Slow and stopped light by light-matter coherence control Jonas Tidström Doctoral Thesis in Photonics Stockholm, Sweden 2009 TRITA-ICT/MAP AVH Report 2009:09 KTH School of Information and ISSN 1653-7610 Communication Theory ISRN KTH/ICT-MAP/AVH-2009:09-SE SE-164 40 Kista ISBN 978-91-7415-429-0 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan framlägges till offentlig granskning för avläggande av filosofie doktorsexamen i fotonik, tors- dagen den 29 november 2009 kl 13:15 i sal 432, Forum, Kungl Tekniska Högskolan, Isafjordsgatan 39 Kista. c Jonas Tidström, September 2009 ° Typesset with LATEX 2ε on September 28, 2009 Universitetsservice US AB, September 2009, Abstract 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 sys- tem (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 1 propagate at a velocity of 1kms− (to be compared with the normal velocity 1 ∼ 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. Further- more, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness to- day 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 vec- tor form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain. iii iv List of publications Paper A Limits on optical pulse compression and delay bandwidth product in electromagnetically induced transparency media Jänes, P., Tidström, J., and Thylén, L. J. Lightwave Tech. 23, 3893 (2005) Paper B Delay bandwidth product of electromagnetically induced transparency media Tidström, J., Jänes, P., and Andersson, L. M. Phys. Rev. A. 75, 053803 (2007) Paper C Overtone generation in driven coherent media Tidström, J. and Andersson, L. M. Phys. Rev. A. 79, 063832 (2009) Paper D Photonic crystal microcavity made of electromagnetically induced trans- parency material Tidström, J., Neff, C. W., and Andersson, L. M. Submitted to J. Opt. Paper E Open system effects on slow light and electromagnetically induced trans- parency Tidström, J., Ericsson, M., Sjöqvist, E., and Andersson, L. M. Submitted to Phys. Rev. A Manuscript F Manipulating light pulses during storage and readout Andersson, L. M. and Tidström, J. To be submitted. v Conference contributions Pulse-distortion in EIT media Tidström, J., Jänes, P., and , Andersson, L. M. Paper WB6 in Slow and Fast Light and Fast Light 2006 Technical Digest (Optical Society of America, Washington, DC, 2006) Limitations of the Delay Bandwidth Product in Electromagnetically In- duced Media Tidström, J. and Andersson, L. M. and Jänes, P. Poster presented at CONSRT/iNOW workshop, Berkeley, 2006 Slow and stored light in atomic vapor Tidström, J., Andersson, L. M. and Thylén, L. Poster presented at Optik i Sverige Skellefteå, 2007 Overtone generation in driven coherent media Tidström, J. and Andersson, L. M. Poster presented at iNOW workshop, Stockholm and Berlin, 2009 and at ADOPT, Kista, 2009 List of related contributions Uhlmann’s geometric phase in presence of isotropic decoherence Tidström, J. and Sjöqvist, E., Phys. Rev. A. 67, 032110 (2003) Uhlmann’s geometric phase in presence of isotropic decoherence Tidström, J. and Sjöqvist, E. Poster presented at Summer school Quantum Logic, Cargese 2004 vi Acknowledgements First of all, I would like to sincerely thank my main supervisor Mauritz Andersson for sharing me his deep knowledge and for having such an astonishing patience with me, all those discussions. It would have been very hard to write this thesis without his help. I would like to thank my supervisor Professor Lars Thylén for accepting me as a P.h.D. student and for introducing me to the fascinating subject of my thesis. I also would like to thank Björn Hessmo for taking his time during all those interesting, valuable and fun discussions at the onset of this thesis, but more than this, for his optimistic “ahh, it’s not so hard” attitude. Peter Jänes for a very nice collaboration and valuable discussions. I would like to thank Erik Sjöqvist and Marie Ericsson (the funky bunch) for their critical, warm and enthusiastic spirit and deep knowledge. It was a pleasure to work with them. Gunnar Björk for critical discussions and views on many things, especially