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Optics Letters

Conditions to preserve quantum entanglement of quadrature fluctuation fields in electromagnetically induced transparency media

You-Lin Chuang, Ray‐Kuang Lee

Published May 7, 2009• 4 citations
Publisher

Abstract

We study the propagation of quantum fields through an electromagnetically induced transparency (EIT) medium with initially two squeezed and one coherent states. Conditions to preserve and to establish nonseparation criteria for perturbed quantized fluctuation fields are demonstrated. The results in this work provide a guideline for using EIT media as quantum light devices.

DOI
10.1364/ol.34.001537

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We study the propagation of quantum fields through an electromagnetically induced transparency (EIT) medium with initially two squeezed and one coherent states. Conditions to preserve and to establish nonseparation criteria for perturbed quantized fluctuation fields are demonstrated. The results in this work provide a guideline for using EIT media as quantum light devices.
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.
Beyond the adiabatic approximation, we develop a quantum theory for optical probe pulses propagating in electromagnetically-induced-transparency (EIT) media by including Langevin noise operators and asking the field operator to satisfy bosonic commutation relation. Influences on the degradation of quantum noise squeezing from optical depth of atomic ensemble, strength of control field, and ground-state decoherence are studied in the slow light, as well as storage and retrieval, for a squeezed probe pulse. Moreover, to give guidelines for realization of quantum interfaces based on EIT media, we demonstrate that the quantum squeezing of output probe pulses could be preserved with a stronger classical control field.
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.
Quantum entanglement is an essential ingredient for the absolute security of quantum communication. Generation of continuous-variable entanglement or two-mode squeezing between light fields based on the effect of electromagnetically induced transparency (EIT) has been systematically investigated in this work. Here, we propose a new scheme to enhance the degree of entanglement between probe and coupling fields of coherent-state light by introducing a two-photon detuning in the EIT system. This proposed scheme is more efficient than the conventional one, utilizing the ground-state relaxation (population decay or dephasing) rate to produce entanglement or two-mode squeezing which adds far more excess fluctuation or noise to the system. In addition, maximum degree of entanglement at a given optical depth can be achieved with a wide range of the coupling Rabi frequency and the two-photon detuning, showing our scheme is robust and flexible. It is also interesting to note that while EIT is the effect in the perturbation limit, i.e. the probe field being much weaker than the coupling field and treated as a perturbation, there exists an optimum ratio of the probe to coupling intensities to achieve the maximum entanglement. Our proposed scheme can advance the continuous-variable-based quantum technology and may lead to applications in quantum communication utilizing squeezed light.
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.