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Optics Letters

Frequency metrology by use of quantum interference

N. Ph. Georgiades, Eugene Simon Polzik, Harry J. Kimble

Published Oct 15, 1996• 31 citations
Publisher

Abstract

Quantum interference in the rate of two-photon excitation of the 6S((1/2)) ?6P(3/2) ? 6D(5/2) transition in atomic cesium is exploited to demonstrate phase-sensitive frequency demodulation for an optical interval of +/- 12.5 THz. By thus using atoms as ultrafast nonlinear mixing elements, we suggest and analyze a new avenue for absolute comparisons of a dense set of frequencies over the range of 200-2000 nm.

DOI
10.1364/ol.21.001688

Related papers

Optical demodulation at 12 THz with applications to frequency metrology

N. Ph. Georgiades, Eugene Simon Polzik, Harry J. Kimble

Quantum interference in excitation of the 6S/sub 1/2/ 6P/sub 3/2/ 6D/sub 5/2/ transition in atomic cesium has been exploited for frequency demodulation of optical fields over an interval of +12 THz. In our scheme, the atom is employed as a nonlinear mixing element to compare the sum frequency for stepwise excitation with the doubled frequency for direct two photon excitation of an atomic ladder.

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Frequency metrology via quantum interference in two-photon excitation

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Quantum interference in atomic two-photon excitation is exploited for optical demodulation, with phase-sensitive detection at /spl plusmn/12 THz having been achieved. By utilizing the atoms as ultrafast nonlinear mixing elements, a new technique for the comparison of essentially arbitrary frequencies over the range 200-2000 nm is presented.

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Nonclassical excitation and quantum interference in a three level atom

Nikos P Georgiades

Non-classical properties and quantum interference (QI) in two-photon excitation of a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally new effects associated with quantum correlations in the squeezed fields and QI due to multiple excitation pathways have been observed. Theoretical studies and extrapolations of these findings have revealed possible applications which are far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast homodyne detection and frequency metrology. The atom used throughout the experiments was Cesium, which was magneto-optically trapped in a vapor cell to produce a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition (corresponding to the 6S1/2F = 4 → 6P3/2F' = 5 → 6D5/2F = 6 transition) was excited by using the quantum-correlated signal (Ɛs) and idler (Ɛi) output fields of a subthreshold non-degenerate optical parametric oscillator, which was tuned so that the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions, respectively. In contrast to excitation with classical fields for which the excitation rate as a function of intensity has always an exponent greater than or equal to two, excitation with squeezed-fields has been theoretically predicted to have an exponent that approaches unity for small enough intensities. This was verified experimentally by probing the exponent down to a slope of 1.3, demonstrating for the first time a purely non-classical effect associated with the interaction of squeezed fields and atoms. In the second part excitation of the two-photon transition by three phase coherent fields Ɛ1 , Ɛ2 and Ɛ0, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole |1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is observed due to two alternative excitation pathways. This is equivalent to nonlinear mixing of the three excitation fields by the atom. Realizing that in the experiment the three fields are spaced in frequency over a range of 25 THz, and extending this scheme to other energy triplets and atoms, leads to the discovery that ranges up to 100's of THz can be bridged in a single mixing step. Motivated by these results, a master equation model has been developed for the system and its properties have been extensively studied.

•Jan 1, 1998•0 citations

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

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

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.

Physical Review A•Oct 9, 2015•7 citations
Quantum interference in the rate of two-photon excitation of the 6S((1/2)) ?6P(3/2) ? 6D(5/2) transition in atomic cesium is exploited to demonstrate phase-sensitive frequency demodulation for an optical interval of +/- 12.5 THz. By thus using atoms as ultrafast nonlinear mixing elements, we suggest and analyze a new avenue for absolute comparisons of a dense set of frequencies over the range of 200-2000 nm.
Non-classical properties and quantum interference (QI) in two-photon excitation of a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally new effects associated with quantum correlations in the squeezed fields and QI due to multiple excitation pathways have been observed. Theoretical studies and extrapolations of these findings have revealed possible applications which are far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast homodyne detection and frequency metrology. The atom used throughout the experiments was Cesium, which was magneto-optically trapped in a vapor cell to produce a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition (corresponding to the 6S1/2F = 4 → 6P3/2F' = 5 → 6D5/2F = 6 transition) was excited by using the quantum-correlated signal (Ɛs) and idler (Ɛi) output fields of a subthreshold non-degenerate optical parametric oscillator, which was tuned so that the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions, respectively. In contrast to excitation with classical fields for which the excitation rate as a function of intensity has always an exponent greater than or equal to two, excitation with squeezed-fields has been theoretically predicted to have an exponent that approaches unity for small enough intensities. This was verified experimentally by probing the exponent down to a slope of 1.3, demonstrating for the first time a purely non-classical effect associated with the interaction of squeezed fields and atoms. In the second part excitation of the two-photon transition by three phase coherent fields Ɛ1 , Ɛ2 and Ɛ0, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole |1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is observed due to two alternative excitation pathways. This is equivalent to nonlinear mixing of the three excitation fields by the atom. Realizing that in the experiment the three fields are spaced in frequency over a range of 25 THz, and extending this scheme to other energy triplets and atoms, leads to the discovery that ranges up to 100's of THz can be bridged in a single mixing step. Motivated by these results, a master equation model has been developed for the system and its properties have been extensively studied.
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.