By reduction of the electromagnetic field fluctations in one quadrature phase, squeezed light can inhibit the phase decay of an atom. This gives three relaxation times: the usual longitudinal relaxation time and two different transverse relaxation times, which are inversely proportional to the variances of the two quadrature phases of the incident light. With sufficient reduction of one variance, the corresponding relaxation time can be made arbitrarily long. The two transverse decay times are observable in the spectrum of the fluorescent light, thus providing measure of the squeezing in the incident light.
By reduction of the electromagnetic field fluctations in one quadrature phase, squeezed light can inhibit the phase decay of an atom. This gives three relaxation times: the usual longitudinal relaxation time and two different transverse relaxation times, which are inversely proportional to the variances of the two quadrature phases of the incident light. With sufficient reduction of one variance, the corresponding relaxation time can be made arbitrarily long. The two transverse decay times are observable in the spectrum of the fluorescent light, thus providing measure of the squeezing in the incident light.
The inhibition of atomic phase decays by squeezed light, as first predicted by Gardiner [Phys. Rev. Lett. 56, 1917 (1986)], has yet to be confirmed experimentally. A major obstacle to such an experiment is the production of an effective squeezed-vacuum--atom coupling, so that the atom interacts only with squeezed modes of the radiation field. In this paper we propose the use of a microscopic plane-mirror Fabry-P\'erot cavity to effect a strong selection of modes coupling to the atom. It is shown that a significant reduction in fluctuations experienced by the atom can be achieved in one quadrature, with an input squeezed beam of modest angular dimensions, provided that the phase (and to lesser extent the amplitude) characteristics of the input beam are suitably matched to the cavity.
The behavior of a two-level atom confined within a cavity, pumped by an intense external field, and damped by a squeezed vacuum reservoir is studied. When the lowest squeezed quadrature of the vacuum is in phase with the pumping field, the relaxation time of the population inversion and of the polarization quadratures of the atom are appreciably enlarged, and hence the atom is decoupled from the reservoir. The effects of finite bandwidth of the squeezing are analyzed and it is shown that they can be used to improve the decoupling.
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 inhibition of atomic-phase decays by squeezed light, and consequent line narrowing, is reexamined for the case of finite-bandwidth squeezing, as produced in the output of a degenerate parametric amplifier. The extension of previous work to incorporate the effect of nonwhite, or colored, noise is accomplished via an adjoint equation, which gives the time evolution of a matrix functional of the incoming field. Simple equations for atomic variables are derived in which noise operators are defined so as to commute with each other and with all other quantities. This facilitates the reduction of a purely quantum-mechanical problem to a classical problem, solvable by classical stochastic-approximation methods. In particular, small-noise-approximation methods and simulations are carried out for a wide range of parameters describing the squeezed-field input. The method of simulation is extended to the computation of correlation functions and spectra for a realistically achievable set of parameters, with consideration given to reflections of the input in the emitted light. The fundamental effect is confirmed, and modifications to previous results are given.
Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.
The long-time behavior of squeezing of intense coherent light is studied with off-resonance Jaynes-Cummings model. The interaction between field and atom includes both one-photon transition type and two-photon transition type. The analytical formulae for quadrature variances are obtained. In one-photon transition case, small detuning only has small effect on squeezing. For two-photon transition, however, the situation is quite different. No squeezing will occur in resonance case. Only detuning can cause squeezing. Then a series of minimum appear in the suppressed quadrature variance during time evolution. In Urge N limit this se-ries tends to zero.