The physical principle of nonlocality is of particular interest both for fundamental tests of quantum theory via Bell inequality violations and for many quantum information processing applications like quantum key distribution (QKD). Over the last decades, corresponding studies have been performed mostly on the basis of two-dimensional quantum states (qubits). In order to gain a deeper insight into the nature of nonlocality, more complex quantum states are studied by increasing the dimension of the state to d-dimensions (qudits). For QKD, for instance, it has been shown, at least theoretically, that increasing the dimension of the alphabet by using qudits increases the effective bit rate of the protocol as well as the resistance to noise compared to qubits.
Sources of entangled pairs of photons can be used for encoding signals in quantum-encrypted communications, allowing a sender, Alice, and a receiver, Bob, to exchange keys without the possibility of eavesdropping. In fact, any quantum information system would require single and entangled photons to serve as qubits. For this purpose, semiconductor quantum dots (QD) have been extensively studied for their ability to produce entangled light and function as single photon sources.
The quality of such sources is evaluated based on three criteria: high efficiency, small multi-photon probability, and quantum indistinguishability. In this work, a simple quantum dot-based LED (E-LED) was used as a quantum light source for on-demand emission, indicating the potential for use as quantum information devices. Limitations of the device include the fine-structure splitting of the quantum dot excitons, their coherence lengths and charge carrier interactions in the structure.
The quantum dot-based light emitting diode was initially shown to operate in pulsed mode under AC bias frequencies of up to several hundreds of MHz, without compromising the quality of emission. In a Hong-ou-Mandel interference type experiment, the quantum dot photons were shown to interfere with dissimilar photons from a laser, achieving high two-photon interference (TPI) visibilities. Quantum entanglement from a QD photon pair was also measured in pulsed mode, where the QD-based entangled-LED (E-LED) was electrically injected at a frequency of 203 MHz.
After verifying indistinguishability and good entanglement properties from the QD photons under the above conditions, a quantum relay over 1km of fibre was demonstrated, using input qubits from a laser source. The average relay fidelity was high enough to allow for error correction for this BB84-type scheme. To improve the properties of the QD emission, an E-LED was developed based on droplet epitaxy (D-E) QDs, using a different QD growth technique. The relevant chapter outlines the process of QD growth and finally demonstration of quantum entanglement from an electrically injected diode, yielding improvements compared to previous E-LED devices.
For the same reason, an alternative method of E-LED operation based on resonant two-photon excitation of the QD was explored. Analysis of Rabi oscillations in a quantum dot with a bound exciton state demonstrated coupling of the ground state and the biexciton state by the external oscillating field of a laser, therefore allowing the transition between the two states. The results include a considerable improvement in the coherence length of the QD emission, which is crucial for future quantum network applications. We believe that extending this research can find application in quantum cryptography and in realising the interface of a quantum network, based on semiconductor nanotechnology.
Contributors:Kenji Kirihara, Anthony J. Rissling, Neal R. Swerdlow, David L. Braff, Gregory A. Light
Amplitude and Intertrial Phase Coherence of Theta and Gamma Oscillations
... theta oscillations... The amplitude of stimulus-driven gamma oscillations is modulated by the phase of ongoing theta oscillations. This cross-frequency coupling indicates a hierarchical organization of cortical oscillatory dynamics in both healthy control subjects (black line) and schizophrenia patients (red line). The x axis indicates theta phase. The y axis indicates gamma amplitude.
... Heuristic model of phase-amplitude cross-frequency coupling. Gamma oscillations (red and blue lines) are largest in the excitatory versus inhibitory phase of ongoing theta oscillations (black line). Note that excitatory and inhibitory phase may vary according to tasks and neural sources.
... cross-frequency coupling... gamma oscillations... Schizophrenia patients have normal theta-phase/gamma-amplitude cross-frequency coupling. The modulation index demonstrates the relative strength of cross-frequency coupling via comparison of observed (O) versus resampled or surrogate (S) electroencephalography data in healthy control subjects (black circle) and schizophrenia patients (red squares). The y axis indicates log transform of modulation index.
... neural oscillations... Schizophrenia patients (SZ) have increased theta amplitude and decreased gamma synchrony. The left column shows time-frequency maps from healthy control subjects (HC) and the middle column shows time-frequency maps from schizophrenia patients. The x axis indicates time in milliseconds and the y axis indicates frequency. Color indicates amplitude in the top row and intertrial phase coherence (ITC) in the bottom row. The right column shows difference between schizophrenia patients and healthy control subjects. Difference maps show only time-frequency points at p < .01.
