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Applied Optics

Effects of laser phase noise on the injection of a high-finesse cavity

Jérôme Morville, D. Romanini, Marc Chenevier, Alexander A. Kachanov

Published Nov 20, 2002• 92 citations
Publisher

Abstract

We study the response of a high-finesse optical cavity to a cw laser during the laser frequency passage through resonance. For a laser that is spectraly larger than the cavity resonance, laser-field phase fluctuations are converted into amplitude fluctuations, and cavity injection is intrinsically noisy. We develop a model based on Schawlow-Townes spontaneous-emission laser broadening and discuss in detail its effects on high-sensitivity spectroscopic techniques such as cavity-enhanced absorption or cavity ring-down spectroscopy. We present realistic simulations of cavity injection during a sweep through resonance and calculation of statistical quantities such as the average injection efficiency. Agreement with experimental observations is established.

DOI
10.1364/ao.41.006980

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We study the response of a high-finesse optical cavity to a cw laser during the laser frequency passage through resonance. For a laser that is spectraly larger than the cavity resonance, laser-field phase fluctuations are converted into amplitude fluctuations, and cavity injection is intrinsically noisy. We develop a model based on Schawlow-Townes spontaneous-emission laser broadening and discuss in detail its effects on high-sensitivity spectroscopic techniques such as cavity-enhanced absorption or cavity ring-down spectroscopy. We present realistic simulations of cavity injection during a sweep through resonance and calculation of statistical quantities such as the average injection efficiency. Agreement with experimental observations is established.
We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.
Lasers with high spectral purity are indispensable for optical clocks and for the coherent manipulation of atomic and molecular qubits in applications such as quantum computing and quantum simulation. While the stabilization of such lasers to a reference can provide a narrow linewidth, the widely used diode lasers exhibit fast phase noise that prevents high-fidelity qubit manipulation. In this paper, we demonstrate a self-injection locked diode laser system that utilizes a high-finesse cavity. This cavity not only provides a stable resonance frequency, it also acts as a low-pass filter for phase noise beyond the cavity linewidth of around 100 kHz, resulting in low phase noise from dc to the injection lock limit. We model the expected laser performance and benchmark it using a single trapped 40 Ca + -ion as a spectrum analyzer. We show that the fast phase noise of the laser at relevant Fourier frequencies of 100 kHz to >2 MHz is suppressed to a noise floor of between −110 dBc/Hz and −120 dBc/Hz, an improvement of 20 to 30 dB over state-of-the-art Pound-Drever-Hall-stabilized extended-cavity diode lasers. This strong suppression avoids incoherent (spurious) spin flips during manipulation of optical qubits and improves laser-driven gates when using diode lasers in applications involving quantum logic spectroscopy, quantum simulation, and quantum computation.
Lasers with high spectral purity are indispensable for optical clocks and coherent manipulation of atomic and molecular qubits for applications such as quantum computing and quantum simulation. Stabilisation of the laser to a reference can provide a narrow linewidth and high spectral purity. However, widely-used diode lasers exhibit fast phase noise that prevents high fidelity qubit manipulation. Here we demonstrate a self-injection locked diode laser system utilizing a medium finesse cavity. The cavity not only provides a stable resonance frequency, but at the same time acts as a low-pass filter for phase noise beyond the cavity linewidth of around 100 kHz, resulting in low phase noise from dc to the injection lock limit. We model the expected laser performance and benchmark it using a single trapped 40^{40}40Ca+^{+}+-ion as a spectrum analyser. We show that the fast phase noise of the laser at relevant Fourier frequencies of 100 kHz to >2 MHz is suppressed to a noise floor of between -110 dBc/Hz and -120 dBc/Hz, an improvement of 20 to 30 dB over state-of-the-art Pound-Drever-Hall-stabilized extended-cavity diode lasers. This strong suppression avoids incoherent (spurious) spin flips during manipulation of optical qubits and improves laser-driven gates in using diode lasers with applications in quantum logic spectroscopy, quantum simulation and quantum computation.
By analyzing the decaying intensity, leaking out a high-finesse cavity previously ``filled'' by a cw laser source (using the cavity ring-down spectroscopy technique), we observed frequency beating between what we think are two orthogonal eigenpolarization states of the intracavity electromagnetic field. The time decay (ring down) is analyzed by varying the angle of the polarization analyzer located in front of the detector. A full modeling of the observed signal is proposed. It is based on the Jones matrix formalism required for modeling the cavity behavior following a rotated phase shifter. The full transfer function is first established in the frequency domain, and then Fourier transformed to recover the temporal response. The same optical cavity, i.e., constituted of the same set of mirrors, is used at two different wavelengths ($\ensuremath{\sim}800$ and $\ensuremath{\sim}880$ nm). It demonstrates the differences in behavior between a high-finesse cavity $(\ensuremath{\sim}400\phantom{\rule{0.16em}{0ex}}000)$ and a lower finesse cavity $(\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}000)$. Beating frequency, characteristics time, and beat amplitude are mainly discussed versus the analyzer angle. A cavity birefringence of $\ensuremath{\sim}1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ rad, resulting from the mirror birefringence is suggested. If the current analysis is in agreement with pulsed CRDS experiments (polarimetry) obtained in an isotropic moderate-finesse cavity, it differs from a recent work report on a high-finesse cavity associated with a source mode locking [Phys. Rev. A 85, 013837 (2012)].
We derive and analyze the master equation for absorptive and dispersive optical bistability in the high-Q cavity limit where the driving laser has both amplitude and phase fluctuations which are larger than the small amplitude and phase fluctuations caused by incoherent spontaneous emission in the cavity. We treat the amplitude and phase fluctuations of the driving laser as independent time dependent Gaussian processes. The causes of jitter and amplitude fluctuations will vary from laser to laser and the fluctuations need not be Gaussian. However, we use Gaussian processes for mathematical tractability and because we expect them to be qualitatively correct. Recently,1 we have shown in the case of absorptive optical bistability when the driving laser has phase fluctuations the fundamental process which determines the statistical properties of the internal field is the competition between locking of the internal field phase to the phase of the driving laser and the diffusion of the phase of the internal field as a consequence of the driving laser fluctuations. The driving laser fluctuations have little effect if the phase locking rate is larger than the phase diffusion rate caused by the driving laser’s fluctuations. However, when the diffusion rate becomes comparable to the locking rate we find the amplitude of the 2 internal field is reduced and the dimensionless parameter2 measuring the importance of transitions from one branch of the OB curve to the other due to fluctuations takes on a value which leads to an appreciable transition rate due to fluctuations.
We study the steady-state operation and noise properties of a laser (or maser) exhibiting phase locking when an ordinary vacuum is replaced by a squeezed vacuum. Such a phase-sensitive laser can be realized by preparing the active medium initially in a coherent superposition of levels involved in the laser transition. We develop a general formalism to treat number-phase fluctuations and quadrature fluctuations. When applied to a one-photon laser with injected atomic coherence, we find that not only is a complete quenching of the (spontaneous-emission) quantum noise possible, but the field can actually be in a squeezed state. The variance in either amplitude or phase quadrature can be below the vacuum noise level by a factor of 2 (50%) at the expense of enhanced fluctuations in the other quadrature.