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Optics Communications

Phase control of subharmonic resonances

Z. Ficek, JOSIP SEKE, Andrey Vladimirovich Soldatov, Gerhard Adam

Published Aug 1, 2000• 7 citations
Publisher
DOI
10.1016/s0030-4018(00)00798-7

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In this paper we present a theory of optical subharmonic generation in a nonlinear Fabry-Perot resonator. Our approach, based on classical electrodynamics, leads to a Mathieu-Hill-type equation. This enables us to describe the generation of optical subharmonic oscillation in terms of a general formalism used to account for parametric phenomena, and to outline the possibility of using a nonlinear Fabry-Perot resonator as a memory device able to store the phase of a signal. The oscillation threshold condition is discussed and the rate of amplitude rise at start-up is evaluated.

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Driving qubits with resonant microwave fields has proven to be an effective technique for controlling qubits and is, therefore, the current industry standard. Although the technique can produce impressive fidelities for quantum gate operations, it is not without faults. Noise at the resonant frequency that is present in the qubit’s environment effectively destroys the delicate quantum information contained in the qubit. In principle this noise can be filtered out but it also renders resonant driving useless. This issue can be circumvented with a recently developed alternative method in which the qubit is driven at around an integer fraction of its resonant frequency, namely the 1/3-subharmonic. Effectively, this enables the filtering of noise around the resonant frequency while still allowing the driving field to propagate to the qubit unimpeded. The validity of this technique has been demonstrated experimentally. In this thesis we explore this novel method for qubit control in a computational setting. We perform general simulations on qubits under subharmonic driving in order to investigate the behavior of the system and to compare the dynamics to corresponding analytical predictions. We find that the analytically derived properties, which are based on several approximations, align well with results obtained from simulations of the full unapproximated Hamiltonian. However, our main objective is to examine the fidelity of subharmonic gate operations and to compare it to its resonant counterpart. To that end, we introduced amplitude-phase fluctuations to the classically treated drive field so as to imitate the inherent uncertainties in coherent sates of light. We found that for fields of this nature, subharmonic driving provided no improvement in the scaling of fidelity. Moreover, we investigated the effects of vacuum noise in the transmission line through which the drive field propagates. Under these conditions, the arguably simple simulations reveal that subharmonic driving improves the fidelity of gate operations even at reasonably small field amplitudes. For extreme coupling strengths, noise at the 1/3-subharmonic takes effect and the state of the qubit decoheres.
We report on the observation of subharmonic resonances in high-order wave mixing associated with the quantized vibrational levels of atoms trapped in a one-dimensional optical lattice created by two intense nearly counterpropagating coupling beams. These subharmonic resonances, occurring at $\ifmmode\pm\else\textpm\fi{}1/2$ and $\ifmmode\pm\else\textpm\fi{}1/3$ of the frequency separation between adjacent vibrational levels, are observed through phase-match angularly resolved six- and eight-wave mixing processes. We investigate how these resonances evolve with the intensity of the incident probe beam, which couples with one of the coupling beams to create anharmonic coherence gratings between adjacent vibrational levels. Our experimental results also show evidence of high-order processes associated with coherence involving nonadjacent vibrational levels. Moreover, we also demonstrate that these induced high-order coherences can be stored in the medium and the associated optical information retrieved after a controlled storage time.
In this paper we present a theory of optical subharmonic generation in a nonlinear Fabry-Perot resonator. Our approach, based on classical electrodynamics, leads to a Mathieu-Hill-type equation. This enables us to describe the generation of optical subharmonic oscillation in terms of a general formalism used to account for parametric phenomena, and to outline the possibility of using a nonlinear Fabry-Perot resonator as a memory device able to store the phase of a signal. The oscillation threshold condition is discussed and the rate of amplitude rise at start-up is evaluated.