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Observation of Two-Photon Excitation for Three-Level Atoms in a Squeezed Vacuum

Keiichi Edamatsu, N. Ph. Georgiades, Eugene Simon Polzik, Harry J. Kimble, A. S. Parkins

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

The two-photon transition (6S(sub 1/2) yields 6D(sub 5/2)) of atomic Cesium is investigated for excitation with squeezed vacuum generated via nondegenerate parametric down conversion. The two-photon excitation rate (R) is observed to have a non-quadratic dependence of R = aI(exp 2) + bI on the incident photon flux (I), reflecting the nonclassical correlations of the squeezed vacuum field.

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The two-photon transition ${6S}_{1/2}\ensuremath{\rightarrow}{6D}_{5/2}$ is investigated for trapped atomic cesium excited by squeezed light. The rate $R$ of two-photon excitation versus intensity $I$ is observed to be consistent with the functional form $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\beta}}_{1}I+{\ensuremath{\beta}}_{2}{I}^{2}$, extending into a region with slope 1.3. This departure from the quadratic form for classical light sources is due to the fundamental alteration of atomic radiative processes by the nonclassical field.

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We study the two-photon excitation rate and the spectrum of a three-level atom in the \ensuremath{\Xi} configuration interacting with a resonant cavity mode which is coupled to a broadband squeezed vacuum through its input-output mirror. We show that the optical Bloch equations in the cavity environment are formally identical to these in free space but, in the bad-cavity limit, with cavity-modified parameters describing the injected squeezed vacuum. It is shown that the two-photon excitation rate (which is proportional to the upper-level population) has two components, one depending linearly and the other quadratically on the squeezed photon number N, in excellent agreement with experiment [Georgiades et al., Phys. Rev. Lett. 75, 3426 (1995)]. The presence of the term quadratic in N is entirely due to the effectively imperfect correlation of the squeezed photon pairs in the bad cavity. We also find that the two-photon excitation spectrum (as measured by the fluorescent emission from the upper level to the intermediate level) exhibits an extremely narrow peak at line center, under appropriate choices of the bad-cavity parameters. All these results are independent of the squeezed phase. \textcopyright{} 1996 The American Physical Society.

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Using the formalism developed earlier, we treat spontaneous emission from a three-level atom (ladder system) interacting with a broadband squeezed vacuum field. We obtain expressions for the transient and steady-state populations of the atomic levels with the conditions that the atom interacts with either a multimode perfect squeezed vacuum field, or a three-dimensional vacuum field in which the squeezed modes lie within a solid angle over which squeezing is propagated. The results are compared with those obtained for the atom interacting with a thermal field. We show that in the perfect case the first excited state is not populated when the squeezed vacuum field is in a minimum-uncertainty squeezed state. Moreover, the second excited state can have a steady-state population larger than 1/2. These features are completely absent when the atom interacts with the thermal field. In addition, for a low-intensity squeezed vacuum field the population in the second excited state exhibits a linear rather than quadratic dependence on the intensity of the squeezed vacuum field. In the three-dimensional case the presence of unsqueezed modes considerably reduces the effect of squeezing on spontaneous emission. However, a significant reduction in a population of the first excited state and a population larger than 1/2 in the second excited state can be achieved provided the squeezing is propagated over a large solid angle. We also discuss the effect of the two-photon detuning between the double carrier frequency of the squeezing and atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{3}$ on the steady-state atomic population.

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Nonlinear two-photon interaction of radiators with broadband squeezed vacuum

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The resonance two-photon interaction of the broadband squeezed vacuum with the dipole-forbidden two-level atoms via nonresonant virtual levels is investigated. It is demonstrated that the broadband squeezed vacuum excites coherently the system of radiators (atoms, molecules) that have dipole-forbidden transitions. The quantum statistics of the generated photon pairs in the process of resonance fluorescence is analyzed. As the broadband squeezed field is amplitude-squared squeezed the interaction of this field with the dipole-forbidden atoms can contribute in further amplitude-squared squeezing. In the high-field limit this squeezing increases when the atom number also increases.

