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Optics Express

Analysis and optimization of channelization architecture for wideband slow light in atomic vapors

Zachary Dutton, Mark Bashkansky, Michael Steiner, John F. Reintjes

Published Jan 1, 2006• 16 citations
Publisher

Abstract

We carry out an analysis of an earlier proposed "channelization" architecture for wideband slow light propagation and pulse delays in atomic vapors using electromagnetically induced transparency (EIT). In the channelization architecture, a wideband input signal pulse is spatially dispersed in the transverse dimension, sent through an EIT medium consisting of an initially spin-polarized atomic vapor illuminated by a monochromatic, co-propagating pump laser, then spatially recombined. An inhomogenous magnetic field is used to Zeeman shift the atomic vapor into two-photon (Raman) resonance with the signal-pump transitions at all locations. Extending on previous analyses, we show in detail how the reconstructed pulse will be delayed only if a slight mis-match from the two-photon resonance is introduced. If the desired delay is taken as a constrained parameter, we find the bandwidth can be increased by large factor. We present an analytic treatment which optimizes the bandwidth given a desired delay and constraints on the pump power and focusing. We find bandwidth increases on the order of 5 times (100 MHz versus 20 MHz) should be possible for delays of interest (10 ns) to applications in telecommunications and radar. Interestingly, due to the mis-match requirement, we find the channelization can not increase the optimal delay-bandwidth product over conventional slow light.

DOI
10.1364/oe.14.004978

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Electromagnetically induced transparency (EIT) effect is an effective means to store light field into the atom ensemble. The extra noise introduced in the stored procedure can be suppressed greatly under the condition of large one-photon detuning and proper two-photon detuning. In this paper, we experimentally investigate the slow light and light storage in 87Rb vapor by using EIT effect, and study the effects of the two-photon detuning on light pulse delay and light memory at 650 MHz one-photon red detuning. In order to avoid some unwanted effects under the high optical depth condition, such as four-wave mixing, etc., the temperature of the atomic cell is controlled at 65 degrees Celsius. The experimental results show that the delay and the retrieval signals are significant in a two-photon detuning range from 0 to 0.5 MHz. The pulse delay decreases with the increase of two-photon detuning. The delay is 0.36 ups at two-photon resonance, and it is 0.07 ups at 1 MHz two-photon detuning. We simulate the delayed light pulse by using a three-level -type EIT model. The shapes of the measured slow light are in agreement with the theoretical results. The retrieval signals are observed at different two-photon detunings. The shapes of the retrieval pulses change with the two-photon detuning. The shape variations of the retrieval pulses cannot be explained by the three-level EIT theoretical model. By considering the atomic Zeeman sublevels interacting with the left-circular and right-circular polarized components of probe and coupling fields, multiple -type EIT systems will be formed. The interference between the retrieval signals from multiple EIT subsystems causes the shape distortions of retrieval pulses. The retrieval efficiency is measured as a function of two-photon detuning. The retrieval efficiency oscillates, and multiple peaks appear with the increase of two-photon detuning. The first peak appears at two-photon resonance, and the second peak appears at 0.48 MHz two-photon detuning. Finally, we measure the retrieval efficiency as a function of the coupling power at 0.48 MHz two-photon detuning. The optimal retrieval efficiency reaches 25% when the coupling power is 100 mW. These results provide experimental reference for the quantum memory of continuous variables in the hot atom ensemble.

