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Physical Review A

Theory of intracavity atom-field interactions with squeezed inputs

T. A. B. Kennedy, Daniel F. Walls

Published Sep 1, 1990• 17 citations
Publisher

Abstract

We give a general theory of the interaction of a large number of two-level atoms in an optical cavity driven by a broadband squeezed input of finite amplitude. No adiabatic elimination of atoms or field is made, and atomic and cavity loss and dispersion are fully incorporated in the theory. We calculate the optical and squeezing spectra that may be observed in transmission and reflection from the cavity; the latter exhibits a novel interference structure superimposed as a result of the squeezed input. Results presented indicate that it is possible to somewhat reduce the vacuum Rabi peaks in transmission, in the strong-coupling regime, with a moderately squeezed input. In the limit of a ``bad cavity,'' the characteristic triplet transmitted under conditions of saturation may have one of its sidebands suppressed and the other enhanced by a squeezed input. These signatures suggest new alternatives for the experimental study of the interaction of atoms with squeezed light.

DOI
10.1103/physreva.42.3051

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We give a general theory of the interaction of a large number of two-level atoms in an optical cavity driven by a broadband squeezed input of finite amplitude. No adiabatic elimination of atoms or field is made, and atomic and cavity loss and dispersion are fully incorporated in the theory. We calculate the optical and squeezing spectra that may be observed in transmission and reflection from the cavity; the latter exhibits a novel interference structure superimposed as a result of the squeezed input. Results presented indicate that it is possible to somewhat reduce the vacuum Rabi peaks in transmission, in the strong-coupling regime, with a moderately squeezed input. In the limit of a ``bad cavity,'' the characteristic triplet transmitted under conditions of saturation may have one of its sidebands suppressed and the other enhanced by a squeezed input. These signatures suggest new alternatives for the experimental study of the interaction of atoms with squeezed light.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
We consider a two-level atom in an optical cavity driven by a coherent field and coupled to broadband squeezed vacuum. In the bad-cavity limit, the cavity field can be adiabatically eliminated, leaving equations of motion for atomic operators similar to those of free-space resonance fluorescence. We calculate the incoherent spectrum of the fluorescent light field and find that the cavity-enhanced spontaneous emission can be suppressed, and a subnatural linewidth obtained, for the correct choice of the phase of the squeezed input relative to the coherent driving field.
Summary form only given. We consider a single two-level atom inside a resonant optical cavity, with cavity loss rate K, atomic fluorescence rate into noncavity modes A, and atom-field coupling g. For large atom cavity coupling (g>A, K) and weak driving fields, the fluorescence from this system exhibits a splitting of the spectral line, known as vacuum-Rabi splitting. When the cavity loss rate is the largest rate in the problem (K>A, g), the fluorescent spectrum is Lorentzian with a cavity-enhanced width. We examine the regime where A>g>K, and find that the spectrum exhibits a hole at line center as a result of quantum interference effects. This effect is formally identical to the phenomenon of electromagnetically induced transparency (EIT) in multilevel atomic systems. We discuss the relationship of these spectral holes to the presence of squeezing in the intracavity field, and present results also for the emission spectra, and incoherent spectra in transmission and fluorescence.
One of the canonical questions in quantum optics is the nature of the radiative properties of an atom when the normal vacuum fluctuations of the electromagnetic reservoir are replaced by the asymmetric, reduced fluctuations of a squeezed vacuum. While the basic radiative linewidth-narrowing effect has been known for over a decade [C. W. Gardiner, Phys. Rev. Lett. 56, 1917 (1986)], experimental realizations with operationally definable definitive manifestations of the quantum nature of the squeezed reservoir have been largely lacking from subsequent investigations. This paper presents measurements on an experimentally realized atom--squeezed-light system, in which the squeezed-light output of a subthreshold optical parametric oscillator illuminates an atom strongly coupled to a high-finesse optical resonator. Transmission of a weak probe field incident on the atom-cavity system is investigated both theoretically and experimentally. Alteration of the transmitted probe spectrum has been observed, as has a transmission modulation that depends on the phase of the squeezed field relative to a saturating coherent field (displaced squeezing). In certain parameter regimes, properties unique to the quantum nature of the squeezed light have been identified in the theoretical treatment, but complications in the experiment prevent their unequivocal measure. It is found that the observed effects of the squeezed light are dramatically reduced relative to the predictions of an idealized theory. This is quantitatively attributed to the effects of atomic beam fluctuations and a simple modeling of the atomic beam as an additional loss mechanism in the theory leads to reasonable agreement with the data.
We calculate the gain at the central frequency for a three-level Λ configuration in a bad cavity with a squeezed input. We show that it is possible to obtain the same effects as in the case of the driven three-level Λ system in a free space and damped to a broadband squeezed vacuum. We also show that the coherence induced by the broadband squeezed vacuum can be generated in the case of an input squeezed vacuum. Our results deal with the three-level Λ system and we can easily generalize to the other possible atomic configurations such as V and cascade.
A cavity QED system is analysed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three-or four-level Λ configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effective two-level atom interacting exclusively with a squeezed reservoir. However, the inclusion of a fourth atomic level, coupled dispersively to one of the two ground states by an auxiliary laser field, introduces an extra degree of freedom and enables the desired interaction to be realized. As a means of detecting the reduced quadrature decay rate of the effective two-level system, we examine the transmission spectrum of a weak coherent probe field incident upon the cavity. The extension to multiple atoms is also considered and we show that such a cavity QED system may also duplicate the dynamics of an ensemble of two-level atoms collectively coupled to broadband squeezed light.