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Physical Review A

Quantum theory for pulse propagation in electromagnetically-induced-transparency media beyond the adiabatic approximation

You-Lin Chuang, Ite A. Yu, Ray‐Kuang Lee

Published Jun 16, 2015• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.91.063818

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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 examine the interaction of a weak probe with NNN atoms in a $\ensuremath{\Lambda}$-level configuration under the conditions of electromagnetically induced transparency (EIT). In contrast to previous works on EIT, we calculate the output state of the resultant slowly propagating light field while taking into account the effects of ground state dephasing and atomic noise for a more realistic model. In particular, we propose two experiments using slow light with a nonclassical probe field and show that two properties of the probe, entanglement and squeezing, characterizing the quantum state of the probe field, can be well-preserved throughout the passage.
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.
Quantum information systems require an interface between photons as a physical system to transport information and atoms which are better suited to store and process it. In this thesis the construction of a novel pulsed, bright and narrow-band light source is presented. It consists of an optical parametric oscillator featuring a periodically poled KTP crystal and a mechanical chopper and produces ?s-pulses of squeezed vacuum. The generated states are resonant to the Rubidium-DI-transition, are almost transform-limited and show more than 3 dB of squeezing. The physical effect of electromagnetically induced transparency (EIT) in hot rubidium vapor can be used to generate ultra-low group velocities and allows for a reversible adiabatic conversion of optical quantum states into collective spin excitations which can be used to stop pulses of light. I report about recent progress in slowing down a pulse of squeezed vacuum by one third of its width while still preserving 0.36 dB of squeezing in the process. I analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-A configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. A basis transformation of atomic and optical states which reduces the analysis of the system to that of electromagnetically induced transparency in a regular three-level configuration is presented. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by adiabatic control of the control fields and present a proof-of principle experiment to adiabatically transfer light between modes of different frequencies in Rb-87 vapor. To that end a digital phase lock circuit has been designed that allows to electronically phase lock an external-cavity diode laser to a reference laser over a 7 GHz frequency range with sub-Hertz precision.
We investigate the quantum squeezing of slow-light solitons generated in a $\mathrm{\ensuremath{\Lambda}}$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). Starting from the Heisenberg-Langevin and Maxwell equations governing the quantum dynamics of atoms and probe laser field, we derive a quantum nonlinear Schr\"odinger equation controlling the evolution of the probe-field envelope. By using a direct perturbation approach to diagonalize the effective Hamiltonian (where the atomic variables have been eliminated), we carry out a detailed calculation on the quantum fluctuations of a slow-light soliton, expanded as a superposition of the complete and orthonormalized set of eigenfunctions obtained by solving the Bogoliubov-de Gennes (BdG) equations describing the quantum fluctuations. We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.