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Physical Review A

Noise in dead zones

Avia Rosenhouse‐Dantsker, A. D. Wilson‐Gordon, Harry Friedmann

Published Dec 1, 1995• 6 citations
Publisher

Abstract

We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system in the Doppler-broadening limit in which the so-called ``dead zone'' of the absorption spectrum is formed. We find that the plot of the noise as a function of the pump-probe detuning (which we shall refer to as the ``noise spectrum'') is hardly affected by the Doppler broadening for the case of a resonant pump. It consists of a large central peak flanked by two smaller peaks at the edges of the dead zone, which are at the Rabi sideband frequencies. Thus the dead zone, which is produced when absorption and gain regions of the absorption spectrum are averaged by Doppler broadening, is a rather noisy region, indicating the occurrence of many competing absorption and emission processes. The probe noise spectrum for a detuned pump is quite different in the presence and absence of Doppler broadening as is the absorption spectrum. On Doppler broadening the absorption spectrum consists of a dead zone centered at the Rayleigh resonance frequency with asymmetric absorption peaks on either side. The noise spectrum has a peak at the center with two sidebands at the edges of the dead zone. The sidebands are of almost the same intensity for short path lengths, but the peak on the side of the three-photon scattering becomes larger than the other peak as the path length increases.

DOI
10.1103/physreva.52.4839

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We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system at points of zero absorption and in the dead-zone. We find that in the Doppler-limit, maximum noise is obtained at the extremum point of the probe dispersion curve as a function of the pump intensity. This implies that in this limit, the noise is maximal at the transition point between focusing and defocusing. On the other hand, in the absence of Doppler broadening, this is true only for the case of a resonant pump.

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A comprehensive study is made of the absorption spectrum of a weak-probe beam irradiating a two-level atom damped by a broadband squeezed vacuum and driven by a strong laser field. We show that for a resonant driving field whose phase does not coincide with the principal directions of the squeezing ellipse, the absorption spectrum is asymmetric and exhibits absorption-emission profiles at the Rabi sidebands. We find that this feature arises from unequal populations of the dressed states of the system, which occur when all components of the Bloch vector are coupled to the driving field. A symmetric spectrum with dispersionlike profiles at the Rabi sidebands is revealed for an off-resonant driving field. Furthermore, the spectrum may exhibit an emission profile at the central frequency, signifying an amplification of the probe beam. We point out that the amplification at the central component is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. We find that the amplification originates from the coherent population oscillations and is impossible in the absence of the squeezed vacuum. In addition, we examine how these features are affected by the detuning of the driving field and an imperfect squeezed vacuum.

Physical Review A•Nov 1, 1995•31 citations
We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system in the Doppler-broadening limit in which the so-called dead zone'' of the absorption spectrum is formed. We find that the plot of the noise as a function of the pump-probe detuning (which we shall refer to as the noise spectrum'') is hardly affected by the Doppler broadening for the case of a resonant pump. It consists of a large central peak flanked by two smaller peaks at the edges of the dead zone, which are at the Rabi sideband frequencies. Thus the dead zone, which is produced when absorption and gain regions of the absorption spectrum are averaged by Doppler broadening, is a rather noisy region, indicating the occurrence of many competing absorption and emission processes. The probe noise spectrum for a detuned pump is quite different in the presence and absence of Doppler broadening as is the absorption spectrum. On Doppler broadening the absorption spectrum consists of a dead zone centered at the Rayleigh resonance frequency with asymmetric absorption peaks on either side. The noise spectrum has a peak at the center with two sidebands at the edges of the dead zone. The sidebands are of almost the same intensity for short path lengths, but the peak on the side of the three-photon scattering becomes larger than the other peak as the path length increases.
We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system at points of zero absorption and in the dead-zone. We find that in the Doppler-limit, maximum noise is obtained at the extremum point of the probe dispersion curve as a function of the pump intensity. This implies that in this limit, the noise is maximal at the transition point between focusing and defocusing. On the other hand, in the absence of Doppler broadening, this is true only for the case of a resonant pump.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.
We have considered the excitation spectra for a three-level atom interacting simultaneously with a strong pump field and a weak signal field. The atom consists of an upper excited state ‖2〉 and two lower states ‖1〉 and ‖3〉 where the transition ‖1〉↔‖3〉 is electric-dipole forbidden from parity considerations. The pump field, whose frequency mode ωb is initially populated, operates near resonance between the states ‖2〉 and ‖3〉, ‖2〉↔‖3〉, while the signal field describes the radiative decays ‖2〉→‖3〉 and ‖2〉→‖1〉, respectively. Using the Green function method, the spectral functions for the signal field have been calculated in the limit of high photon densities of the pump field describing the following processes: (i) one-photon process; the spectra consist of a main peak at the signal frequency ω=ω21 and a pair of sidebands at ω=ω21±Ω−(ω23−ωb)/2, where Ω2=Ω2b/2+(ω23−ωb)2/4 with Ωb and (ω23−ωb) being the Rabi frequency and the detuning of the pump field, respectively. The intensity of the main peak at ω=ω21 is positive indicating signal-field absorption while those of the sidebands are always negative implying amplification (stimulated emission) of the signal field. The sum of the intensities (in absolute value) of the sidebands is twice that of the main peak at resonance while in the off-resonance case it depends on the value of the ratio (ω23−ωb)/2Ω. (ii) Stimulated three-photon process; the spectra consists of a pair of sidebands peaked at ω=ω21−2ωb±Ω−(ω23−ωb)/2 whose intensity is negative indicating amplification. At resonance the sidebands have equal intensities but at finite detuning asymmetry arises enhancing one peak while diminishing the intensity of the other. (iii) Stimulated two-photon process; the stimulated Raman spectra consist of a peak at ω=ω31, which has a delta function distribution, and a pair of strongly amplified sidebands at ω=ω31±Ω+(ω23−ωb)/2. The computed spectra for the three processes are presented graphically for different values of Rabi frequencies and detunings.
The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.
A comprehensive study is made of the absorption spectrum of a weak-probe beam irradiating a two-level atom damped by a broadband squeezed vacuum and driven by a strong laser field. We show that for a resonant driving field whose phase does not coincide with the principal directions of the squeezing ellipse, the absorption spectrum is asymmetric and exhibits absorption-emission profiles at the Rabi sidebands. We find that this feature arises from unequal populations of the dressed states of the system, which occur when all components of the Bloch vector are coupled to the driving field. A symmetric spectrum with dispersionlike profiles at the Rabi sidebands is revealed for an off-resonant driving field. Furthermore, the spectrum may exhibit an emission profile at the central frequency, signifying an amplification of the probe beam. We point out that the amplification at the central component is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. We find that the amplification originates from the coherent population oscillations and is impossible in the absence of the squeezed vacuum. In addition, we examine how these features are affected by the detuning of the driving field and an imperfect squeezed vacuum.