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.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, 19980 citations

Atoms as nonlinear mixers for detection of quantum correlations at ultrahigh frequencies

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

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.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 AMar 1, 199756 citations

Nonresonant Excitation of the Atomic Spectrum in a Light Field

G. A. Delone, Nikolai B. Delone, B. A. Zon +2 more

Soviet Physics UspekhiSep 30, 19750 citations

Super-elastic electron excitation of atoms in magnetic & optical fields

Andrew James Murray, W. R. MacGillivray, Martyn Hussey

Bulletin of the American Physical SocietyOct 22, 20090 citations

Generation of multiple electron beams by cold atom electron source

H.B. Wang, Haoyu Huang, Jianing Sun +4 more

Abstract We report the generation of multiple electron beams using a cold atom electron source (CAES) combined with a spatial light modulator (SLM). In the experiment, neutral ${ }^{87} \mathrm{Rb}$ atoms are confined in a magneto-optical trap and cooled to approximately $700 \mu \mathrm{~K}$ . By shaping the intensity profile of the excitation laser via the SLM, the spatial distribution of the excited atoms can be precisely controlled. The excited atoms are then ionized by a dye laser, and the ionized electrons are extracted and focused by an electric field to form multiple electron beams. As a demonstration, we generate regular arrays of $3 \times 3,4 \times 4,5 \times 5,6 \times 6$ beams, each with a spot size of about $100 \mu \mathrm{~m}$ and a normalized transverse emittance of $\sim 0.4 \times 10^{-9} \mathrm{~m} \cdot \mathrm{rad} \cdot \sqrt{\mathrm{eV}}$ . This programmable electron beam technique holds potential for applications in electron-beam lithography and wafer inspection.Abstract We report the generation of multiple electron beams using a cold atom electron source (CAES) combined with a spatial light modulator (SLM). In the experiment, neutral ${ }^{87} \mathrm{Rb}$ atoms are confined in a magneto-optical trap and cooled to approximately $700 \mu \mathrm{~K}$. By shaping the intensity profile of the excitation laser via the SLM, the spatial distribution of the excited atoms can be precisely controlled. The excited atoms are then ionized by a dye laser, and the ionized electrons are extracted and focused by an electric field to form multiple electron beams. As a demonstration, we generate regular arrays of $3 \times 3,4 \times 4,5 \times 5,6 \times 6$ beams, each with a spot size of about $100 \mu \mathrm{~m}$ and a normalized transverse emittance of $\sim 0.4 \times 10^{-9} \mathrm{~m} \cdot \mathrm{rad} \cdot \sqrt{\mathrm{eV}}$. This programmable electron beam technique holds potential for applications in electron-beam lithography and wafer inspection.

Chinese Physics BApr 27, 20260 citations

{\mathrm{Ax}}_{\mathrm{s}}

E-|

{\mathrm{Ax}}_{\mathrm{i}}

〉 for the quantized signal and idler fields.

Abstract We report the generation of multiple electron beams using a cold atom electron source (CAES) combined with a spatial light modulator (SLM). In the experiment, neutral

{ }^{87} \mathrm{Rb}

atoms are confined in a magneto-optical trap and cooled to approximately

700 \mu \mathrm{~K}

. By shaping the intensity profile of the excitation laser via the SLM, the spatial distribution of the excited atoms can be precisely controlled. The excited atoms are then ionized by a dye laser, and the ionized electrons are extracted and focused by an electric field to form multiple electron beams. As a demonstration, we generate regular arrays of

3 \times 3,4 \times 4,5 \times 5,6 \times 6

beams, each with a spot size of about

100 \mu \mathrm{~m}

and a normalized transverse emittance of

\sim 0.4 \times 10^{-9} \mathrm{~m} \cdot \mathrm{rad} \cdot \sqrt{\mathrm{eV}}

. This programmable electron beam technique holds potential for applications in electron-beam lithography and wafer inspection.