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Physical Review A

Quantum interference in two-photon spectroscopy for laser stabilization and cesium-cell comparison

Chien-Ming Wu, Tze-Wei Liu, Wang-Yau Cheng

Published Oct 9, 2015• 7 citations
Publisher

Abstract

An alternate method of two-photon spectroscopy is presented where cesium atoms interact with a phase-modulated laser beam. Doppler-free two-photon spectroscopy of the cesium atom $6S\ensuremath{\rightarrow}8S$ hyperfine transition was used to experimentally demonstrate quantum interfered two-photon spectra. We calculated the photon-atom interaction by second-order perturbation theory and assumed that the one-photon frequency is detuned far from any intermediate state. Then we calculated the relative transition rates of all spectral lines resolved by the laser carrier and sidebands. A physical picture of multipathway quantum interference in the frequency domain is given that explains the unusual line strength, based on the trick that a phase-modulated laser beam can be decomposed into a series of coherent and collinear laser modes (carrier and sidebands). For all pairs of modes in which the sum frequency of each pair was on resonance with the cesium atom $6S\ensuremath{\rightarrow}8S$ transition, the superposition of all pathways induced by the different mode pairs resulted in a destructive interference, which then leads to a lack of absorption. We have shown in this paper that our calculation agrees very well with our experimental results in terms of the relative interfered line strengths, which were functions of modulation depth. We further discuss some related issues concerning laser stabilization and we demonstrate an approach for simultaneously comparing two cesium cells.

