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arXiv:quant-ph/0609103 · Physical Review Letters

Opacity of Electromagnetically Induced Transparency for Quantum Fluctuations

Pablo Barberis-Blostein, Marc Bienert

Published Jan 18, 2007• 25 citations
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Abstract

We analyze the propagation of a pair of quantized fields inside a medium of three-level atoms in a Lambda configuration. We calculate the stationary quadrature noise spectrum of the field, in the case where the probe field is in a squeezed state and the atoms show electromagnetically induced transparency. We find an oscillatory transfer of the initial quantum properties between the probe and pump fields which is most strongly pronounced when both fields have comparable intensities. This implies that the quantum state measured after propagation can be completely different from the initial state, even though the mean values of the field are unaltered.

DOI
10.1103/physrevlett.98.033602

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European Quantum Electronics Conference (EQEC)•Apr 12, 2005•0 citations
We analyze the propagation of a pair of quantized fields inside a medium of three-level atoms in a Lambda configuration. We calculate the stationary quadrature noise spectrum of the field, in the case where the probe field is in a squeezed state and the atoms show electromagnetically induced transparency. We find an oscillatory transfer of the initial quantum properties between the probe and pump fields which is most strongly pronounced when both fields have comparable intensities. This implies that the quantum state measured after propagation can be completely different from the initial state, even though the mean values of the field are unaltered.
The propagation of a pair of quantized fields inside a medium of three-level atoms in the $\ensuremath{\Lambda}$ configuration is analyzed. We calculate the stationary quadrature noise spectrum of the field after propagating through the medium in the case where the field has a general (but small) noise spectrum and the atoms are in a coherent population trapping state and show electromagnetically induced transparency. Although the mean values of the field remain unaltered as the field propagates, there is an oscillatory interchange of noise properties between the probe and pump fields. Also, as the field propagates, there is an oscillatory creation and annihilation of correlations between the probe and pump quadratures. We further study the field propagation of squeezed states when there is two-photon resonance, but the field has a detuning $\ensuremath{\delta}$ from atomic resonance. We show that the field propagation is very sensitive to $\ensuremath{\delta}$. The propagation in this case can be explained as a combination of a frequency-dependent rotation of maximum squeezed quadrature with an interchange of noise properties between pump and probe fields. It is also shown that the effect of the Doppler width in a squeezed state propagation is considerable.
The interaction of a quantized field with three-level atoms in a $\ensuremath{\Lambda}$ configuration inside a two mode cavity is analyzed. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is in a squeezed state and the atoms show electromagnetically induced transparency. If the Rabi frequencies of both dipole transitions of the atoms are different from zero, we show that the output probe field has four maxima of squeezing absorption. We show that in some cases two of these frequencies can be very close to the transition frequency of the atom, in a region where the mean value of the field entering the cavity is hardly altered. Furthermore, part of the absorbed squeezing of the probe field is transferred to the pump field. For some conditions this transfer of squeezing can be complete.
The interaction of a quantized field with three-level atoms in $\ensuremath{\Lambda}$ configuration inside a two-mode cavity is analyzed in the small-noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency. The effect of the atoms' base level decoherence in the cavity output field is also studied. It is found that the output field is very sensitive to two-photon detuning.
Within the frame of quantized dark-state polaritons in electromagnetically induced transparency media, noise fluctuations in the quadrature components are studied. Squeezed state transfer, quantum correlation, and noise entanglement between probe field and atomic polarization are demonstrated in single- and double-Λ configurations, respectively. Even though a larger degree of the squeezing parameter in the continuous variable helps to establish stronger quantum correlations, the inseparability criterion is satisfied only within a finite range of the squeezing parameter. The results obtained in the present study may be useful for guiding experimental realization of quantum memory devices for applications in quantum information and computation.
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.