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Journal of the Optical Society of America B

Manipulation of squeezed state in electromagnetically induced transparency system via dynamic Stark effect

Yuan Li, Zhonghua Li, Dan Wang, Jiangrui Gao, Junxiang Zhang

Published Oct 30, 2012• 2 citations
Publisher

Abstract

We calculate the delay time and noise spectrum of a squeezed state throughout an electromagnetically induced transparency medium with dynamic Stark splitting. It is shown that the noise spectrum splits into two parts with the same delay time, so that the delayed squeezing can survive well in two channels. Furthermore, we show that the two squeezing channels as well as the delay time can be manipulated via one-photon detuning and detection frequency such that the quantum state with high delay time and squeezing can be well preserved. This avoids the influence of large noise from laser near zero detection frequency.

DOI
10.1364/josab.29.003177

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We calculate the delay time and noise spectrum of a squeezed state throughout an electromagnetically induced transparency medium with dynamic Stark splitting. It is shown that the noise spectrum splits into two parts with the same delay time, so that the delayed squeezing can survive well in two channels. Furthermore, we show that the two squeezing channels as well as the delay time can be manipulated via one-photon detuning and detection frequency such that the quantum state with high delay time and squeezing can be well preserved. This avoids the influence of large noise from laser near zero detection frequency.
One of the important applications of electromagnetically induced transparency (EIT) is to delay and store light in atomic ensembles. In this paper, the noise spectrum of the delayed quantum light throughout an EIT medium is investigated. With zero detection frequency, we can have minimum noise of delayed light in two-photon resonance of EIT, and the noise is larger than the minimum noise at off two-photon resonance due to the phase-to-amplitude noise conversion. It is shown that the noise for nonzero detection frequency can be suppressed by operating the system at off two-photon resonance, even when the unavoidable dephasing is included.
We demonstrate experimentally the delay of squeezed light and entanglement using Electromagnetically Induced Transparency (EIT) in a rubidium vapour cell. We perform quadrature amplitude measurements of the probe field and find no appreciable excess noise from the EIT process. From input squeezing of 3.2+/-0.5 dB at low sideband frequencies, we observed the survival of 2.0+/-0.5 dB of squeezing at the EIT output. By splitting the squeezed light on a beam-splitter, we generated biased entanglement between two beams. We transmit one of the entangled beams through the EIT cell and correlate the quantum statistics of this beam with its entangled counterpart. We experimentally observed a 2.2+/-0.5 micros delay of the biased entanglement and obtained a preserved degree of wavefunction inseparability of 0.71+/-0.01, below the unity value for separable states.
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 $\ensuremath{\Lambda}$ 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.
We investigate the propagation and storage of a squeezed vacuum as the probe light in a collection of N four-level tripod configuration atoms under the condition of single or double electromagnetically induced transparency (EIT). The squeezing of the probe light is well preserved in both the single transparency channel and the double transparency one. On the other hand, the effects of the ground state dephasing rates on the propagation and storage of the squeezed vacuum are investigated. It is found that the maximum squeezing at the transparency points is suppressed by the dephasing rates in single or double EIT. Meanwhile, the mapping of the squeezing of the probe light onto the atomic ground coherences or onto the two atomic dark-state polaritons is also studied. In the absence of the Langevin atomic noise, the quasi-ideal squeezing transfer between the squeezed vacuum and the atomic ground coherences or the dark-state polaritons can be realized in such a system. When considering the Langevin atomic noise, the quantum characteristics of the atomic coherences at resonance are submerged by the Langevin noise, while in the scenario of the dark-state polariton, it is found that squeezing transfer onto one polariton is damaged, but the squeezing transfer onto the other polariton survives even in the presence of the Langevin noise.
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.