### 24 results for qubit oscillator frequency

Contributors: Sigillito, Anthony James, Lyon, Stephen A, Electrical Engineering Department

Date: 2017-04-28

**frequency** and double quantum transitions (magnetic-dipole
forbidden...**qubit** onto and off of resonance with a magnetic driving field. In this...**Qubits**...**qubits**....**qubit** coherence times should substantially increase.
Finally,...**qubits**. Here, single **qubit** addressability
becomes an issue. Ideally...**qubits** is the electron spin bound
to phosphorus donors in silicon...**frequencies** or lower
temperatures the **qubit** coherence times should...**qubit** addressability.
First, we demonstrate that nuclear spin...**Qubits** in Silicon and Germanium ... Many proposals for quantum information devices rely on electronic or nuclear spins in
semiconductors because of their long coherence times and compatibility with industrial
fabrication processes. One of the most notable **qubits** is the electron spin bound
to phosphorus donors in silicon, which offers coherence times exceeding seconds at
low temperatures. These donors are naturally isolated from their environments to the
extent that silicon has been coined a "semiconductor vacuum". While this makes for
ultra-coherent **qubits**, it is difficult to couple two remote donors so quantum information
proposals rely on high density arrays of **qubits**. Here, single **qubit** addressability
becomes an issue. Ideally one would address individual **qubits** using electric fields
which can be easily confined. Typically these schemes rely on tuning a donor spin
**qubit** onto and off of resonance with a magnetic driving field. In this thesis, we measure
the electrical tunability of phosphorus donors in silicon and use the extracted
parameters to estimate the effects of electric-field noise on **qubit** coherence times. Our
measurements show that donor ionization may set in before electron spins can be sufficiently tuned. We therefore explore two alternative options for **qubit** addressability.
First, we demonstrate that nuclear spin **qubits** can be directly driven using electric
fields instead of magnetic fields and show that this approach offers several advantages
over magnetically driven spin resonance. In particular, spin transitions can occur at
half the spin resonance **frequency** and double quantum transitions (magnetic-dipole
forbidden) can occur.
In a second approach to realizing tunable **qubits** in semiconductors, we explore
the option of replacing silicon with germanium. We first measure the coherence and
relaxation times for shallow donor spin **qubits** in natural and isotopically enriched
germanium. We find that in isotopically enriched material, coherence times can exceed
1 ms and are limited by a single-phonon T1 process. At lower **frequencies** or lower
temperatures the **qubit** coherence times should substantially increase.
Finally, we measure the electric field tunability of donors in germanium and find
a four order-of-magnitude enhancement in the spin-orbit Stark shift and confirm that
the donors should be tunable by at least 4 times the electron spin ensemble linewidth
(in isotopically enriched material). Germanium should therefore also be more sensitive
to electrically driven nuclear magnetic resonance. Based on these results germanium
is a promising alternative to silicon for spin **qubits**.

Contributors: Srinivasan, Srikanth, Houck, Andrew, Electrical Engineering Department

Date: 2013-12-06

**Qubits**...**qubit** (TCQ), to the toolbox available for exploring such physics. The ...**qubit** energy and dipole coupling strength. High **frequency** flux control...**qubit** energy and dipole coupling strength. High frequency flux control...**qubit** coherence measurements and the calculation of a lower bound on the ... Superconducting circuits have shown promise for exploring quantum optics and computing. This thesis presents an additional element, the tunable coupling **qubit** (TCQ), to the toolbox available for exploring such physics. The TCQ is shown to have independently tunable **qubit** energy and dipole coupling strength. High **frequency** flux control lines allow the varying of the TCQ's properties on very fast time scales. This enables **qubit** coherence measurements and the calculation of a lower bound on the maximum range of coupling strength tunability. Finally, an experiment demonstrating the TCQ's applicability in quantum state transfer is discussed.

Contributors: Fan, Jaimie, Buschman, Timothy J.