DOI
10.1103/physreva.92.042504

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An alternate method of two-photon spectroscopy is presented where cesium atoms interact with a phase-modulated laser beam. Doppler-free two-photon spectroscopy of the cesium atom 6S\ensuremath→8S6S\ensuremath{\rightarrow}8S6S\ensuremath→8S hyperfine transition was used to experimentally demonstrate quantum interfered two-photon spectra. We calculated the photon-atom interaction by second-order perturbation theory and assumed that the one-photon frequency is detuned far from any intermediate state. Then we calculated the relative transition rates of all spectral lines resolved by the laser carrier and sidebands. A physical picture of multipathway quantum interference in the frequency domain is given that explains the unusual line strength, based on the trick that a phase-modulated laser beam can be decomposed into a series of coherent and collinear laser modes (carrier and sidebands). For all pairs of modes in which the sum frequency of each pair was on resonance with the cesium atom 6S\ensuremath→8S6S\ensuremath{\rightarrow}8S6S\ensuremath→8S transition, the superposition of all pathways induced by the different mode pairs resulted in a destructive interference, which then leads to a lack of absorption. We have shown in this paper that our calculation agrees very well with our experimental results in terms of the relative interfered line strengths, which were functions of modulation depth. We further discuss some related issues concerning laser stabilization and we demonstrate an approach for simultaneously comparing two cesium cells.
Doppler-free two-photon (DFTP) spectroscopy is a standard technique for precision measurement of transition frequencies of dipole-forbidden transitions. Here, we report the observation of quantum interference (QI) of optical transition pathways in DFTP spectroscopy of the cesium $6S\text{\ensuremath{-}}7D$ transitions chosen as a prototype system. The QI manifests itself as asymmetric line shapes of the hyperfine lines of the 7D7D7D states, observed through spontaneous emission following excitation by a narrow-linewidth cw laser. The interference persists despite the lines being spectrally well resolved. Ignoring the effect and fitting the spectrum to a Voigt profile causes large systematic shifts in the determination of the line centers, while accounting for QI resolves the apparent line shift and enables the precise determination of hyperfine splitting in the 7D7D7D states. We calculate the spectral line shape including the effect of QI and show that it agrees with the experimental observations. Our results are broadly applicable to other species and have implications for portable secondary optical clocks and precision measurements of hyperfine splittings, isotope shifts, and transition frequencies.
A two-photon transition in cold Rb atoms will be probed with a phase-coherent wide bandwidth femtosecond laser comb. Frequency domain analysis yields a high-resolution picture where phase coherence among various transition pathways through different intermediate states produces interference effects on the resonantly enhanced transition probability. This result is supported by the time domain Ramsey interference effect. The two-photon transition spectrum is analyzed in terms of the pulse repetition rate and carrier frequency offset, leading to a cold-atom-based frequency stabilization scheme for both degrees of freedom of the femtosecond laser.
We present results on a multiple-optical-path quantum interference project suitable for the advanced undergraduate laboratory. The experiments combine a conceptually rich set of atomic physics experiments which may be economically developed at a technical level accessible to undergraduate physics or engineering majors. In the experiments, diode-laser driven two-quantum, two-color excitation of cesium atoms in a vapor cell is investigated and relative strengths of the individual hyperfine components in the 6s2S1/2→7s2S1/26s^{2}S_{1/2} \rightarrow 7s^{2}S_{1/2}6s2S1/2​→7s2S1/2​ transition are determined. Measurement and analysis of the spectral variation of the two quantum excitation rate clearly shows strong variations due to interfering amplitudes in the overall transition amplitude. Projects such as the one reported here allow small teams of undergraduate students with combined interests in experimental and theoretical physics to construct instrumentation, perform sophisticated experiments, and do realistic modelling of the results.
The cesium D2{D}_{2}D2​ line closed hyperfine transition $F=4\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=5$ was simultaneously coupled and probed in a hot atomic beam. We experimentally showed that, when the probe laser frequency approached that of the two-photon-resonance corresponding to electromagnetically induced absorption conditions, an enhanced transparency of the coupling laser appeared, combined with a further central absorption peak at zero probe laser detuning. Simultaneously, the coupling laser parametric dispersion showed a broad negative pattern together with a narrower steep positive phase shift in correspondence with the two-photon resonance, with sub-Doppler half-widths down to about 10kHz10\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}10kHz.
Vapor-cell spectroscopy is an essential technique in many fields and is particularly relevant for quantum technologies. Most atom- and ion-trapping experiments rely on simultaneous spectroscopy of two atomic transitions, employing a separate apparatus for each transition. We demonstrate simultaneous spectroscopy on two atomic transitions, within a single apparatus, using spatially overlapped beams from two independent lasers. This method enables compact setups and offers superior spectroscopic performance, leading to sharper spectroscopy peaks, stronger absorption signals, and superior laser stability. Doppler-free locking features become accessible over a frequency range several hundred megahertz wider than for standard saturated absorption spectroscopy. Exploring the full parameter space associated with dual-frequency spectroscopy reveals a latticelike structure of sharp resonance features, which enhances experimental versatility by allowing laser frequency stabilization within a wide manifold of locations in two-dimensional frequency space. We present data for 133Cs^{133}\mathrm{Cs}133Cs and 85Rb^{85}\mathrm{Rb}85Rb and compare our results to a theoretical model. Employing the technique for frequency stabilization close to the D2{D}_{2}D2​ line of 85Rb^{85}\mathrm{Rb}85Rb results in an improvement in frequency stability by a factor typically between 2 and 3 for averaging times of up to 1 s. The technique will advance portable quantum technologies and facilitate high-precision measurements.
This thesis demonstrates the experimental implementation of a homodyne interference technique to detect weak atomic transitions. The demonstration of the technique uses two pathways to excite the cesium atom from its ground state to an excited state. One is a Stark-induced transition that is regulated by controlling a dc field across the cesium atoms. This is excited by a 411 nm laser field. A two-photon transition excited by an 822 nm laser field concurrently excites the same transition. The simultaneous excitation of the two pathways results in a quantum interference of the transition amplitudes. Phase modulating one of the beams gives rise to an amplitude modulation of the net excitation rate resulting in an amplitude modulated fluorescence signal. We observe the fluorescence at 794.6 nm due to the decay of the excited state to the ground state via an intermediate state. The strength of the amplitude modulation of the fluorescence signal is a measure of weak signal transition amplitude which in this demonstration is the controllable Stark-induced transition. Results of this work have shown improvements of two to three orders of magnitude in signal to noise over direct detection of the weak interaction. With possible improvements that are discussed it is projected to be much better.