Acta Physica Sinica•Jan 1, 2016•3 citations
We carry out an analysis of an earlier proposed "channelization" architecture for wideband slow light propagation and pulse delays in atomic vapors using electromagnetically induced transparency (EIT). In the channelization architecture, a wideband input signal pulse is spatially dispersed in the transverse dimension, sent through an EIT medium consisting of an initially spin-polarized atomic vapor illuminated by a monochromatic, co-propagating pump laser, then spatially recombined. An inhomogenous magnetic field is used to Zeeman shift the atomic vapor into two-photon (Raman) resonance with the signal-pump transitions at all locations. Extending on previous analyses, we show in detail how the reconstructed pulse will be delayed only if a slight mis-match from the two-photon resonance is introduced. If the desired delay is taken as a constrained parameter, we find the bandwidth can be increased by large factor. We present an analytic treatment which optimizes the bandwidth given a desired delay and constraints on the pump power and focusing. We find bandwidth increases on the order of 5 times (100 MHz versus 20 MHz) should be possible for delays of interest (10 ns) to applications in telecommunications and radar. Interestingly, due to the mis-match requirement, we find the channelization can not increase the optimal delay-bandwidth product over conventional slow light.
We propose a "channelization" architecture to achieve wide-band electromagnetically induced transparency (EIT) and ultra-slow light propagation in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong, resonant "pump" laser on the atomic medium, which allows slow and unattenuated propagation of a weaker "signal" beam, but only when a two-photon resonance condition is satisfied. Our wideband architecture is accomplished by dispersing a wideband signal spatially, transverse to the propagation direction, prior to entering the atomic cell. When particular Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic field with a linear gradient such that the two-photon resonance condition is satisfied for each individual frequency component. Because slow light is a group velocity effect, utilizing differential phase shifts across the spectrum of a light pulse, one must then introduce a slight mismatch from perfect resonance to induce a delay. We present a model which accounts for diffusion of the atoms in the varying magnetic field as well as interaction with levels outside the ideal three-level system on which EIT is based. We find the maximum delay-bandwidth product decreases with bandwidth, and that delay-bandwidth product 1 should be achievable with bandwidth 50 MHz (5 ns delay). This is a large improvement over the 1 MHz bandwidths in conventional slow light systems and could be of use in signal processing applications.
We experimentally demonstrate a proof-of-principle of a previously proposed ``channelization'' architecture for wideband slow-light propagation in atomic vapors using electromagnetically induced transparency (EIT). We use two optical frequencies to generate a sine wave signal which is delayed in rubidium vapor. The optical frequencies were tuned near the EIT resonances of two Zeeman sublevels, which are shifted from each other well beyond the EIT linewidth by a uniform magnetic field. We varied the Zeeman shift between these two levels (relative to the optical frequency splitting) and measured the delay versus Zeeman shift. Significant delays were observed and were in agreement with a theoretical model treating each Zeeman sublevel as part of an independent three-level system. We achieved delay of a signal with a bandwidth 16 times the EIT linewidth and confirmed our earlier theoretical models that delay occurs only when the optical spectral separation slightly exceeds the Zeeman splitting.
Specially designed focusing of light beams has been proposed as a means of improving the performances of optical buffers based on cells containing hot atomic vapors (e.g., rubidium vapor). There is also a companion proposal improve performance by use of incoherent optical pumping under suitable conditions. Regarding the proposal use focusing: The utility of atomic-vapor optical buffers as optical storage and processing devices has been severely limited by nonuniform spatial distributions of intensity in optical beams, arising from absorption of the beams as they propagate in atomic-vapor cells. Such nonuniformity makes it impossible the physical conditions throughout a cell, thereby making it impossible the performance of the cell as an optical buffer. In practical terms simplified for the sake of brevity, to optimize as used here means design the cell so as maximize the group delay of an optical pulse while keeping the absorption and distortion of the pulse reasonably small. Regarding the proposal use incoherent optical pumping: For reasons too complex describe here, residual absorption of light is one of the main impediments achievement of desirably long group delays in hot atomic vapors. The present proposal is directed toward suppressing residual absorption of light. The idea of improving the performance of slow-light optical buffers by use of incoherent pumping overlaps somewhat with the basic idea of Raman-based slow-light systems. However, prior studies of those systems did not quantitatively answer the question of whether the performance of an atomic vapor or other medium that exhibits electromagnetically induced transparency (EIT) with Raman gain is superior that of a medium that exhibits EIT without Raman gain.
In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.
Electromagnetically-induced transparency (EIT) in three-level Λ-systems is based on quantum interference effects involving coherence between the two lower levels, which allow propagation of a resonant probe light beam in the presence of a strong coupling field. We have observed transparency in ultra-narrow (<10 kHz) windows at the resonant 1.083 μm transition for purely electronic spins in gaseous 4 He* at room temperature. Slow light is an interesting outcome of the EIT phenomenon due to extreme dispersion within the narrow transparency window. We have obtained group delays of about 4 μs in a 2.5 cm long He* cell. A complete theoretical analysis explains our observations emphasizing the positive role of collisions. Slow light with 1-GHz Doppler broadening opens the door to applications of controllable large-bandwidth delays in radars.
Electromagnetically induced transparency (EIT) effect is an effective means to store light field into the atom ensemble. The extra noise introduced in the stored procedure can be suppressed greatly under the condition of large one-photon detuning and proper two-photon detuning. In this paper, we experimentally investigate the slow light and light storage in 87Rb vapor by using EIT effect, and study the effects of the two-photon detuning on light pulse delay and light memory at 650 MHz one-photon red detuning. In order to avoid some unwanted effects under the high optical depth condition, such as four-wave mixing, etc., the temperature of the atomic cell is controlled at 65 degrees Celsius. The experimental results show that the delay and the retrieval signals are significant in a two-photon detuning range from 0 to 0.5 MHz. The pulse delay decreases with the increase of two-photon detuning. The delay is 0.36 ups at two-photon resonance, and it is 0.07 ups at 1 MHz two-photon detuning. We simulate the delayed light pulse by using a three-level -type EIT model. The shapes of the measured slow light are in agreement with the theoretical results. The retrieval signals are observed at different two-photon detunings. The shapes of the retrieval pulses change with the two-photon detuning. The shape variations of the retrieval pulses cannot be explained by the three-level EIT theoretical model. By considering the atomic Zeeman sublevels interacting with the left-circular and right-circular polarized components of probe and coupling fields, multiple -type EIT systems will be formed. The interference between the retrieval signals from multiple EIT subsystems causes the shape distortions of retrieval pulses. The retrieval efficiency is measured as a function of two-photon detuning. The retrieval efficiency oscillates, and multiple peaks appear with the increase of two-photon detuning. The first peak appears at two-photon resonance, and the second peak appears at 0.48 MHz two-photon detuning. Finally, we measure the retrieval efficiency as a function of the coupling power at 0.48 MHz two-photon detuning. The optimal retrieval efficiency reaches 25% when the coupling power is 100 mW. These results provide experimental reference for the quantum memory of continuous variables in the hot atom ensemble.