Contributors:Owen, Edmund Thomas, Barnes, Crispin H. W.
Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies.
The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function.
In Ch. 3, a new method for generating maximally entangled two-qubit states using a pair of interacting particles in a one-dimensional harmonic oscillator is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two qubits are initially in the same state, no entanglement is generated as there is no direct qubit-qubit
interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor
systems are suggested.
One of the most commonly used qubits is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this qubit to the electron's momentum. In order to incorporate this e ffect
into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields.
In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.
Contributors:Walter, S, Nunnenkamp, Andreas, Bruder, C
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:Walter, Stefan, Nunnenkamp, Andreas, Bruder, Christoph
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.
Contributors:Lörch, N, Nigg, SE, Nunnenkamp, Andreas, Tiwari, RP, Bruder, C
Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.
Contributors:Li, Larry, Juniper, Matthew
In the analysis of thermoacoustic systems, a flame is usually characterised
by the way its heat release responds to acoustic forcing. This
response depends on the hydrodynamic stability of the flame. Some
flames, such as a premixed bunsen flame, are hydrodynamically globally
stable. They respond only at the forcing frequency. Other flames,
such as a jet diffusion flame, are hydrodynamically globally unstable.
They oscillate at their own natural frequencies and are often assumed
to be insensitive to low-amplitude forcing at other frequencies.
If a hydrodynamically globally unstable flame really is insensitive to
forcing at other frequencies, then it should be possible to weaken
thermoacoustic oscillations by detuning the frequency of the natural
hydrodynamic mode from that of the natural acoustic modes. This
would be very beneficial for industrial combustors.
In this thesis, that assumption of insensitivity to forcing is tested
experimentally. This is done by acoustically forcing two different selfexcited
flows: a non-reacting jet and a reacting jet. Both jets have
regions of absolute instability at their base and this causes them to
exhibit varicose oscillations at discrete natural frequencies. The forcing
is applied around these frequencies, at varying amplitudes, and
the response examined over a range of frequencies (not just at the
forcing frequency). The overall system is then modelled as a forced
van der Pol oscillator.
The results show that, contrary to some expectations, a hydrodynamically
self-excited jet oscillating at one frequency is sensitive to
forcing at other frequencies. When forced at low amplitudes, the jet
responds at both frequencies as well as at several nearby frequencies,
and there is beating, indicating quasiperiodicity. When forced at
high amplitudes, however, it locks into the forcing. The critical forcing
amplitude required for lock-in increases with the deviation of the
forcing frequency from the natural frequency. This increase is linear,
indicating a Hopf bifurcation to a global mode.
The lock-in curve has a characteristic ∨ shape, but with two subtle
asymmetries about the natural frequency. The first asymmetry concerns
the forcing amplitude required for lock-in. In the non-reacting
jet, higher amplitudes are required when the forcing frequency is above
the natural frequency. In the reacting jet, lower amplitudes are required
when the forcing frequency is above the natural frequency. The
second asymmetry concerns the broadband response at lock-in. In the
non-reacting jet, this response is always weaker than the unforced response,
regardless of whether the forcing frequency is above or below
the natural frequency. In the reacting jet, that response is weaker
than the unforced response when the forcing frequency is above the
natural frequency, but is stronger than it when the forcing frequency
is below the natural frequency.
In the reacting jet, weakening the global instability – by adding coflow
or by diluting the fuel mixture – causes the flame to lock in at lower
forcing amplitudes. This finding, however, cannot be detected in the
flame describing function. That is because the flame describing function
captures the response at only the forcing frequency and ignores all
other frequencies, most notably those arising from the natural mode
and from its interactions with the forcing. Nevertheless, the flame describing
function does show a rise in gain below the natural frequency
and a drop above it, consistent with the broadband response.
Many of these features can be predicted by the forced van der Pol
oscillator. They include (i) the coexistence of the natural and forcing
frequencies before lock-in; (ii) the presence of multiple spectral peaks
around these competing frequencies, indicating quasiperiodicity; (iii)
the occurrence of lock-in above a critical forcing amplitude; (iv) the
∨-shaped lock-in curve; and (v) the reduced broadband response at
lock-in. There are, however, some features that cannot be predicted.
