quantum dots in a two-mode cavity, we determine the conditions of two-photon and single-photon resonance. It is shown that the exciton-phonon interaction reduces the Rabi frequencies of each model and the Forster interaction between double quantum dots even at absolute zero temperature. The exciton-phonon interaction also makes a contribution to the static exciton-exciton dipole interaction energy. Furthermore, the additional interactions can modify the conditions of photon resonance significantly. A more realistic case of two nonidentical quantum dots is also considered. The influence of parameter misfits on the quantum system is discussed.

Both quantum transport measurements in the Pauli blockade regime and microwave cavity transmission measurements are important tools for spin-qubit readout and characterization. Based on a generalized input-output theory we derive a theoretical framework to investigate how a double quantum dot (DQD) in a transport setup interacts with a coupled microwave resonator while the current through the DQD is rectified by Pauli blockade. We show that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms. In the case of a silicon DQD, we show how the valley quasidegeneracy can impose limitations on this scheme. We also demonstrate that a large number of unknown DQD parameters including (but not limited to) the valley splitting can be estimated from the resonator response simultaneous to a transport experiment, providing more detailed knowledge about the microscopic environment of the DQD. Furthermore, we describe and quantify a back action of the resonator photons on the steady-state leakage current.

We have performed time-resolved measurements of the time scale for conversion of excitons in dark states to bright (light-emitting) states in GaAs quantum dots. The dark states are pumped using two-photon absorption, while the bright state emission is observed in single-photon emission. This conversion time is connected to the spin flip time for carriers in the quantum dots. The time scale is found to be of the order of several hundred picoseconds.