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Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying **qubit** state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single **qubit** rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an **oscillator**), high speed operations (compared with conventional atom-laser interactions), and multi-**qubit** entanglement operations with speed that is not fundamentally limited by the trap **oscillation** **frequency**. We also present a method to provide higher stability in the radial mode ion **oscillation** **frequencies** of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent **oscillations** of an ion trapped in an **oscillating** rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher **frequency** motion. These ultrafast atomic **qubit** manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.

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Superconducting **qubits**

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This dissertation examines the design, fabrication, and characterization of a superconducting lumped-element tunable LC resonator that is used to vary the coupling between two superconducting **qubits**. Some level of **qubit**-**qubit** coupling is needed to perform gating operations. However, with fixed coupling, single **qubit** operations become considerably more difficult due to dispersive shifts in their energy levels transitions that depend on the state of the other **qubit**. Ideally, one wants a system in which the **qubit**-**qubit** coupling can be turned off to allow for single **qubit** operations, and then turned back on to allow for multi-**qubit** gate operations. I present results on a device that has two fixed-**frequency** transmon **qubits** capacitively coupled to a tunable thin-film LC resonator. The resonator can be tuned in situ over a range of 4.14 GHz to 4.94 GHz by applying an external magnetic flux to two single-Josephson junction loops, which are incorporated into the resonator’s inductance. The **qubits** have 0-to-1 transition **frequencies** of 5.10 GHz and 4.74 GHz. To isolate the system and provide a means for reading out the state of the **qubit** readout, the device was mounted in a 3D Al microwave cavity with a TE101 mode resonance **frequency** of about 6.1 GHz. The flux-dependent transition **frequencies** of the system were measured and fit to results from a coupled Hamiltonian model. With the LC resonator tuned to its minimum resonance **frequency**, I observed a **qubit**-**qubit** dispersive shift of 2χ_qq≈ 0.1 MHz, which was less than the linewidth of the **qubit** transitions. This dispersive shift was sufficiently small to consider the coupling “off”, allowing single **qubit** operations. The **qubit**-**qubit** dispersive shift varied with the applied flux up to a maximum dispersive shift of 2χ_qq≈ 6 MHz. As a proof-of-principle, I present preliminary results on performing a CNOT gate operation on the **qubits** when the coupling was “on” with 2χ_qq≈ 4 MHz. This dissertation also includes observations of the temperature dependence of the relaxation time T1 of three Al/AlOx/Al transmons. We found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK. We found that this anomalous behavior was consistent with loss due to non-equilibrium quasiparticles in a transmon where one electrode in the tunnel junction had a smaller volume and slightly smaller superconducting energy gap than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with a smaller gap, leading to an increased density of quasiparticles at the junction and a corresponding decrease in the relaxation time. I present a model of this effect, use the model to extract the density of non-equilibrium quasiparticles in the device, and find the values of the two superconducting energy gaps.

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Singlet-Triplet **Qubits**

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cutoff **frequency**... spin **qubit**

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- Other

superconducting **qubits**... transmon **qubits**

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Rabi **frequencies**... **qubit** gates

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Spin **Qubits**

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Superconducting **qubits**

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