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Journal of Modern Optics

Atomic dynamics and radiative properties of a two-level atom in a resonant cavity coupled to a finite bandwidth squeezed input

Sintayehu Tesfa

Published Dec 17, 2008• 3 citations
Publisher

Abstract

Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.

DOI
10.1080/09500340802517686

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Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.
We analyse the effects of the external coherent radiation and squeezed input on a two-level atom placed in a cavity applying the corresponding master equation. We study the atomic dynamics as well as the squeezing and statistical properties of the cavity radiation by analytically solving the associated differential equations. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent and squeezed input. However, a strong external coherent radiation splits the line of the emission spectrum, whereas the squeezing broadens the width and significantly decreases the height of the spectrum. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing.
Analysis of the effects of decoherence on the radiative and squeezing properties of a coherently driven two-level atom trapped in a resonant cavity applying the corresponding master equation is presented. The atomic dynamics as well as the squeezing and statistical properties of the emitted radiation are investigated. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent radiation and thermal fluctuations entering the cavity. Moreover, a strong external coherent radiation results in the splitting of the line of the emission spectrum, whereas the decoherence broadens the width and significantly decreases the height. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing, despite the presence of the decoherence which is expected to destroy the quantum features.
The fluorescence spectrum of a strongly driven two-level atom located inside an optical cavity damped by a narrow-bandwidth squeezed vacuum is studied. We use a dressed atom model approach, first applied to squeezed vacuum problems by Yeoman and Barnett, to derive the master equation of the system and discuss the role of the cavity and the squeezed vacuum in the narrowing of the spectral lines and the population trapping effect. We find that in the presence of a single-mode cavity the effect of squeezing on the fluorescence spectrum is more evident in the linewidths of the Rabi sidebands rather than in the linewidth of the central component. Even in the absence of squeezing, the cavity can reduce the linewidth of the central component almost to zero, whereas the Rabi sidebands can be narrowed only to some finite value. In the presence of a two-mode cavity and a two-mode squeezed vacuum the signature of squeezing is evident in the linewidths of all spectral lines. We also establish that the narrowing of the spectral lines is very sensitive to the detuning of the driving field from the atomic resonance. Moreover, we find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth case only if the input squeezed modes are perfectly matched to the cavity modes and if there is non-zero squeezing at the Rabi sidebands.
The resonance fluorescence of a two-level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum is analysed. We extend the Yeoman and Barnett technique to a non-zero detuning of the driving field from the atomic resonance and discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of the spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural line-width in order to satisfy the Markoff approximation. The narrowing of the spectral lines is interpreted in terms of the quadrature-noise spectrum. We find that, depending on the Rabi frequency, detuning and the squeezing phase, different factors contribute to the line narrowing. For a strong resonant driving field there is no squeezing in the emitted field and the fluorescence spectrum exactly reveals the noise spectrum. In this case the narrowing of the spectral lines arises from the noise reduction in the input squeezed vacuum. For a weak or detuned driving field the fluorescence exhibits a large squeezing and, as a consequence, the spectral lines have narrowed linewidths. Moreover, the fluorescence spectrum can be asymmetric about the central frequency despite the symmetrical distribution of the noise. The asymmetry arises from the absorption of photons by the squeezed vacuum which reduces the spontaneous emission. For an appropriate choice of the detuning some of the spectral lines can vanish despite that there is no population trapping. Again this process can be interpreted as arising from the absorption of photons by the squeezed vacuum. When the absorption is large it may compensate the spontaneous emission resulting in the vanishing of the fluorescence lines.
We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.
The dynamics of a coherently driven two-level atom with parametric amplifier and coupled to a vacuum reservoir is analyzed. The combination of the master equation and the quantum Langevin equation is presented to study the quantum properties of light. By using these equations, we have determined the time evolution of the expectation values of the cavity mode and atomic operators. Moreover, with the aid of these results, the correlation properties of noise operators, and the large-time approximation scheme, we calculate the mean photon number, power spectrum, second-order correlation function, and quadrature variances for the cavity-mode light and fluorescence. It is found that the half-width of the power spectrum for the fluorescent light in the presence of a parametric amplifier increases, while it decreases for the cavity-mode light. Moreover, we have found the probability for the atom to be in the upper level in the presence of a parametric amplifier.