The determination of the amplitude-response characteristic is an important means of checking a network design. However, this measurement is usually a time-consuming procedure and at best does not yield a continuous curve. A device which would produce a continuous curve corresponding to the amplitude-response characteristic would be extremely useful in network design and development. It is shown that the system response to a frequency-modulated signal can be made to approximate the amplitude-response characteristic if the frequency is varied slowly enough so that the "quasi-stationary" conditions exist. The physical realization of this slowly varying frequency requires an oscillator with an extremely large frequency range, controllable by one circuit parameter. The greatest difficulties involved in the design of this oscillator were the development of a simple and stable subtractor and the synthesis of the frequency-determining networks. A mathematical analysis was made to determine the characteristics of the network necessary to produce a logarithmic relation between the oscillatorfrequency and the control position. The audio-frequency sweep generator was constructed using networks designed to approximate the required characteristics and when tested proved to have a satisfactory output waveform. Any improvement in the oscillator performance would require a better approximation to the specified network characteristics.
The oscillatory activities form neural networks are involved in many behaviors, and animals need to be able to control the frequencies of these activities to respond to the environmental challenges. Neurons in many systems have frequency-dependent properties and preferred frequencies (also known as resonance). We hypothesize that the activity frequency of an oscillatory network is determined by the preferred frequencies of the neurons and of the synapses in the network. We examined this hypothesis by investigating the frequency-dependent properties of the neurons and of the synapses in the pyloric network in the crab Cancer borealis. We also examined what factors affect the preferred frequencies and how changing in these factors influence the frequency of the network activity. We first showed that the preferred frequency of neurons could be measured with the voltage-clamp technique. Measuring the preferred frequency with the voltage-clamp technique allowed us to have a full control of the voltage range and the waveform of the oscillation. By shifting the voltage range of the oscillation, we found that the pacemaker PD neuron has a higher preferred frequency when it is oscillating at a higher voltage range, and the preferred frequency of the follower LP neuron is only affected by the upper bound of the oscillation. The PD neuron also has different preferred frequencies when oscillating with different waveforms. Specifically, one waveform parameter, the 75 - 100% rising slope, showed a negative correlation with the preferred frequency. After knowing that the voltage range and the waveform of the oscillation are correlated with the preferred frequency, we used dynamic clamp to alter the voltage range and the waveform of the PD oscillation during the ongoing activity and measured the pyloric frequency. Based on our hypothesis, we expected the voltage range and the waveform would have similar effects on the pyloric frequency as they do on the preferred frequency. Indeed, our result showed that the shifts in the pyloric frequency during the dynamic clamp experiments could be explained by the changes in the voltage range and in the waveform parameters. Finally, we examined the frequency-dependencies of the amplitude and the phase of the synaptic current. The amplitudes of the synaptic currents between the AB/PD and LP neuron showed preferred frequencies. Interestingly, the preferred frequencies of the synapses were significantly lower than those of the presynaptic neurons and also than the pyloric frequency. While the voltage range of the presynaptic PD oscillation did not affect the preferred frequency of the AB/PD to LP synapse, the preferred frequency of the LP to PD synapse was higher when the upper bound, but not the lower bound, of the LP oscillation was increased. Moreover, the strength of the synaptic resonance depended on the upper bound of the presynaptic oscillation. To produce the strongest resonance, the upper bound of the presynaptic oscillation need to be within the voltage range at which the synapse is most sensitive to the presynaptic membrane potential. In addition to the amplitude, the phase of the synapses also showed frequency-dependence. At low frequencies (< 1 Hz), the synaptic current reached its peak before the presynaptic membrane potential did, and this phase relationship reversed at high frequencies (> 1 Hz). Overall, in this study, we demonstrated that many properties of the neurons and synapses depend on the frequency of the oscillation and have preferred frequencies. Moreover, these preferred frequencies can be regulated by many factors, including the voltage range and the waveform of the oscillation. Because some of these frequency-dependent properties are able to influence the network frequency, the factors affecting their preferred frequencies could change the network frequency in the same way. As a result, the frequency of an oscillatory network is not determined by a single factor, but by the dynamic interactions among the frequency-dependent properties of the network components.