A graph-theoretical representation of multiphoton resonance processes in superconducting quantum circuits

We propose a graph-theoretical formalism to study generic circuit quantum electrodynamics systems consisting of a two level qubit coupled with a single-mode resonator in arbitrary coupling strength regimes beyond rotating-wave approximation. We define colored-weighted graphs, and introduce different products between them to investigate the dynamics of superconducting qubits in transverse, longitudinal, and bidirectional coupling schemes. The intuitive and predictive picture provided by this method, and the simplicity of the mathematical construction, are demonstrated with some numerical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting qubit systems driven by intense ac fields

Absorption spectra of superconducting qubits driven by bichromatic microwave fields

We report experimental observation of two distinct quantum interference patterns in the absorption spectra when a transmon superconducting qubit is subjected to a bichromatic microwave field with the same Rabi frequencies. Within the two-mode Floquet formalism with no dissipation processes, we propose a graph-theoretical representation to model the interaction Hamiltonian for each of these observations. This theoretical framework provides a clear visual representation of various underlying physical processes in a systematic way beyond rotating-wave approximation. The presented approach is valuable to gain insights into the behavior of multichromatic field driven quantum two-level systems, such as two-level atoms and superconducting qubits. Each of the observed interference patterns is represented by appropriate graph products on the proposed color-weighted graphs. The underlying mechanisms and the characteristic features of the observed fine structures are identified by the transitions between the graph vertices, which represent the doubly dressed states of the system. The good agreement between the numerical simulation and experimental data confirms the validity of the theoretical method. Such multiphoton interference may be used in manipulating the quantum states and/or generate nonclassical microwave photons

Mid-circuit measurements on a single species neutral alkali atom quantum processor

We demonstrate mid-circuit measurements in a neutral atom array by shelving data qubits in protected hyperfine-Zeeman sub-states while non-destructively measuring an ancilla qubit. Measurement fidelity was enhanced using microwave repumping of the ancilla during the measurement. The coherence of the shelved data qubits was extended during the ancilla readout with dynamical decoupling pulses, after which the data qubits are returned to mf = 0 computational basis states. We demonstrate that the quantum state of the data qubits is well preserved up to a constant phase shift with a state preparation and measurement (SPAM) corrected process fidelity of F = 97.0(5)%. The measurement fidelity on the ancilla qubit after correction for state preparation errors is F = 94.9(8)% and F = 95.3(1.1)% for |0> and |1> qubit states, respectively. We discuss extending this technique to repetitive quantum error correction using quadrupole recooling and microwave-based quantum state resetting.Comment: v3: additional appendices with fidelity analysis adde

Progress towards a primary pressure standard with cold atoms

This thesis describes a method of using an ultra-cold ensemble of atoms confined in a trap as an atomic primary pressure standard. The development of the standard and its current status are described in detail. This standard uses a 3D MOT to trap ⁸⁷Rb and then transfer them to a quadrupole magnetic trap where the atoms undergoes collisions with a background gas. By measuring the number of atoms left in the magnetic trap as a function of time one extract a loss rate and from this rate determine the background gas density. This loss rate is a product of the density of the background, multiplied by the loss cross section averaged over the velocity distribution of the background gas. By computing the average loss cross section in the magnetic trap and measuring the loss rate, the density of the background gas can be determined. This gives a calibration free measurement of density of a background gas in the UHV range (10-⁶ ‑ 10-⁹) Torr or (10-⁴ - 10-⁷) Pa which allows for it to be used as a standard. In conjunction with this, preparation of the atoms prior to the loss rate measurement is investigated to ensure accuracy and reproducibility of the standard. Finally a comparison between UBC's atomic standard and NIST's (National Institute for Standards and Technology) orifice flow standard is conducted via an ionization gauge which employed as a transfer standard.All measurement are carried out using Argon gas as the background gas of study.Science, Faculty ofPhysics and Astronomy, Department ofGraduat

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Abstract In this work we introduce a histor