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arXiv:1807.09095

An experiment on multiple pathway quantum interference for the advanced undergraduate physics laboratory

Clark Vandam, Aaron M. Hankin, A. Sieradzan, Mark D. Havey

Published Jul 21, 2018• 0 citations
arXivHTMLPDF

Abstract

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 $6s^{2}S_{1/2} \rightarrow 7s^{2}S_{1/2}$ 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.

DOI
10.48550/arxiv.1807.09095

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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.
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.
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We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman’s rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2′×4′ optical breadboard.
Results of a theoretical investigation of two-photon, two-color excitation and linear depolarization spectra in atomic cesium are presented. The case of two-beam excitation, where one photon is absorbed through a quadrupole amplitude and the other through a dipole amplitude, is considered. When excitation is through a spin multiplet, the final-state population produced depends sensitively on the relative transition amplitudes through the nondengenerate spin-multiplet terms. In addition, the transition rate contains interference terms depending on the relative directions of the two beams. These terms are manifested strongly when the intermediate states are nonresonant and when the two beams have approximately the same frequency. Application of the results to the 6s2{\mathrm{}}^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\rightarrow}5d2{\mathrm{}}^{2}2Dj{\mathit{D}}_{\mathit{j}}Dj​\ensuremath{\rightarrow}11p2{\mathrm{}}^{2}2P3/2{\mathit{P}}_{3/2}P3/2​, quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.
We develop a theoretical model of two-photon amplification in laser-driven potassium atoms and use it to analyze the recent experiments reported by Pfister et al. [Phys. Rev. A 60, R4249 (1999)]. The model takes into account most of the essential factors influencing the amplification process, including the atomic hyperfine structure (which makes multiphoton emission possible) and the simultaneous interaction with intense drive and probe beams with arbitrary detunings. We determine the origin and analyze the properties of different multiphoton gain resonances that appear in the light-matter interaction. In particular, the influence of the drive and probe field amplitudes and detunings on the strength and frequency of the two-photon amplification resonance is studied in detail, showing clearly the differences with respect to the behavior of single-photon or other multiphoton amplification processes. In addition, we investigate interferences between different quantum pathways originating from the hyperfine structure and determine the conditions under which they can enhance or suppress multiphoton resonances. The predictions of the model are in good agreement with the observations, indicating that it can be used to understand recent experiments on two-photon lasing reported by Pfister et al. [Phys. Rev. Lett. 86, 4512 (2001)].