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arXiv:0804.0085 · Europhysics Letters (EPL)

Feedback control of the fluorescence light squeezing

Alberto Barchielli, Matteo Gregoratti, M. Licciardo

Published Jan 1, 2009• 12 citations
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Abstract

We consider a trapped two-level atom stimulated by a coherent monochromatic laser and we study how to enhance the squeezing of the fluorescence light in the presence of a Wiseman-Milburn feedback mechanism, based on the homodyne detection of a fraction of the emitted light. We analyze the effect of the control parameters on the properties of the spectrum of light and we also discuss the relation between light squeezing and atomic states, which qualitatively changes when the control is present. We also show that feedback can produce sub-natural line narrowing of the fluorescence light, without the presence of squeezing in the stimulating light. The whole problem is tackled inside the framework of the quantum trajectory theory.

DOI
10.1209/0295-5075/85/14006

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We consider a trapped two-level atom stimulated by a coherent monochromatic laser and we study how to enhance the squeezing of the fluorescence light in the presence of a Wiseman-Milburn feedback mechanism, based on the homodyne detection of a fraction of the emitted light. We analyze the effect of the control parameters on the properties of the spectrum of light and we also discuss the relation between light squeezing and atomic states, which qualitatively changes when the control is present. We also show that feedback can produce sub-natural line narrowing of the fluorescence light, without the presence of squeezing in the stimulating light. The whole problem is tackled inside the framework of the quantum trajectory theory.
Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.
Among the formulations of the theory of quantum measurements in continuous time, quantum trajectory theory is very suitable for the introduction of measurement based feedback and closed loop control of quantum systems. In this paper we present such a construction in the concrete case of a two-level atom stimulated by a coherent, monochromatic laser. In particular, we show how fast feedback à la Wiseman and Milburn can be introduced in the formulation of the theory. Then, the spectrum of the free fluorescence light is studied and typical quantum phenomena, squeezing and sub-natural line-narrowing, are presented.
This thesis considers two types of applications of quantum feedback control; feedback creation of nonclassical states of light, and controlling nonclassical properties of an ensemble of atoms. An electro-optical feedback loop will create an in-loop field with nonclassical photon statistics similar to squeezed light, resulting in fluorescence line-narrowing of a two-level atom coupled to such light. We extend this theory to study a three-level atom coupled to broadband squashed light, and confirm the two-level atom line-narrowing using a more realistic non-Markovian description of the feedback loop. The second type of application utilizes continuous QND measurement of atomic ensembles. If we measure the collective spin, then the system experiences conditional spin squeezing dependent on the measurement results. We show that feedback based on these results can continuously drive the system into the same conditioned state, resulting in deterministically reproducible spin squeezing. If we measure the atom number fluctuations of a BEC, then, due to the nonlinearity of atomic self interactions, this is also information about phase fluctuations. We show that feedback based on this information can greatly reduce the collisional broadening of the linewidth of an atom laser out-coupled from the condensate.
The squeezed light has been applied widely in our life.We can get the quartered squeezing spectra from the resonance fluorescence of a two-level atom driven by a monochromatic field.It shows that the squeezing spectra will change markedly with the varieties of the intensity and the frequency of the driving field.The appearance of the squeezing on in-phase or on out-phase,and the degree of the squeezing,and the number of the squeezing modes are all controlled via changing the intensity and the frequency of the monochromatic driving field.
Abstract The squeezing spectrum of the fluorescence field emitted from a four-level atom in J = 1/2 to J = 1/2 configuration driven by two coherent fields is studied. We find that the squeezing properties of the fluorescence radiation are significantly influenced by the presence of vacuum-induced coherence in the atomic system. It is shown that such coherence induces spectral squeezing in phase quadratures of the fluorescence light for both weak and strong driving fields. The dependence of the squeezing spectrum on the relative phase of the driving fields is also investigated. Effects such as enhancement or suppression of the squeezing peaks are shown in the spectrum as the relative phase is varied. An analytical explanation of the numerical findings is presented using dressed-states of the atom-field system.
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.