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arXiv:1507.05757 · Physical Review A

Nonlinear spectroscopy of Sr atoms in an optical cavity for laser stabilization

Bjarke T. R. Christensen, Martin R. Henriksen, Stefan Alaric Schäffer, Philip G. Westergaard, David Tieri, Jun Ye, Murray Holland, Jan W. Thomsen

Published Nov 6, 2015• 34 citations
arXivHTMLPDF

Abstract

We study the nonlinear interaction of a cold sample of $^{88}\mathrm{Sr}$ atoms coupled to a single mode of a low finesse optical cavity in the so-called bad cavity limit, and we investigate the implications for applications to laser stabilization. The atoms are probed on the weak intercombination line $|5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\ensuremath{-}\phantom{\rule{0.16em}{0ex}}|5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}\ensuremath{\rangle}$ at 689 nm in a strongly saturated regime. Our measured observables include the atomic induced phase shift and absorption of the light field transmitted through the cavity represented by the complex cavity transmission coefficient. We demonstrate high signal-to-noise-ratio measurements of both quadratures---the cavity transmitted phase and absorption---by employing frequency modulation (FM) spectroscopy (noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy). We also show that when FM spectroscopy is employed in connection with a cavity locked to the probe light, observables are substantially modified compared to the free-space situation in which no cavity is present. Furthermore, the nonlinear dynamics of the phase dispersion slope is experimentally investigated, and the optimal conditions for laser stabilization are established. Our experimental results are compared to state-of-the-art cavity QED theoretical calculations.

DOI
10.1103/physreva.92.053820

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The development of simple and reliable high stability clock lasers is of great importance for future state-of-the-art optical clocks [1]-[5] and for future transportable optical clocks [6], [7]. Further development of clock lasers with better stability has so far been hindered by thermal noise in the reference cavity used for laser stabilization and conventional approaches for improvements may be technically challenging. It has been proposed [8]-[11] to improve the stability and reduce the complexity of state-of-the-art laser frequency stabilization by exploiting cavity QED systems consisting of atoms with a narrow optical transition coupled to a single mode of an optical cavity. The laser stabilization performance of a cavity QED system is affected by a number of system parameters such as the finite temperature of the atoms, the number of involved atoms and the laser power [12]-[14]. However, the dynamics of those elements have not yet been fully explored. Here we present a simple cavity QED system consisting of laser cooled strontium-88 atoms coupled to an optical cavity. We relate measurable quantities to the complex transmission coefficient which relates the input field to the output field. The optimal input power for stabilizing a laser to this system is experimentally determined and the optimal shot-noise-limited linewidth of the system is evaluated to 500 mHz. Furthermore, theoretical shot-noise-limited linewidths of similar cavity QED systems are evaluated for a number of different two electron systems.

