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Physical Review A

Squeezing from ghost transitions

Klaus M. Gheri, Daniel F. Walls

Published May 1, 1994• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.4134

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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 present a detailed analysis of the quantum-nondemolition (QND) properties of a measurement scheme employing coherently driven three-level atoms in the \ensuremath{\Lambda} or cascade configuration inside an optical cavity. We propose to use a strong signal field to empty one of the transitions and dress the signal-transition levels. The atoms become transparent for the signal beam, which sees a ``ghost transition.'' When a probe is applied and tuned to the vicinity of one of the light-shifted levels, the probe phase is extremely sensitive to fluctuations of the signal intensity. This enhances the QND coupling and enables the system to operate at lower cooperativities.
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.
The quadrature squeezing spectra produced in the resonance fluorescence of a two-level atom driven by a strong coherent field and a weak amplitude-fluctuating field are investigated. For far-off-resonance and strong excitation, the resonance fluorescence exhibits two-mode squeezing around the Rabi sideband frequencies. Thus we have a source of two mode squeezing that is very easily frequency tuned simply by adjusting the generalized Rabi frequency. The presence of the strength of the stochastic process reduces the degree of squeezing obtainable. The quadrature squeezing spectra are also effected by the relative phase of the two fields.
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.
The interaction of a quantized field with three-level atoms in a $\ensuremath{\Lambda}$ configuration inside a two mode cavity is analyzed. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is in a squeezed state and the atoms show electromagnetically induced transparency. If the Rabi frequencies of both dipole transitions of the atoms are different from zero, we show that the output probe field has four maxima of squeezing absorption. We show that in some cases two of these frequencies can be very close to the transition frequency of the atom, in a region where the mean value of the field entering the cavity is hardly altered. Furthermore, part of the absorbed squeezing of the probe field is transferred to the pump field. For some conditions this transfer of squeezing can be complete.