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Physical Review A

Bright squeezing from self-induced transparencies in dressed three-level atoms

M. K. Olsen, Klaus M. Gheri, Daniel F. Walls

Published Dec 1, 1994• 3 citations
Publisher

Abstract

We investigate two schemes for the efficient conversion of coherent input light into bright-squeezed output light. Both schemes utilize strong signal and weak probe fields, interacting with three-level ladder-configuration atoms inside optical cavities. The schemes differ in the resonance requirements of the cavities and produce noise suppression for quite different tuning regimes. Quantum-noise reduction is a consequence of the dressing of the atoms with two coherent fields. By tuning the probe light in the right fashion, spontaneous emission from the excited state can be made to counteract signal-light intensity fluctuations.

DOI
10.1103/physreva.50.5289

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We show that significant squeezing in a strong signal light field can be generated with three-level atoms in a ghost-transition setup by tuning a weak probe beam inside the Autler-Townes doublet created by the strong signal light. Close to the Rabi level, i.e., within the absorption line, processes involving both amplitude quadratures become important. Significant atomic two-photon coherence provides a vehicle for signal-amplitude fluctuations to trigger fluctuations in the probe amplitude. Subsequently, atomic coherence will feed these probe fluctuations back into the signal and enable substantial noise suppression.
We show that three-level atoms excited by two cavity modes in a Lambda configuration close to electromagnetically induced transparency can produce strongly squeezed bright beams or correlated beams which can be used for quantum nondemolition measurements. The input intensity is the experimental "knob" for tuning the system into a squeezer or a quantum nondemolition device. The quantum correlations become ideal at a critical point characterized by the appearance of a switching behavior in the mean fields intensities. Our predictions, based on a realistic fully quantum three-level model including cavity losses and spontaneous emission, allow direct comparison with future experiments.
We present a scheme to generate unitarily two-mode and four-mode field squeezing in optical cavities with the near-resonantly dressed three-level atoms in the $\mathrm{\ensuremath{\Lambda}}$ configuration. The dressing fields open two coherent population trapping (CPT) windows, within which the atoms stay predominantly in the dark state and yield strong nonlinearities for both the dressing fields themselves and the other applied fields. The two-mode squeeze operator is separated from degrees of freedom of atoms in a common CPT window, and the multimode squeeze operator is segregated in different CPT windows. The resulting two-mode and multimode interaction strengths are at least one order higher than in the previous dispersive schemes, where all fields are far off resonant with the atoms. The present near-resonant scheme is robust to spontaneous emission since atoms are nearly trapped in a long-lived superposition state.
We show that \ensuremath{\Lambda} three-level atoms interacting with two coherent light fields tuned close to two-photon or dark resonance behave as a saturable dispersive nonlinearity. If one of the light fields is allowed to resonate within an optical cavity the quantum noise in a quadrature of the output light can be almost completely suppressed. As no dynamic retuning of the cavity is required to achieve noise reduction and cold atomic media are readily available in traps which conform in essence to the proposed configuration, an experimental realization would seem within reach.
We present a detailed analysis of the noise properties of a potential lasing scheme employing a coherently driven three-level system in the \ensuremath{\Lambda} configuration inside an optical cavity. We derive expressions for the steady-state laser intensity and the width of the intensity fluctuations and show that the output fields exhibit sub-Poissonian statistics for suitable operating conditions. The fundamental mechanism responsible for noise suppression is identified as increased intensity dissipation inside the cavity through emission and absorption by the atoms, which counteracts the intensity fluctuations.
Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.