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International Laser Science Conference

Transformation of coherent states of the electromagnetic field to quasi-Fock states

Valentine I. Zakharov

Published Jan 1, 1986• 0 citations
Publisher

Abstract

The possibility of a practically total reduction of quantum photon fluctuations in cw laser radiation is discussed. This effect appears as a result of two-photon radiation absorption using a resonance transition in atoms excited from the ground state to the upper level, relaxing to the other states. For this case the possibility of induced two-photon emission is excluded, that is, the source of additional photon number fluctuations in a field mode.1 In this process the Fock states with the photon number n ≥ 2 are continuously reduced from the coherent state of the excited field. For the large time values of interaction the Fock states |n = 0 > and |n = 1> remain in the field. The effect of spin orientations of photons of the excited field on the quantum noise reduction process for the two-photon absorption by atoms on the transitions between the S → S and S → D terms is analyzed. The possibility of transformation of coherent and thermal fields (λ ≃ 6022 Å and λ = 5787 Å) into quasi-Fock states, as a result of its two-photon resonance absorption by Na homogeneous vapor, is considered.

DOI
10.1364/ils.1986.thl15

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The possibility of a practically total reduction of quantum photon fluctuations in cw laser radiation is discussed. This effect appears as a result of two-photon radiation absorption using a resonance transition in atoms excited from the ground state to the upper level, relaxing to the other states. For this case the possibility of induced two-photon emission is excluded, that is, the source of additional photon number fluctuations in a field mode.1 In this process the Fock states with the photon number n ≥ 2 are continuously reduced from the coherent state of the excited field. For the large time values of interaction the Fock states |n = 0 > and |n = 1> remain in the field. The effect of spin orientations of photons of the excited field on the quantum noise reduction process for the two-photon absorption by atoms on the transitions between the S → S and S → D terms is analyzed. The possibility of transformation of coherent and thermal fields (λ ≃ 6022 Å and λ = 5787 Å) into quasi-Fock states, as a result of its two-photon resonance absorption by Na homogeneous vapor, is considered.
This paper discusses the principles of reduction of quantum noise in optical radiation. The dynamics of photon number fluctuations in direct and cascade two-photon processes is investigated. The paper considers the cases of absorption and emission for the fields originally prepared in coherent and thermal states. It is shown that photon antibunching and bunching should occur for the passed radiation. The photon antibunching effect is only in definite time intervals of field interaction with resonance absorbing or emitting systems. The possible cases of accumulation of photon antibunching effects are considered.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.
We have considered the induced processes that occur in a driven two-level atom, where a laser photon is absorbed and emitted by the ground and by the excited states of the atom, respectively. In the low-intensity limit of the laser field, the induced spectra arising when a laser photon is absorbed by the ground state of the atom consist of two peaks describing induced-absorption and stimulated-emission processes, respectively, where the former prevails over the latter. Asymmetry of the spectral lines occurs at off-resonance and its extent depends on the detuning of the laser field. The physical, process where a laser photon is emitted by the excited state is the reverse of that arising from the absorption of a laser photon by the ground state of the atom. The former differs from the latter in that the emission of a laser photon by the excited state occurs in the low-frequency regime and that the stimulated-emission process prevails over that of the induced absorption. In this case, amplification of ultrashort pulses is likely to occur without the need of population inversion between the optical transitions. The computed spectra are graphically presented and discussed.
Summary form only given. The destructive quantum interference of resonantly excited transitions within a lambda-system in case of two photon resonance leads to a medium, which is coherently prepared in a superpositional dark state. The corresponding distinct enhancement of radiation transmission is well known as electromagnetically induced transparency. Interaction of quantized fields with such a medium yields a correlation of quantum phase fluctuations of the fields even for independent cw lasers. The experiments are done on the Na D/sub 1/ line by means of a temperature stabilized sodium vapor cell. One frequency component is modulated by a broad spectrum of phase fluctuations of about 50 MHz width by means of an electrooptical phase modulator driven by a noise generator. A transfer of noise to the other frequency components within a lambda- or a closed double-lambda transition scheme during transmission through the dark state medium is observed using the heterodyne spectroscopy. The verified exponential decay of the width of the beat signal in dependence on the medium optical density proofs the noise transfer and hence the correlation of phase fluctuations between the corresponding frequency components. This behaviour as well as the different limits of decay for lambda- (towards the transparency linewidth) and closed double-lambda (towards zero) scheme is in good qualitative agreement with the theory.
Summary form only given. The destructive quantum interference of resonantly excited transitions within a lambda-system in case of two photon resonance leads to a medium, which is coherently prepared in a superpositional dark state. The corresponding distinct enhancement of radiation transmission is well known as electromagnetically induced transparency. Interaction of quantized fields with such a medium yields a correlation of quantum phase fluctuations of the fields even for independent cw lasers. The experiments are done on the Na D/sub 1/ line by means of a temperature stabilized sodium vapor cell. One frequency component is modulated by a broad spectrum of phase fluctuations of about 50 MHz width by means of an electrooptical phase modulator driven by a noise generator. A transfer of noise to the other frequency components within a lambda- or a closed double-lambda transition scheme during transmission through the dark state medium is observed using the heterodyne spectroscopy. The verified exponential decay of the width of the beat signal in dependence on the medium optical density proofs the noise transfer and hence the correlation of phase fluctuations between the corresponding frequency components. This behaviour as well as the different limits of decay for lambda- (towards the transparency linewidth) and closed double-lambda (towards zero) scheme is in good qualitative agreement with the theory.