They include (i) the asymmetry of the forcing amplitude required
for lock-in, found in both jets; (ii) the asymmetry of the response at
lock-in, found in the reacting jet; and (iii) the interactions between
the fundamental and harmonics of both the natural and forcing frequencies,
found in both jets.
Contributors:Zou, X, Seshia, Ashwin
Resonant MEMS accelerometers offer the potential for very high resolution and wide bandwidth measurements over a large input dynamic range. The read-out is implemented by constructing an oscillator with the resonator as the primary frequency determining element. The noise of this oscillator front-end typically determines the resolution of the device, and the noise floor is set by the modulation of operative noise processes by the system dynamics. The resonator element is typically operated in the linear regime to prevent the detrimental impact of resonator non-linearities on noise conversion limiting frequency stability. However, by operating at higher drive power levels it is possible to also increase the signal-to-noise ratio for sufficiently large input frequencies. This paper shows that improved device performance over a wide bandwidth is possible by employing appropriate amplitude and phase feedback schemes to optimally bias the resonator thus enabling both short-term and long-term measurements with an electrically tunable resolution.
Contributors:Lörch, Niels, Amitai, Ehud, Nunnenkamp, Andreas, Bruder, Christoph
We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.
Contributors:Deng, Jian, Caulfield, Colm-cille
Using two-dimensional direct numerical simulations, we investigate the flow in a fluid of kinematic viscosity ν and density ρ around elliptical foils of density ρ_s with major axis c and minor axis b for three different aspect ratios: AR = b/c = 1 (a circle); AR = 0.5; and AR = 0.1. The vertical location of these foils y_s(t) = A sin(2πf₀t) oscillates with amplitude A and frequency f₀ in two distinct ways: ‘pure’ oscillation, where the foils are constrained to remain in place; and ‘flying’ oscillation, where horizontal motion is allowed. We simulate the flow for a range of the two appropriate control parameters, the nondimensional amplitude or Keulegan-Carpenter number KC = 2πA/c and the nondimensional frequency or Stokes number β = f₀c²/ν. We observe three distinct patterns of asymmetry, labelled ‘S-type’ for synchronous asymmetry, ‘QP_H-type’ and ‘QP_L-type’ for quasi-periodic asymmetry at sufficiently high and sufficiently low (i.e. AR = 0.1) aspect ratios respectively. These patterns are separated at the critical locus in KC − β space by a ‘freezing point’ where the two incommensurate frequencies of the QP-type flows combine, and we show that this freezing point tends to occur at smaller values of KC as AR decreases. We find for the smallest aspect ratio case (AR = 0.1) that the transition to asymmetry, for all values of KC, occurs for a critical value of an ‘amplitude’ Stokes number βA = β(KC)² = 4π² f0A²/ν ≃ 3. The QP_L-type asymmetry for AR = 0.1 is qualitatively different in physical and mathematical structure from the QP_H-type asymmetry at higher aspect ratio. The flow at the two ends of the ellipse become essentially decoupled from each other for the QP_L -type asymmetry, the two frequencies in the horizontal force signature being close to the primary frequency, rather than twice the primary frequency as in the QP_H-type asymmetry. Furthermore, the associated coefficients arising from a Floquet stability analysis close to the critical threshold are profoundly different for low aspect ratio foils. Freedom to move slightly suppresses the transition to S-type asymmetry, and for certain parameters, if a purely oscillating foil subject to S-type asymmetry is released to move, flow symmetry is rapidly recovered due to the negative feedback of small horizontal foil motion. Conversely, for the ‘higher’ aspect ratios, the transition to QP_H-type asymmetry is encouraged when the foil is allowed to move, with strong positive feedback occurring between the shed vortices from successive oscillation cycles. For AR = 0.1, freedom to move significantly encourages the onset of asymmetry, but the newly observed ‘primary’ QP_L-type asymmetry found for pure oscillation no longer occurs when the foil flies, with S-type asymmetry leading ultimately to locomotion at a constant speed occurring all along the transition boundary for all values of KC and β.