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Quantum Electronics and Laser Science Conference

Optical demodulation at 12 THz with applications to frequency metrology

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

Published Jun 7, 1996• 0 citations
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Abstract

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.

Related papers

Frequency metrology by use of quantum interference

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

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.

Optics Letters•Oct 15, 1996•31 citations

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.

Conference on Precision Electromagnetic Measurements•Dec 24, 2002•0 citations

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

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Measurements of quantum correlations are reported for a frequency difference of 25 THz between the signal and idler output fields generated by a subthreshold nondegenerate optical parametric oscillator. By simultaneously exciting a two-photon transition in atomic Cs by a combination of signal, idler, and ``references oscillator'' fields, we record modulation of the excited-state population due to quantum interference between two alternative excitation pathways. The observed phase-sensitive modulation is proportional to the correlation function 〈E-|${\mathrm{Ax}}_{\mathrm{s}}$E-|${\mathrm{Ax}}_{\mathrm{i}}$〉 for the quantized signal and idler fields.

Physical Review A•Mar 1, 1997•56 citations

Quantum interference in two-photon excitation with squeezed and coherent fields

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

Two-photon excitation of a three-level atom in a ladder configuration $(\stackrel{\ensuremath{\rightarrow}}{1}\stackrel{\ensuremath{\rightarrow}}{2}3)$ by simultaneous illumination with fields in squeezed vacuum and coherent states results in quantum interference for the excitation process. The particular configuration considered here is one for which the signal and idler output fields of a subthreshold nondegenerate optical parametric oscillator are in resonance with the two-stepwise dipole atomic transitions $(\stackrel{\ensuremath{\rightarrow}}{1}2,\stackrel{\ensuremath{\rightarrow}}{2}3),$ while a ``reference oscillator'' field is in two-photon resonance with the quadrupole transition $(\stackrel{\ensuremath{\rightarrow}}{1}3).$ In an extension of the work of Ficek and Drummond [Phys. Rev. A 43, 6247 (1991)], a theoretical formulation based on the full quantum master equation for the problem is presented. The combined effects of quantum interference and the nonclassical character of the squeezed state are investigated, and offer the potential for a new detection strategy for quantum fluctuations of the electromagnetic field with ultrahigh frequencies (10's--100's THz). Based on the theory developed, we analyze quantum interference in excitation in several special cases relevant to experimental realizations, including the effects of a small focusing angle of the squeezing onto the atoms, and unusual population inversions. Special emphasis is given to identifying intrinsically quantum optical field effects versus classical field effects. Procedures that could distinguish between the two (i.e., classical and nonclassical) are suggested.

Physical Review A•Jan 1, 1999•27 citations

Quantum interference in two-photon excitation of the 6s - 7s transition in atomic cesium

Clark Vandam, Aaron M. Hankin, A. Sieradzan +1 more

Bulletin of the American Physical Society•May 23, 2009•0 citations
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.
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.
Measurements of quantum correlations are reported for a frequency difference of 25 THz between the signal and idler output fields generated by a subthreshold nondegenerate optical parametric oscillator. By simultaneously exciting a two-photon transition in atomic Cs by a combination of signal, idler, and ``references oscillator'' fields, we record modulation of the excited-state population due to quantum interference between two alternative excitation pathways. The observed phase-sensitive modulation is proportional to the correlation function 〈E-|Axs{\mathrm{Ax}}_{\mathrm{s}}Axs​E-|Axi{\mathrm{Ax}}_{\mathrm{i}}Axi​〉 for the quantized signal and idler fields.
Two-photon excitation of a three-level atom in a ladder configuration $(\stackrel{\ensuremath{\rightarrow}}{1}\stackrel{\ensuremath{\rightarrow}}{2}3)$ by simultaneous illumination with fields in squeezed vacuum and coherent states results in quantum interference for the excitation process. The particular configuration considered here is one for which the signal and idler output fields of a subthreshold nondegenerate optical parametric oscillator are in resonance with the two-stepwise dipole atomic transitions $(\stackrel{\ensuremath{\rightarrow}}{1}2,\stackrel{\ensuremath{\rightarrow}}{2}3),$ while a ``reference oscillator'' field is in two-photon resonance with the quadrupole transition $(\stackrel{\ensuremath{\rightarrow}}{1}3).$ In an extension of the work of Ficek and Drummond [Phys. Rev. A 43, 6247 (1991)], a theoretical formulation based on the full quantum master equation for the problem is presented. The combined effects of quantum interference and the nonclassical character of the squeezed state are investigated, and offer the potential for a new detection strategy for quantum fluctuations of the electromagnetic field with ultrahigh frequencies (10's--100's THz). Based on the theory developed, we analyze quantum interference in excitation in several special cases relevant to experimental realizations, including the effects of a small focusing angle of the squeezing onto the atoms, and unusual population inversions. Special emphasis is given to identifying intrinsically quantum optical field effects versus classical field effects. Procedures that could distinguish between the two (i.e., classical and nonclassical) are suggested.