1,974 research outputs found
Quartic Forms in Many Variables
We show that a quartic -adic form with at least variables possesses
a non-trivial zero. We also prove new results on systems of cubic, quadratic
and linear forms. As an example, we show that for a system comprising two cubic
forms variables are sufficient.Comment: 8 page
-adic Zeros of Quintic Forms
It is shown that a quintic form over a p-adic field with at least 26
variables has a non-trivial zero, providing that the cardinality of the residue
class field exceeds 9.Comment: Minor correction
Feedback control of persistent-current oscillation based on the atomic-clock technique
We propose a scheme of stabilizing the persistent-current Rabi oscillation
based on the flux qubit-resonator-atom hybrid structure. The LC resonator
weakly interacts with the flux qubit and maps the persistent-current Rabi
oscillation onto the intraresonator electric field. This field is further
coupled to a Rydberg-Rydberg transition of the Rb atom. The
Rabi-frequency fluctuation of the flux qubit is deduced from measuring the
atomic population and stabilized via feedback controlling the external flux
bias. Our numerical simulation indicates that the feedback-control method can
efficiently suppress the background fluctuations in the flux qubit, especially
in the low-frequency limit. This technique may be extensively applicable to
different types of superconducting circuits, paving a new way to
long-term-coherence superconducting quantum information processing.Comment: 4 figure
Theoretical Description of Micromaser in the Ultrastrong-Coupling Regime
We theoretically investigate an ultrastrongly-coupled micromaser based on
Rydberg atoms interacting with a superconducting LC resonator, where the common
rotating-wave approximation and slowly-varying-envelope approximation are no
longer applicable. The effect of counter-rotating terms on the masing dynamics
is studied in detail. We find that the intraresonator electric energy declines
and the microwave oscillation frequency shifts significantly in the regime of
ultrastrong coupling. Additionally, the micromaser phase fluctuation is
suppressed, resulting in a reduced spectral linewidth.Comment: 10 pages, 3 figure
Charge-Qubit-Resonator-Interface-Based Nonlinear Circuit QED
We explore applications of nonlinear circuit QED with a charge qubit
inductively coupled to a microwave LC resonator in the photonic engineering and
ultrastrong-coupling multiphoton quantum optics. Simply sweeping the
gate-voltage bias achieves arbitrary Fock-state pulsed maser, where the single
qubit plays the role of artificial gain medium. Resonantly pumping the
parametric qubit-resonator interface leads to the squeezing of resonator field,
which is utilizable to the quantum-limited microwave amplification. Moreover,
upwards and downwards multiphoton quantum jumps may be observed in the steady
state of the driving-free system.Comment: 3 figure
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