Date: 2017-07-26

**frequency** **oscillations** occur in the brains of those with epilepsy does...**frequency** **oscillation** remains an open question. However, in the process...**frequency** **oscillation** between epileptic and non-epileptic brains can be...**frequency** **oscillations** occur in both the brains of those with epilepsy...**frequency** **oscillation** on various weight combinations within the phase ... The current variety of treatment options for epilepsy leaves 30% of those who suffer from this chronic neurological disease without a cure. Therefore, this senior thesis project aims to uncover new insights about the brain structure that underlies susceptibility to epilepsy in hopes that a greater understanding of this underlying structure will catalyze the discovery of novel therapeutic methods which target these underlying differences in brain structure. To drive the discovery of new insights about underlying structure, this project addresses the following tension found in the literature: high **frequency** **oscillations** occur in both the brains of those with epilepsy and in the brains of those without epilepsy. Only when high **frequency** **oscillations** occur in the brains of those with epilepsy does the brain enter a state of unstable dynamics and seizure activity. This suggests that there is a difference in underlying structure between epileptic and non-epileptic brains, and this study uses computational modeling of neuronal firing to characterize these differences.
First, based on a firing rate model, we find that within the phase space of the weight values, there is a band of stability from which one might predict the stability of a set of weights. Then, in the next two versions of the model, we add Hebbian plasticity and homeostatic plasticity. Only through the addition of Hebbian plasticity and homeostatic plasticity does high **frequency** **oscillation**, the manipulation described in our driving question, have a lasting effect on the weights. With the addition of a rate based Hebbian plasticity model to the base firing rate model, we find that weights can be perturbed from this band of stability through Hebbian plasticity. Adding a weight based homeostatic plasticity model to the base firing rate and Hebbian plasticity model then gives insight into the fact that having a target weight within a certain location with respect to the band of stability can rescue stability of a set of original weights from the destabilizing effects of Hebbian plasticity. Finally, we explore the effect of high **frequency** **oscillation** on various weight combinations within the phase space, and we find that certain weight combinations are projected to an unstable state through high **frequency** **oscillation** while other weight combinations remain at a stable state even in the face of high **frequency** **oscillation**. The unifying characteristic of those weights which remain stable in the face of high **frequency** **oscillation** remains an open question. However, in the process of investigating high **frequency** **oscillations**, it was found that weights on the edge of the band of stability are more robust to instability through Hebbian plasticity than weights on the band of stability that are further from the edge.
These results suggest that the differential response to high **frequency** **oscillation** between epileptic and non-epileptic brains can be attributed at least in part to the location of weights with respect to the band of stability.

Contributors: Szócs, László J., Houck, Andrew

Date: 2013-07-30

Photon-**Qubit** Coupling...**qubits**. Both
**qubit** devices failed to exhibit signs of light-matter coupling...cavity-**qubit** dynamics in the multimodal regime
for various light-matter...**frequency**
¿0/(2¿) = 92 MHz, two of which contained superconducting transmon ... This thesis presents the results of experimental work aimed at realizing the multimodal Rabi Hamiltonian of quantum optics in a circuit QED device. We have
fabricated and tested three coplanar waveguide resonators of fundamental **frequency**
¿0/(2¿) = 92 MHz, two of which contained superconducting transmon **qubits**. Both
**qubit** devices failed to exhibit signs of light-matter coupling, as deduced through
two different measurement techniques. The experimental progress was supplemented
with numerical simulations of the multimodal Jaynes-Cummings and Rabi Hamiltonians, which attempted to study cavity-**qubit** dynamics in the multimodal regime
for various light-matter coupling strengths. For a 2-mode Rabi model, we report
the observation of a novel localization-delocalization transition in photon occupation
between the two modes, which displays signatures that should be readily measured
in experiment. Future work should continue attempts to realize strong, multimodal
light-matter coupling in circuit QED so as to verify the existence of this transition.

Contributors: Martin, Christan David, Hasson, Uri, Ghazanfar, Asif

Date: 2014-07-07

**Oscillations** are present both in natural speech and in the brain. This...theta-**frequency** band **oscillations** for speech
comprehension as well as ...theta-**frequency** band has been shown to
remarkably improve intelligibility...theta-**frequency**
range can restore intelligibility to a degraded, previously...theta-**frequency** **oscillations** in auditory
regions, specifically the superior ... **Oscillations** are present both in natural speech and in the brain. This may be more than a
mere coincidence. Re-instating information in the theta-**frequency** band has been shown to
remarkably improve intelligibility. Moreover, a recent theory has proposed the existence of
an internal tracking mechanism that parses and decodes incoming speech at a theta rhythm.
This study sought to clarify the importance of theta-**frequency** band **oscillations** for speech
comprehension as well as to establish their significance as a speech processing mechanism in
the human auditory cortex. Here, it is shown that exposure to information in the theta-**frequency**
range can restore intelligibility to a degraded, previously unintelligible stimulus,
producing an auditory pop-out effect. This effect was observed regardless of whether
participants were exposed to the intact sentence in the auditory or the visual domain.
Compressing or extending the presentation speed of the intact sentence reduced the size of
the effect, except for an extension rate of 1.5 times the original speed. At a neural level, it was
previously unknown whether theta **oscillations** in auditory regions are internally generated or
merely reflect stimulus driven evoked responses. Electrocorticographical recordings from one
clinical patient provide evidence for the existence of theta-**frequency** **oscillations** in auditory
regions, specifically the superior temporal gyrus, which are internally generated and
effectively track incoming speech.

