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Physical Review A

Laser oscillation and light entanglement via dressed-state phase-dependent electromagnetically induced transparency

Jingyan Li, Xiangming Hu

Published Nov 30, 2009• 10 citations
Publisher

Abstract

We show that it is possible to achieve laser oscillation and two-mode entanglement by using dressed-state phase-dependent electromagnetically induced transparency (EIT) in a double $\ensuremath{\Lambda}$ system. Under certain conditions, two beams of bichromatic fields induce the depopulation of a coherent superposition state of the two excited states and the quantum beat of a pair of cavity fields. While one of two beams of bichromatic fields dresses the atoms, the other and the pair of cavity fields are in phase-controlled EIT interaction with the dressed atoms. On the basis of this, the pair of cavity fields not only operates well above threshold and exhibit subshot noise but also is in an entangled state. This mechanism suggests an efficient way to achieve bright entangled source of light.

DOI
10.1103/physreva.80.053829

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We show that it is possible to achieve laser oscillation and two-mode entanglement by using dressed-state phase-dependent electromagnetically induced transparency (EIT) in a double \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system. Under certain conditions, two beams of bichromatic fields induce the depopulation of a coherent superposition state of the two excited states and the quantum beat of a pair of cavity fields. While one of two beams of bichromatic fields dresses the atoms, the other and the pair of cavity fields are in phase-controlled EIT interaction with the dressed atoms. On the basis of this, the pair of cavity fields not only operates well above threshold and exhibit subshot noise but also is in an entangled state. This mechanism suggests an efficient way to achieve bright entangled source of light.
We examine the field-field and field-atom entanglements generated by \ensuremath{\Lambda}-type three-level atoms placed in an optical cavity driven above threshold by two coherent input optical fields. It is shown that under realistic experimental conditions entanglement between the two output cavity fields as well as between the fields and the atoms can be achieved when the two cavity fields are both one- and two-photon (Raman) resonant with the atomic transitions, as in the configuration for electromagnetically induced transparency (EIT). The entanglement has similar features to pump-signal-idler three-color entanglement in an above-threshold optical parametric oscillator [Villar et al., Phys. Rev. Lett. 97, 140504 (2006)]. This cavity-enhanced atom-field cooperative coupling could enable convenient and efficient generation of bright, nondegenerate, narrow-band entangled fields, which may find potential applications in realistic quantum communications and networking protocols.
We analyse the possibilities for quantum state engineering offered by a model for Kerr-type nonlinearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [2002, Phys. Rev. A, 65, 33833]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows some insights into the generation of an entangled state of cavity modes.
We show that it is possible to obtain continuous variable entanglement for four optical fields via phase-dependent electromagnetically induced transparency in a four-level system in double-$\ensuremath{\Lambda}$ configuration. Due to quantum interference, the four fields constitute two quantum beats, behave as a pair of collective modes, and experience high cross Kerr nonlinearities. As a result, entanglement occurs between the two collective modes and between any two individual fields from the different collective modes.
We study atomic coherence and interference in four-level atoms confined in an optical cavity and explores the interplay between cavity QED and electromagnetically induced transparency (EIT). The destructive interference can be induced in the coupled cavity-atom system with a free-space control laser tuned to the normal mode resonance and leads to suppression of the normal mode excitation. Then by adding a pump laser coupled to the four-level atoms from free space, the control-laser induced destructive interference can be reversed and the normal mode excitation is restored. When the free-space control laser is tuned to the atomic resonance and forms a Λ-type EIT configuration with the cavity-atom system, EIT is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. With the free-space pump laser driving the cavity-confined atoms in a four-level configuration, the narrow transmission peak of the cavity EIT can be split into two peaks and the dressed intra-cavity dark states are created analogous to the dressed states in free space. We report experimental studies of such coherently coupled cavity-atom system realized with cold Rb atoms confined in an optical cavity and discuss possible applications in quantum nonlinear optics and quantum information science.
The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross-phase-modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, Phys. Rev. A 65, 33 833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schr\"odinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on nonlinear interaction via double EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a 50:50 beam splitter and two photodetectors. In order to show the entanglement of an entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.