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Physical Review Letters

Vacuum-Field Dressed-State Pumping

Yifu Zhu, A. Lezama, THOMAS W. MOSSBERG, Maciej Lewenstein

Published Oct 24, 1988• 84 citations
Publisher

Abstract

The steady-state behavior of two-level atoms, driven by a strong field and relaxing into a frequency-dependent vacuum reservoir, has been studied in an experiment involving Ba atoms in a confocal cavity. Enhancement or suppression of the atomic excitation is observed when the cavity is tuned to either of the strong-field fluorescence sidebands. These effects result from a redistribution of the population among the dressed atom-field states induced by the cavity-modified vacuum field. The enhancement effect may be useful in achieving significant steady-state inversion.

DOI
10.1103/physrevlett.61.1946

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The steady-state behavior of two-level atoms, driven by a strong field and relaxing into a frequency-dependent vacuum reservoir, has been studied in an experiment involving Ba atoms in a confocal cavity. Enhancement or suppression of the atomic excitation is observed when the cavity is tuned to either of the strong-field fluorescence sidebands. These effects result from a redistribution of the population among the dressed atom-field states induced by the cavity-modified vacuum field. The enhancement effect may be useful in achieving significant steady-state inversion.
We investigate properties of a two-level atom coupled to a single cavity mode, and driven by a strong, in general off-resonance, external field. The cavity field is tuned to resonance with a Mollow sideband. We show that the steady-state atomic population may be highly (nearly totally) inverted, a phenomenon forbidden in semiclassical theory, and that a strong enhancement of the resonance fluorescence results. This system is suggested as an alternative approach to create the atomic inversion necessary for laser or maser generation without using additional atomic levels. We also investigate properties of the cavity field, derive an analytical expression for the photon number distribution in the good cavity or strong-coupling limit, and discuss the conditions under which this system acts as a single-atom dressed-state laser.
Placing an optical cavity around a two-level atom modifies the electromagnetic vacuum to which it couples. Effects such as inhibited and enhanced spontaneous emission are known to result. Recently one of us predicted a new nonclassical effect of vacuum engineering.1 A two-level transition may be laser driven into an inverted steady state. Semiclassical theory forbids this fully quantum mechanical result. Unlike squeezing and antibunching, this inversion is not a property of the linearized quantum fluctuations. We present numerical and analytical results which clarify the physics of the inversion. The maximum inversion possible is determined. We attempt to identify obstacles to the experimental realization of steady-state inversion. Multiple atoms and multiple cavity modes do not destroy the effect. A significant difficulty appears to be localizing the atoms at the cavity beamwaist until they reach steady state. The inversion may be observed via fluorescence changes as the cavity is blocked and unblocked or via the presence of a fluoresence maximum as a function of the driving field intensity.
The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.
A two-level atom illuminated by a laser may be driven into a population-inverted steady state if it is coupled to a cavity. This is a result of the quantum nature of the electromagnetic field and is forbidden by the semiclassical theory. We numerically and analytically analyze this inversion. We find the maximum possible inversion and determine the rate of approach to the steady state. The quantized cavity modifies the electromagnetic vacuum seen by the atom; this connects our work to that on cavity-enhanced spontaneous emission and on dynamical line narrowing. Experimental signatures of the inversion and potential experimental difficulties are considered. For example, neither the presence of many atoms in the mode nor many modes in the cavity destroys the inversion.