Contributors: Siow, Matthew, Couzin, Iain

Date: 2013-07-26

**oscillation** **frequency**
compared to the other two zones of the same junction...**oscillations** that
allow it to gain maximum stability. In this paper, we...**oscillations** at trail junctions to determine how army ants optimize their...**oscillation** **frequencies** and periods of army ant
traffic are uniform and...**oscillation** **frequency**
increases as traffic becomes more unidirectional ... Army ants (Eciton burchellii) have been studied for nearly a century, but
observable patterns in their traffic organization have not yet been explored,
despite the fact that this organization contributes greatly to their optimal foraging.
Using pheromones and tactile cues to transmit information from ant to ant, they
coordinate their movements in order to optimize traffic and create a collective
behavior that increases the overall efficiency of the colony. Garnier et al. (2013)
discovered that E. burchellii traffic possesses regular, periodic **oscillations** that
allow it to gain maximum stability. In this paper, we explored these traffic
**oscillations** at trail junctions to determine how army ants optimize their network of
foraging trails. After conducting research at La Selva Biological Station in Costa
Rica, we found that the mean **oscillation** **frequencies** and periods of army ant
traffic are uniform and unrelated to traffic direction. Despite this overarching
uniformity, each zone of a trail junction possesses a different **oscillation** **frequency**
compared to the other two zones of the same junction. Lastly, **oscillation** **frequency**
increases as traffic becomes more unidirectional. By displaying differential
oscillatory behavior at trail junctions, army ants spontaneously adapt to their
constantly changing environment in order to optimize traffic dynamics. Finally, we
propose ideas for future research that have the potential to delve deeper into the
study of trail junctions.

Contributors: Johnsen, Peter, Houck, Andrew A., Bernevig, Bogdan A.

Date: 2015-07-27

**qubit** energy, demonstrating that we are in the strong coupling **qubit**-field...**qubit** based
on the Josephson junction. We observe photon number splitting...**qubit**, we will be able
to realize strong photon-photon interactions for...**qubit** excitation. This system can exhibit
behavior known as photon blockade...**frequency** shift ¿, we are unable to observe photon blockade
or measure...**qubit** to a region of the
transmission line with a higher electric field ... Superconducting circuits are an ideal platform for simulating many
body physics with photons. Such simulations are greatly enhanced by
the ability to engineer photon-photon interactions. Single photon-photon
interactions are difficult to design because of the massive nonlinearities
required to achieve a strong interaction between individual photons. Nonlinearities
arising from single photons are present in the dispersive limit of
Jaynes-Cummings Hamiltonian. In this limit, the interaction of two photons
is mediated by a virtual **qubit** excitation. This system can exhibit
behavior known as photon blockade, where the presence of a single photon
in an optical cavity prevents other photons from entering the cavity. The
light exiting the cavity is then antibunched, which serves both as evidence
of the quantization of the electromagnetic field and as a signature of photon
blockade. Experimentally, we explore the strong **qubit**-field coupling
regime of the Jaynes-Cummings Hamiltonian with circuit quantum electrodynamics.
Using conventional microfabrication techniques, we build a
superconducting microwave resonator coupled to a transmon **qubit** based
on the Josephson junction. We observe photon number splitting of the
**qubit** energy, demonstrating that we are in the strong coupling **qubit**-field
coupling regime, allowing us to perform quantum non-demolition measurements
of the cavity photon number, and providing conclusive evidence of
the quantization of the electromagnetic field into photons. Further, we observe
nonlinear effects arising from a small photon number consistent with
the nonlinear Kerr Hamiltonian approximation of the Jaynes-Cummings
Hamiltonian. Because the cavity dissipation ¿ is larger than the single
photon cavity **frequency** shift ¿, we are unable to observe photon blockade
or measure photon antibunching. By moving the **qubit** to a region of the
transmission line with a higher electric field and using a tunable SQUID
(superconducting quantum interference device) as a **qubit**, we will be able
to realize strong photon-photon interactions for use in quantum simulators.

