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American Journal of Physics

Advanced undergraduate lab on quantum beats

Matthew Wright, R. Beban, Olivia Chierchio, L. McCluney, Tara Peña, J. John

Published Jan 23, 2025• 1 citation
Publisher

Abstract

Spontaneous emission has been studied by physicists for decades and continues to reveal exciting physics. We describe an experiment to study the spontaneous emission of a monoatomic vapor at room temperature as a fundamental experiment for upper-level physics undergraduates. The experiment begins by exciting a population of Rb atoms in a room temperature vapor cell with a laser pulse shorter than the average lifetime of the excited states. The resulting fluorescence signal is recorded as a function of time, and the excited state lifetime can be determined by measuring the decay rate. By analyzing the Fourier transform of the time-dependent polarized fluorescence signal, quantum interference (i.e., quantum beating) is observed among the hyperfine energy levels. This experiment can be completed by upper-level undergraduates in physics to demonstrate and connect hands-on experiments with concepts in atomic and quantum physics classes.

DOI
10.1119/5.0223788

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•Aug 1, 2009•1 citation
Spontaneous emission has been studied by physicists for decades and continues to reveal exciting physics. We describe an experiment to study the spontaneous emission of a monoatomic vapor at room temperature as a fundamental experiment for upper-level physics undergraduates. The experiment begins by exciting a population of Rb atoms in a room temperature vapor cell with a laser pulse shorter than the average lifetime of the excited states. The resulting fluorescence signal is recorded as a function of time, and the excited state lifetime can be determined by measuring the decay rate. By analyzing the Fourier transform of the time-dependent polarized fluorescence signal, quantum interference (i.e., quantum beating) is observed among the hyperfine energy levels. This experiment can be completed by upper-level undergraduates in physics to demonstrate and connect hands-on experiments with concepts in atomic and quantum physics classes.
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.
We report on an experiment in which the fluorescence decay time of 5P levels of Rb atoms in a coated vapor cell exceeds several of milliseconds, many orders of magnitude longer than normal decay time of excited of rubidium atoms. We found that this peculiarly long - term decay is not exponential and can only be observed in a high quality coated cell with a long lifetime of optical pumped atoms on atomic ground-state sublevels. A numerical simulation based on a complete density matrix is presented. It supports the population pumping process through the ground-state sublevels of Rb atoms as the most plausible mechanism for the observed phenomenon and it consistently demonstrates all the relevant features of the experiment. The investigation can be used, for example, to explore the quality of a various anti-relaxation coatings used for the resonant cells.
We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.
Entangled multiparticle quantum states cannot be expressed as a product of singleparticle states; they can give rise to correlations between separated particles unaccountable within the framework of classical physics and are of considerable interest to those concerned with the foundations of quantum mechanics. Two separated identical atoms having, for example, two excited levels with energy interval h12 are brought into an entangled linear superposition of excited states by absorption of two correlated photons. The quantum description of either atom alone shows incoherently populated excited states; the single-atom emission probability shows no quantum interference. However, the joint probability for fluorescent emission manifests, as a function of the time interval between radiative decay of both atoms, quantum beats1 at frequency 12. This quantum interference is insensitive to atomic motion and atomic density, and it can be engendered by photons whose spectral widths are smaller than the beat frequency.
Measurements of hyperfine polarization quantum beats are used to determine the magnetic dipole (A) and electric quadrupole (B) coupling constants in the excited atomic Cs 8p2P3/28p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}8p2P3/2​ level. The experimental approach is a combination of pulsed optical pumping and time-delayed stimulated-emission probing of the excited level. From the measured evolution of the atomic linear polarization degree as a function of probe delay time, we determine the hyperfine coupling constants A=7.42(6)A=7.42(6)A=7.42(6) MHz and B=0.14(29)B=0.14(29)B=0.14(29) MHz.
Energy pooling (EP) was observed in Rb vapor following pulsed optical excitation to the 5P1/2 state. The 5P3/2 state was populated by the energy transfer process: Rb(5P1/2)+Rb(5S1/2) --> Rb(5P3/2)+Rb(5Sl/2). The resulting densities of Rb atoms at the 5P1/2 level were obtained from the absorption of narrow spectral line from a Rb hollow cathode lamp, connecting the 5P1/2 state to 7S state. Since the effective lifetimes of the 5P1/2 and 5P3/2 states are approximately equal, the densities of the 5P3/2 level were obtained from the D2 to D1 fluorescence ratios where D1 and D2 are lines of the 5P1/2 --> 5S1/2 and 5P3/2 --> 5S1/2 transition. Because the time of the fine structure exchanging is much shorter than the lifetime of the 5D state, the fluorescence originating from the 5D state produced by the 5P1/2 + 5P3/2 and 5P3/2 + 5P3/2 processes follows the instantaneous production rate of the 5P1/2 + 5P1/2 process. It is clear that 5P/2 + 5P3/2 and 5P3/2 + 5P3/2 collisions can significantly influence the results obtained for the 5P1/2 + 5P1/2 rate since the energy defect for 5D state is much smaller for 5P1/2 + 5P3/2 and 5P3/2 + 5P3/2 collisions than for 5P1/2 + 5P1/2 collisions. Effective lifetimes of the 5P levels were calculated using radiation trapping theory. The time-integrated populations and signals were studied and analyzed. The resulting fluorescence included the direct component emitted in the decay of the optically excited 5P1/2 state and the sensitized component arising from the collisions for populating 5D state at different cell temperature. These relative intensities were combined with the measured excited atom densities to yield absolute energy-pooling rate coefficients. The cross sections (in units of 10(-14) cm2) for the energy-pooling collisions [i. e. , 5P1/2 + 5P1/2, 5P1/2 + 5P3/2, 5P3/2 + 5P3/2] are 0.78, 2.9 and 3.1, respectively. The dependence of the rates upon energy defect deltaE was examined, but the 5D3/2 level was approximately equally populated in 5P3/2 + 5P3/2 (deltaE = 68 cm(-1)) and 5P3/2 + 5P1/2 (deltaE = 306 cm(-1)) collisions. The 5P1/2 + 5P3/2 collisions are as efficient as 5P3/2 + 5P3/2 for populating 5D3/2 state.