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Physical Review A

Transparency or spectral narrowing for two-mode squeezing and entanglement

Xiangming Hu, C. H. Oh

Published May 27, 2011• 4 citations
Publisher

Abstract

We analyze the nonadiabatic effects on the propagation of a two-mode squeezed field inside a medium of three-level $\ensuremath{\Lambda}$ atoms that display the dark resonance. We identify the different effects for the two-mode quantum properties: (i) unconditional transparency for the sum squeezing and (ii) induced transparency or spectral narrowing for the difference squeezing depending on the relative widths of the initial correlation spectrum to the transparency window. These effects combine to induce transparency or spectrum narrowing for the bipartite entanglement. The potential applications range from quantum information to laser spectroscopy and frequency standards.

DOI
10.1103/physreva.83.053842

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We analyze the nonadiabatic effects on the propagation of a two-mode squeezed field inside a medium of three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ atoms that display the dark resonance. We identify the different effects for the two-mode quantum properties: (i) unconditional transparency for the sum squeezing and (ii) induced transparency or spectral narrowing for the difference squeezing depending on the relative widths of the initial correlation spectrum to the transparency window. These effects combine to induce transparency or spectrum narrowing for the bipartite entanglement. The potential applications range from quantum information to laser spectroscopy and frequency standards.
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.
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.
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 effect of a dark state on the entanglement properties of the two-mode field from a laser-driven Λ-type three-level atomic system is investigated by taking into account the spontaneously generated coherence (SGC). When the dark state is present, it is found that the entanglement between the two cavity modes can be significantly enhanced compared to the case without the dark state. When the value of SGC is maximal, the dark state population depending on the initial values of the system can affect the entanglement dramatically. Moreover, the effects of a squeezed parameter and Rabi frequency on entanglement evolution are also presented in the presence of a dark state.
A quantum analysis of the interaction of two propagating, quasimonochromatic fields with three-level \ensuremath{\Lambda}-type atoms is presented. It is shown that the recently predicted effect of pulse matching [S. Harris, Phys. Rev. Lett. 70, 552 (1993)]--the generation of fields with matched Fourier components--is due to the nonadiabatic response of the medium. This effect leads to a correlation of the high-frequency phase fluctuations of the fields, and may therefore be used to reduce the noise in short-time measurements of phase differences.