Contributors: Dewey, Peter, Smits, Alexander J, Mechanical and Aerospace Engineering Department

Date: 2013-05-21

**frequency** and wake resonant **frequencies** are finite, this also suggests...**frequencies**. It is found that when the driving **oscillation** **frequency** ...**frequency** of the flexible structure is coincident with the wake resonant...**frequency** there is a local peak in propulsive efficiency. The global ...**oscillation** **frequency** and chordwise traveling wave wavelength that develops ... Experiments are conducted to better understand the effects of flexibility in generating unsteady bio-inspired propulsion. It is found that by exploiting the effects of flexibility, the thrust production and propulsive efficiency can be up to twice that of a rigid propulsor. The wakes are highly dependent on the input parameters to the system such as the **oscillation** **frequency** and chordwise traveling wave wavelength that develops along a flexible surface. In general, the wakes of flexible propulsors tend to concentrate their momentum in the direction of motion whereas the wakes of rigid propulsors have relatively larger momentum in the transverse direction leading to a decrease in propulsive efficiency. A linear stability analysis is conducted on the wakes to determine the wake resonant **frequencies**. It is found that when the driving **oscillation** **frequency** of the apparatus matches the wake resonant **frequency** there is a local peak in propulsive efficiency. The global peak in efficiency occurs only when the structural resonant **frequency** of the flexible structure is coincident with the wake resonant **frequency**, which only occurs under very specific conditions. This implies that there is an optimum flexibility to maximize propulsive efficiency; being either too stiff or too flexible is detrimental to propulsive performance. Since both the structural resonant **frequency** and wake resonant **frequencies** are finite, this also suggests that animals must utilize flexible propulsive surfaces if they are to optimize their efficiencies. Finally, a non-dimensional scaling argument is made that is shown to collapse the thrust production, power input to the fluid, and propulsive efficiency for a range of propulsors with various flexibilities and aspect ratio.

Contributors: Wollack, Edward, Petta, Jason, Staggs, Suzanne

Date: 2016-07-12

**qubits** in real time before the typical **qubit**
lifetime has passed. Both...**frequency**-domain multiplexing
device, which would allow for the integration ... The advent of circuit Quantum Electrodynamics (cQED) has allowed for the creation and
manipulation of atom-like systems with quantum behavior using standard nanofabrication
techniques. This work explores the implementation of side-coupled superconducting niobium
resonators on sapphire and silicon, with future applications towards the integration
of quantum dots. The overall goal of the project was to create a **frequency**-domain multiplexing
device, which would allow for the integration of multiple quantum dots on a single
device. Simulation and measurement results are presented for the multiplexing device, including
discussions on quality factor. Here, we also propose a design for an instrument to
simultaneously measure an arbitrary number of **qubits** in real time before the typical **qubit**
lifetime has passed. Both the analog and digital implementation are discussed in detail, and
preliminary results are presented.

Contributors: Malek Akhlagh, Mohammad Moein, Tureci, Hakan E., Electrical Engineering Department

Date: 2017-12-12

**qubit** properties that is free of an artificially introduced high frequency...**qubit** properties that is free of an artificially introduced high **frequency**...**qubit** dynamics, valid for any **qubit**-resonator coupling strength. Any discrete-level...**qubits** like transmon. We apply this method to the problem of spontaneous...**qubit** coupled to an open multimode resonator, without resorting to the ... We present a Heisenberg-Langevin formalism to study the effective dynamics of a superconducting **qubit** coupled to an open multimode resonator, without resorting to the rotating wave, two level, Born or Markov approximations. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the openness of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of weakly nonlinear **qubits** like transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the **qubit** dynamics, valid for any **qubit**-resonator coupling strength. Any discrete-level quantum system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When inside a cavity, these quantities can be strongly modified with respect to vacuum. Generally, this modification can be captured by including only the closest resonant cavity mode. In circuit QED architecture, with substantial coupling strengths, it is however found that such rates are strongly influenced by far off-resonant modes. A multimode calculation over the infinite set of cavity modes leads to divergences unless an artificial cutoff is imposed. Previous studies have not pointed out what the source of this divergence is. Quite interestingly, the renormalization of spectrum is mutual, i.e. the electromagnetic modal structure of the cavity is also modified due to scattering by the atom. In cavity QED, this phenomenon is manifested as a diamagnetic term, known as the $A^2$ contribution. We show that unless the effect of $A^2$ is accounted for up to all orders exactly, any multimode calculations of circuit QED quantities is bound to diverge. Subsequently, we present the calculation of finite radiative corrections to **qubit** properties that is free of an artificially introduced high **frequency** cut-off.