AIP conference proceedings•Jan 1, 2000•0 citations
The two-photon transition (6S(sub 1/2) yields 6D(sub 5/2)) of atomic Cesium is investigated for excitation with squeezed vacuum generated via nondegenerate parametric down conversion. The two-photon excitation rate (R) is observed to have a non-quadratic dependence of R = aI(exp 2) + bI on the incident photon flux (I), reflecting the nonclassical correlations of the squeezed vacuum field.
The two-photon transition ${6S}_{1/2}\ensuremath{\rightarrow}{6D}_{5/2}$ is investigated for trapped atomic cesium excited by squeezed light. The rate RRR of two-photon excitation versus intensity III is observed to be consistent with the functional form $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\beta}}_{1}I+{\ensuremath{\beta}}_{2}{I}^{2}$, extending into a region with slope 1.3. This departure from the quadratic form for classical light sources is due to the fundamental alteration of atomic radiative processes by the nonclassical field.
We study the two-photon excitation rate and the spectrum of a three-level atom in the \ensuremath{\Xi} configuration interacting with a resonant cavity mode which is coupled to a broadband squeezed vacuum through its input-output mirror. We show that the optical Bloch equations in the cavity environment are formally identical to these in free space but, in the bad-cavity limit, with cavity-modified parameters describing the injected squeezed vacuum. It is shown that the two-photon excitation rate (which is proportional to the upper-level population) has two components, one depending linearly and the other quadratically on the squeezed photon number N, in excellent agreement with experiment [Georgiades et al., Phys. Rev. Lett. 75, 3426 (1995)]. The presence of the term quadratic in N is entirely due to the effectively imperfect correlation of the squeezed photon pairs in the bad cavity. We also find that the two-photon excitation spectrum (as measured by the fluorescent emission from the upper level to the intermediate level) exhibits an extremely narrow peak at line center, under appropriate choices of the bad-cavity parameters. All these results are independent of the squeezed phase. \textcopyright{} 1996 The American Physical Society.
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.
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.
Using the formalism developed earlier, we treat spontaneous emission from a three-level atom (ladder system) interacting with a broadband squeezed vacuum field. We obtain expressions for the transient and steady-state populations of the atomic levels with the conditions that the atom interacts with either a multimode perfect squeezed vacuum field, or a three-dimensional vacuum field in which the squeezed modes lie within a solid angle over which squeezing is propagated. The results are compared with those obtained for the atom interacting with a thermal field. We show that in the perfect case the first excited state is not populated when the squeezed vacuum field is in a minimum-uncertainty squeezed state. Moreover, the second excited state can have a steady-state population larger than 1/2. These features are completely absent when the atom interacts with the thermal field. In addition, for a low-intensity squeezed vacuum field the population in the second excited state exhibits a linear rather than quadratic dependence on the intensity of the squeezed vacuum field. In the three-dimensional case the presence of unsqueezed modes considerably reduces the effect of squeezing on spontaneous emission. However, a significant reduction in a population of the first excited state and a population larger than 1/2 in the second excited state can be achieved provided the squeezing is propagated over a large solid angle. We also discuss the effect of the two-photon detuning between the double carrier frequency of the squeezing and atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{3}$ on the steady-state atomic population.
The resonance two-photon interaction of the broadband squeezed vacuum with the dipole-forbidden two-level atoms via nonresonant virtual levels is investigated. It is demonstrated that the broadband squeezed vacuum excites coherently the system of radiators (atoms, molecules) that have dipole-forbidden transitions. The quantum statistics of the generated photon pairs in the process of resonance fluorescence is analyzed. As the broadband squeezed field is amplitude-squared squeezed the interaction of this field with the dipole-forbidden atoms can contribute in further amplitude-squared squeezing. In the high-field limit this squeezing increases when the atom number also increases.