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arXiv:0712.1805 · Physical Review A

Quantum control of electromagnetically induced transparency dispersion via atomic tunneling in a double-well Bose-Einstein condensate

James Owen Weatherall, Christopher P. Search, M. Jääskeläinen

Published Jul 21, 2008• 7 citations
arXivHTMLPDF

Abstract

Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level $\ensuremath{\Lambda}$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\ensuremath{\Omega}}_{\ensuremath{\mu}}$, as in standard EIT systems. Tunneling between the wells at the frequency $g$ provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by $g$. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.

DOI
10.1103/physreva.78.013830

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Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency \ensuremathΩ\ensuremathμ{\ensuremath{\Omega}}_{\ensuremath{\mu}}\ensuremathΩ\ensuremathμ​, as in standard EIT systems. Tunneling between the wells at the frequency ggg provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by ggg. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.
Electromagnetically induced transparency is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity.Here we consider electromagnetically induced transparency in an atomic Bose-Einstein condensate trapped in a double well potential.One well is prepared as in standard electromagnetically induced transparency with a weak probe laser and control laser in a Λ configuration while tunneling between the wells provides a coherent coupling between identical electronic states in the two wells leading to the formation of spatially delocalized inter-well dressed states.The macroscopic inter-well coherence of the Bose-Einstein condensate wave function qualitatively modifies the normal electromagnetically induced transparency linear susceptibility and leads to the formation of additional absorption resonances and larger dispersion than electromagnetically induced transparency.We show that these new resonances can be interpreted in terms of the inter-well dressed states and the formation of a novel type of dark state involving the control laser and the inter-well tunneling.
We offer a general treatment of electromagnetically induced transparency (EIT) in a five level system consisting of four metastable ground states. Two additional rf-microwave fields coherently couple the two ground states of the standard EIT $\ensuremath{\Lambda}$ atom to a pair of additional hyperfine states in the ground state manifold, generating two sets of dressed states that interact via the probe and control lasers, which couple to the electronic excited state. These new hyperfine dressed states manifest themselves in the linear optical susceptibility of the probe as new resonances in addition to the Autler-Townes doublet characteristic of EIT. In particular, we show that the existence of two new narrow resonances, whose width are limited only by ground state decoherence, appear inside the normal EIT transparency window. We show that by controlling the intensity of these rf-microwave fields, one can engineer both the position and width of these narrow resonances and thereby exercise additional control over both the dispersion and group velocity of the probe.
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.
In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser, and a strong classical coupling laser, which form a three-level $\ensuremath{\Lambda}$-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and interatomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.
The interaction of a weak probe laser with an inverted Y-type four-level atomic system driven by two additional coherent fields is investigated theoretically. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. The propagation of the probe field can be switched from superluminal near the resonance to subluminal on resonance within the single transparency window when two coupling lasers are on resonance. We propose an atomic 87Rb system for experimental observation.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.