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8-Port Homodyne Detection of EIT-Enhanced Cross-Phase Modulation Using Broadband Signal Pulses

Grzegorz Dmochowski

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

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.

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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.

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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.
In third order nonlinear mediums, the intensity of one optical field can modify the phase of another optical field. This is known as cross-phase modulation (XPM) and is important for Quantum Information Processing (QIP) as phase shifts of single-photons that exceed π rad can be used to implement two-qubit quantum logic gates. For a conventional XPM scheme, the Kerr nonlinearity responsible for XPM is too small for appreciable phase shifts to be achieved with low intensity optical fields. However, Electromagnetically Induced Transparency (EIT) can increase this nonlinearity by several orders of magnitude. This thesis discusses the experimental construction of a laser-atomic system capable of EIT modulated XPM. This includes construction of a rubidium magneto-optical trap (RbMOT), characterization of this RbMOT, demonstration of EIT in the RbMOT, and a system capable of detecting optical phase shifts produced by EIT. The talk will conclude with an outlook on further implementations to the experiment that will increase this nonlinearity such that phase shifts at the single-photon level are possible. | 76 pages
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.
In this thesis I report the first experimental observation of an interaction between a postselected single photon and an electromagnetic field containing a few thousand photons.This is the first observation of the nonlinear interactions due to a single freely propagatingphoton. To achieve this pioneering result, we have theoretically and experimentally studied nonlinear optics at the few-photon level. To the best of our knowledge, the pulse energy levels used for our experiments are the lowest energies used for cross-phase modulation in free space.Photon-photon interaction is vanishingly weak; the strength of this interaction can be enhanced in the presence of a material medium as mediator. In our experiment, we use an atomic coherence effect, namely Electromagnetically-induced Transparency (EIT), to produce a `giant' nonlinear interaction between two optical fields. We have observed a nonlinear phase shift of 18 ± 4 µrad per freely propagating single photon. This is done by sending very weak coherent state pulses into the medium and subsequently detecting single photons, inferring the existence of a photon in the interaction region.The optical setup, electronics and software that have been developed during the completion of this thesis provide the basis for several exciting future light-matter interaction experiments. We have produced phase-stable laser beams to create EIT in our cold Rubidium sample prepared in a Magneto-optical Trap (MOT). The laser system and the improved MOT setup have been built to be stable so that we can do very long data acquisition runs. We also have develop ed to ols and software with high precision and stability such that we can measure phase shifts down to micro-radian level.
We report on the direct measurement of low-light-level cross-phase modulation (XPM) based on electromagnetically induced transparency (EIT) in the pulsed regime. A phase shift of 0.02 rad of a probe pulse modulated by a signal pulse with a peak intensity of 3 $\mathrm{\ensuremath{\mu}}\mathrm{W}/{\mathrm{cm}}^{2}$ was observed, which is the lowest intensity ever achieved for the N-type EIT-based XPM system. The experimental data make a quantitative prediction of the single-photon-level XPM phase shift arising from two interacting pulses with unequal group velocities that is consistent with the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)]. Furthermore, a proof-of-principle experiment demonstrating an enhancement of the nonlinear optical Kerr effect by shining the signal pulse twice is presented.
This thesis explores the theoretical foundations of cross-phase modulation (XPM) between optical fields in the N-configuration atom. This is the process by which the refractive index experienced by one field can be modulated by controlling the intensity of another. The electro-optical version of this effect was first discovered by John Kerr in 1875 and found applications in photonics as a means of very rapidly modulating the phase and intensity of electromagnetic fields. Due to recent advances in experimental techniques there has been growing interest in generating nonlinear optical interactions in coherently prepared atomic ensembles. \n \nThe use of coherently prepared media brings the possibility of achieving a much larger cross-phase modulation than is possible using classical materials. This is particularly useful when trying to create large optical nonlinearities between low-intensity electromagnetic fields. Much of the current research into cross-phase modulation is directed towards realising potential applications in the emerging field of quantum information processing. Above all, the possibility of constructing an all-optical quantum computer has been at the heart of much research and controversy in the field. \n \nIn this thesis the theory of steady-state, transient and pulsed cross-phase modulation is developed. Moreover, care has been taken to relate all research back to experimentally feasible situations. As such, the relevance of the theory is justified by consideration of the situation present in rubidium-87. Due to the close relationship between XPM in the N-configuration atom and electromagnetically induced transparency in the Lambda-atom, many similarities and insights act as link between these two fields. Indeed, it is frequently demonstrated that the key to understanding the various properties of XPM in the N-configuration atom is by comparison with the situation in the corresponding Lambda-atom equivalent.
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.