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Physical Review A

Dynamical interaction of an atomic oscillator with squeezed radiation inside a cavity

G. S. Agarwal, S. Dutta Gupta

Published Mar 1, 1989• 22 citations
Publisher

Abstract

The dynamical interaction of an oscillator with squeezed radiation inside a cavity is considered. Exact solution of the dynamical equation is presented using the Wigner function for the combined system of the atomic oscillator and the squeezed radiation. This solution enables us to study (i) relaxation of the oscillator for arbitrary bandwidth of the squeezed radiation, and (ii) effects of squeezed radiation on vacuum-field Rabi splittings. Explicit results for fluctuation spectra and the oscillator polarizabilities are given. New resonances in the fluctuation spectra appear as the radiation in the cavity becomes more and more squeezed. Strong narrowing of the vacuum-field Rabi splitting due to squeezed radiation is predicted. Very large enhancement of the oscillator polarizability at Rabi side peaks is also predicted. The modification of the cavity output due to the atomic oscillator is discussed.

DOI
10.1103/physreva.39.2961

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The dynamical interaction of an oscillator with squeezed radiation inside a cavity is considered. Exact solution of the dynamical equation is presented using the Wigner function for the combined system of the atomic oscillator and the squeezed radiation. This solution enables us to study (i) relaxation of the oscillator for arbitrary bandwidth of the squeezed radiation, and (ii) effects of squeezed radiation on vacuum-field Rabi splittings. Explicit results for fluctuation spectra and the oscillator polarizabilities are given. New resonances in the fluctuation spectra appear as the radiation in the cavity becomes more and more squeezed. Strong narrowing of the vacuum-field Rabi splitting due to squeezed radiation is predicted. Very large enhancement of the oscillator polarizability at Rabi side peaks is also predicted. The modification of the cavity output due to the atomic oscillator is discussed.
We have investigated the interaction of a single atom with a single mode of the radiation field in an ideal cavity when the field is initially in a squeezed-vacuum state. In particular, we present results for the spectrum of the emitted light and for the time evolution of the squeezing inside the cavity. Our results contrast sharply with previous studies of single two-level atom interaction with a continuum of squeezed-vacuum modes. In particular, the results are shown to be insensitive to the initial phase of the atomic dipole relative to the squeezed field, and the squeezing is destroyed by the coherent interaction, in a time essentially independent of the initial degree of squeezing. Most features of the spectrum are very similar to those predicted for an initial thermal state, although the two-peaked structure associated with vacuum-field Rabi splitting is more apparent for a squeezed state with a small average number of photons than for a thermal state with the same number of photons.
Analysis of the effects of a finite bandwidth squeezed input on the atomic dynamics and radiative properties of a coherently pumped two-level atom trapped in a resonant cavity is presented. It is found that the atom prefers to stay in the lower energy level more often at steady state regardless of the strength of the coherent radiation and squeezed input. Pronounced dipping in the population inversion occurs when the finiteness of the bandwidth of the reservoir modes is taken into consideration. Moreover, due to the narrowing of the bandwidth, the spectral width of the emitted radiation turns out to increase and the height of the central line to decrease with the strength of the squeezed input. The peaks of the sidebands become prominent and shifted side ways with the strength of the amplification constant of the parametric oscillation. It is also found that the emitted radiation exhibits photon anti-bunching, whereas the photon statistics oscillates between sub- and super-Poissonian. Unfortunately, the successively emitted cavity radiation does not exhibit squeezing despite the presence of the squeezed input.
Summary form only given. We extend the analytical technique to the case of a fully quantized dressed-atom model with a detuned driving laser field and incorporate the cavity effect on the fluorescence spectrum. We find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth squeezed vacuum only if there is nonzero squeezing at the Rabi sidebands. We show that this condition is readily achieved with a squeezed vacuum that is the output from a nondegenerate parametric oscillator, whereas for a squeezed vacuum that is the output from a degenerate parametric oscillator a squeezing bandwidth comparable to the Rabi frequency is required.
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 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 investigate effects that the presence of a second atom has on the dynamic characteristics of a field and an atom in a single-mode cavity, with particular reference to the nonclassical features of the atom–field interaction. The field statistics are marginally altered, but the field and the atomic dipole squeezing are significantly altered. The vacuum-field Rabi splitting, which produces only two peaks in the emission spectrum of an isolated atom, gives a far more complex spectrum when another atom is present in the cavity.