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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Double electromagnetically induced transparency and its application in quantum information

Zeng-Bin Wang, Karl-Peter Marzlin, Barry C. Sanders

Published Aug 31, 2006• 0 citations
Publisher

Abstract

Strong optical cross-phase modulation (XPM) for weak fields is tremendously important for optical quantum information (QI) processing and for all-optical switches in classical communication. A sufficiently large XPM would allow the design of deterministic controlled quantum gates for photonic qubits and thus enable universal optical quantum computation. Recently, several proposals have been brought forward to create large XPM using double electromagnetically induced transparency (DEIT) in which two weak signal light pulses travel at equally slow group velocity, but creating DEIT still poses an experimental challenge. We give a brief overview about DEIT and discuss its applications and limitations. A scheme that combines the best features of previous proposals and optimizes the large XPM parameter for DEIT schemes is outlined. Finally we devise a scheme to perform universal quantum information processing, which respects the bound on the achievable nonlinearity and addresses the requirement of quantum error correction.

DOI
10.1117/12.682572

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Strong optical cross-phase modulation (XPM) for weak fields is tremendously important for optical quantum information (QI) processing and for all-optical switches in classical communication. A sufficiently large XPM would allow the design of deterministic controlled quantum gates for photonic qubits and thus enable universal optical quantum computation. Recently, several proposals have been brought forward to create large XPM using double electromagnetically induced transparency (DEIT) in which two weak signal light pulses travel at equally slow group velocity, but creating DEIT still poses an experimental challenge. We give a brief overview about DEIT and discuss its applications and limitations. A scheme that combines the best features of previous proposals and optimizes the large XPM parameter for DEIT schemes is outlined. Finally we devise a scheme to perform universal quantum information processing, which respects the bound on the achievable nonlinearity and addresses the requirement of quantum error correction.
We report on the first experimental demonstration of low-light-level cross-phase modulation (XPM) with double slow light pulses based on the double electromagnetically induced transparency (EIT) in cold cesium atoms. The double EIT is implemented with two control fields and two weak fields that drive populations prepared in the two doubly spin-polarized states. Group velocity matching can be obtained by tuning the intensity of either of the control fields. The XPM is based on the asymmetric M-type five-level system formed by the two sets of EIT. Enhancement in the XPM by group velocity matching is observed. Our work advances studies of low-light-level nonlinear optics based on double slow light pulses.
Weak-light all-optical switches would enhance photonics capabilities and enable important optical quantum information processing tasks, but optical switching based on third-order optical nonlinearity is proving to be elusive and controversial. I discuss strategies to generate large cross-phase modulation by combining double electromagnetically induced transparency, competing atomic transitions, electron population engineering for pulse speed control, and using boundary conditions to confine the transverse field beyond the diffraction limit.
Large nonlinearity at the single-photon level can pave the way for the implementation of universal quantum gates. However, realizing large and noiseless nonlinearity at such low light levels has been a great challenge for scientists in the past decade. Here, we propose a scheme that enables substantial nonlinear interaction between two light fields that are both stored in an atomic memory. Semiclassical and quantum simulations demonstrate the feasibility of achieving large cross-phase modulation (XPM) down to the single-photon level. The proposed scheme can be used to implement parity gates from which CNOT gates can be constructed. Furthermore, we present a proof of principle experimental demonstration of XPM between two optical pulses: one stored and one freely propagating through the memory medium. Researchers have developed a new technique that shows promise for constructing optical quantum logic gates. Theoretical simulations performed by Mahdi Hosseini and co-workers from the Australian National University and Macquarie University in Australia show that inducing cross-phase modulation between two single-photon light fields stored in a rubidium atomic memory should provide large phase shifts and thus allow the realization of parity gates and CNOT gates, both of which are needed for quantum computing. The researchers estimate that using cold atoms confined in a dipole trap and short-duration single-photon wavepackets should make it possible to realize phase shifts of the order of 10 mrad — orders of magnitude larger than schemes that employ electromagnetically induced transparency.
We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.
This thesis summarizes my work on the interactions between light and matter in the context of optical quantum information processing. I have designed and implemented a phase-sensitive detection scheme for optical-frequency electromagnetic fields, which has been used to measure μrad phase shifts on nanosecond timescales. This phase measurement was developed for the express purpose of detecting cross-phase modulation (XPM), a key ingredient in the construction of optical logic gates. I have implemented the 'N-scheme', a form of XPM which exploits electromagnetically-induced transparency (EIT) and which was promised to yield 'giant' optical nonlinearities sufficient for all-optical quantum information processing. Using a cloud of laser-cooled 85Rb atoms as the nonlinear medium, I present the first ever experimental study of EIT-enhanced XPM in the controversial regime of broadband signal pulses and spectrally narrow EIT windows. The results of this experiment constitute a breakdown of the original proposal for EIT-enhanced XPM. In light of these findings, I conclude with a theoretical analysis of the feasibility of using N-scheme as implemented in our lab to perform a non-demolition measurement of a single photon (a crucial step when using XPM to generate a universal optical logic gate). While possible in principle, the experimental conditions necessary to achieve a signal-to-noise ratio above unity are found to be practically unrealistic, suggesting a more sophisticated scheme is necessary.
This study demonstrates that tripod atom-field electronic structure can yield rich electromagnetically induced transparency phenomena, even at room temperature. In particular, we introduce double double electromagnetically induced transparency (DDEIT), wherein signal and probe fields each have two transparency windows. Their group velocities can be matched in either the first or second pair of transparency windows. Moreover, signal and probe fields can each experience coherent Raman gain in the second transparency window. Our investigation has demonstrated that the self-phase modulation (SPM) and cross-phase modulation (XPM) vanish at the center of two transparency windows for resonant coupling field. However, the values of the XPM and SPM in the region of the second EIT window are improved by a factor of 100010001000 compared to their values in the region of the first EIT window under the same conditions, and have non-zero values at the center of the second EIT window for nonresonant coupling field. Additionally, we derive an analytical solution for the wave equation describing the propagation of the probe field whose amplitude-envelope function is described by the fundamental mode Laguerre-Gaussian function. Our solution exhibits that the group velocity of the probe field reduces as the field propagates through the medium. The group velocity reduction is a consequence of spatially-varying susceptibility. The variation of the susceptibility is established by employing signal field whose amplitude-envelope functions is also described by the fundamental mode Laguerre-Gaussian function. For Doppler-broadened media, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of electromagnetically induced transparency (EIT) windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes quantified by the Rabi frequency, for slowing the probe field. Our scheme exploits the fact that the second transparency window is sensitive to a temperature-controlled signal-field nonlinearity, whereas the first transparency window is insensitive to this nonlinearity.