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We study the nonlinear interaction of a cold sample of 88Sr^{88}\mathrm{Sr}88Sr atoms coupled to a single mode of a low finesse optical cavity in the so-called bad cavity limit, and we investigate the implications for applications to laser stabilization. The atoms are probed on the weak intercombination line ∣5s21S0\ensuremath⟩\ensuremath−∣5s5p3P1\ensuremath⟩|5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\ensuremath{-}\phantom{\rule{0.16em}{0ex}}|5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}\ensuremath{\rangle}∣5s21S0​\ensuremath⟩\ensuremath−∣5s5p3P1​\ensuremath⟩ at 689 nm in a strongly saturated regime. Our measured observables include the atomic induced phase shift and absorption of the light field transmitted through the cavity represented by the complex cavity transmission coefficient. We demonstrate high signal-to-noise-ratio measurements of both quadratures---the cavity transmitted phase and absorption---by employing frequency modulation (FM) spectroscopy (noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy). We also show that when FM spectroscopy is employed in connection with a cavity locked to the probe light, observables are substantially modified compared to the free-space situation in which no cavity is present. Furthermore, the nonlinear dynamics of the phase dispersion slope is experimentally investigated, and the optimal conditions for laser stabilization are established. Our experimental results are compared to state-of-the-art cavity QED theoretical calculations.
The development of simple and reliable high stability clock lasers is of great importance for future state-of-the-art optical clocks [1]-[5] and for future transportable optical clocks [6], [7]. Further development of clock lasers with better stability has so far been hindered by thermal noise in the reference cavity used for laser stabilization and conventional approaches for improvements may be technically challenging. It has been proposed [8]-[11] to improve the stability and reduce the complexity of state-of-the-art laser frequency stabilization by exploiting cavity QED systems consisting of atoms with a narrow optical transition coupled to a single mode of an optical cavity. The laser stabilization performance of a cavity QED system is affected by a number of system parameters such as the finite temperature of the atoms, the number of involved atoms and the laser power [12]-[14]. However, the dynamics of those elements have not yet been fully explored. Here we present a simple cavity QED system consisting of laser cooled strontium-88 atoms coupled to an optical cavity. We relate measurable quantities to the complex transmission coefficient which relates the input field to the output field. The optimal input power for stabilizing a laser to this system is experimentally determined and the optimal shot-noise-limited linewidth of the system is evaluated to 500 mHz. Furthermore, theoretical shot-noise-limited linewidths of similar cavity QED systems are evaluated for a number of different two electron systems.
Summary form only given. We observe the quantized motion of single atoms strongly coupled to a high-finesse optical cavity and investigate dynamics of cavity-assisted atom cooling. Single caesium atoms are trapped in a blue-detuned standing-wave intracavity dipole trap, formed by a lock laser which is used to stabilize the cavity resonance frequency. A probe laser is coupled into the cavity mode and its transmission spectrum is monitored by means of photon-counting heterodyne spectroscopy [2].Measured heterodyne spectra of single atoms in the cavity are shown in Fig. 1 for two different lock-laser intensities and compared with theoretical models. The motional Raman sidebands are offset from the carrier beat signal at 1 MHz by the atomic vibrational frequency (±ν). They show asymmetric lineshapes due to the anharmonicity of the dipole potential.We investigate the dependence of the positions and lineshapes of the motional Raman sidebands on experimantal parameters such as the cavity-atom detuning, and lock-laser intensity. Information on the atomic temperature, cooling and heating rates, as well as the atomic position in the cavity with respect to an antinode of the cavity probe field are found by comparing the observed spectra with theoretical predictions [1]. In addition, this technique can also be used to analyze the cooling dynamics of a cavity-assisted EIT cooling scheme which has been recently studied and demonstrated in [3,4].
In this Letter we realize a narrow spectroscopic feature using a technique that we refer to as magnetically induced optical transparency. A cold ensemble of ^{88}Sr atoms interacts with a single mode of a high-finesse optical cavity via the 7.5 kHz linewidth, spin forbidden ^{1}S_{0} to ^{3}P_{1} transition. By applying a magnetic field that shifts two excited state Zeeman levels, we open a transmission window through the cavity where the collective vacuum Rabi splitting due to a single level would create destructive interference for probe transmission. The spectroscopic feature approaches the atomic transition linewidth, which is much narrower than the cavity linewidth, and is highly immune to the reference cavity length fluctuations that limit current state-of-the-art laser frequency stability.
Hybrid systems of cold atoms and optical cavities are promising systems for increasing the stability of laser oscillators used in quantum metrology and atomic clocks. In this paper we map out the atom-cavity dynamics in such a system and demonstrate limitations as well as robustness of the approach. We investigate the phase response of an ensemble of cold 88Sr^{88}\mathrm{Sr}88Sr atoms inside an optical cavity for use as an error signal in laser frequency stabilization. With this system we realize a regime where the high atomic phase shift limits the dynamical locking range. The limitation is caused by the cavity transfer function relating input field to output field. The cavity dynamics is shown to have only little influence on the prospects for laser stabilization, making the system robust towards cavity fluctuations and ideal for the improvement of future narrow linewidth lasers.
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.
As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.