climbing. I want to thank Curtis Neff for the “good old days”. It was very stimulating to work with him and I owe him many thanks. He also converted me from Windows to Mac, a good thing indeed. I especially would like to thank Daniel Ljunggren for stimulating, sometimes loud, but always great, long and vitalizing discussions. Jonas Almlöf and Sébastien Sauge for stimulating discussions with interesting viewpoints and a refreshed thinking. I would also like to thank Maria Tegner, Anders Månsson, Marcin Swillo, Christian Kothe, Marek Chaciński, and my former room mates Piero Luca Mana and Isabel Sainz Abascal. Many thanks to Andreas Svahnström for fast assistance with computer issues and also for the fun discussions. I would like to especially thank Eva Andersson for helping out with everything. All my present and former colleagues at KTH. All other to whom I am in dept. Thank you all! vii viii Abbreviations and conventions Abbreviations EIT electromagnetically induced transparency DBP delay bandwidth product CPT coherent population trapping STIRAP stimulated Raman adiabatic passage FWHM full-width half-maximum ECDL external cavity diode laser FSR free spectral range ON orthonormal CW continuous wave H.a. Hermitian adjoint Conventions is defined by . =≡ is represented by standard scalar product · on the order of ∼ approximately x≈ a vector ψ a vector in a Hilbert space | i Aˆ an operator Aˆ a vector operator 1ˆ operator identity 1 matrix identity ix x Contents 1 Introduction 3 1.1 Why is light-matter interaction interesting? . ..... 3 1.2 Outlineofthethesis .......................... 4 2 The field and the matter 7 2.1 Thefield................................. 7 2.1.1 Maxwell’s equations and the wave equation . 7 2.1.2 The optical dispersion relation . 9 2.1.3 Slowly varying envelope approximation . 10 2.1.4 What is the velocity of light? . 11 2.2 Thematter ............................... 13 2.2.1 TheLorentzmodel....................... 13 2.2.2 Quantum mechanical approach 1, pure states . 15 2.2.3 Quantum mechanical approach 2, density operator . 18 3 Coherent interaction 21 3.1 The Λ-system.............................. 22 3.2 Darkstates,CPT,STIRAP . 25 3.3 Electromagnetically induced transparency . 27 3.4 BandwidthofEIT ........................... 33 3.5 Inhomogeneous broadening (narrowing) . 35 3.6 Slowlight ................................ 38 3.7 Storedlight ............................... 40 3.8 Overtone generation and strong probe regime . 43 4 Open system effects 49 4.1 Whatdoestheword‘coherence’mean?. 49 4.2 The consequences of an interactive environment . 50 4.3 Coherencevectorformalism . 53 xi 5 Applications 59 5.1 Delaylineandpulsecompression . 59 5.2 Opticalmemory ............................ 61 5.3 Dispersion engineering via light-matter coherence . ....... 62 5.4 High precision spectroscopy, sensors, atomic clocks, metrology . 62 5.5 QvalueenhancementduetoEIT . 63 5.6 Otherapplications ........................... 64 6 The medium 67 6.1 Rubidium ................................ 68 6.2 Energylevels .............................. 70 7 Experimental setup 75 7.1 Thelightsource ............................ 77 7.2 Thegas-cell............................... 79 7.3 Spectroscopy .............................. 80 7.4 Acoustoopticalmodulators . 81 7.5 Polarizingoptics ............................ 81 7.6 Thecoilandtheshield......................... 82 7.7 Detection ................................ 84 7.8 Experimental control . 84 8 Experimental results 85 8.1 Thetwo-photonresonance. 85 8.2 Stoppingthelight ........................... 89 8.3 Manipulating the light-matter coherence . 90 9 Discussion and outlook 93 10 Contributions to the original work by the author 97 xii Till mina föräldrar och min syster Till Malin och framtiden Chapter 1 Introduction 1.1 Why is light-matter interaction interesting? A definite answer is hard to find. But one could perhaps say something like: ev- erywhere you look you see — light1. Everything around us in our daily life reflects or emits light, all the colors we see are just different wavelengths of the light. All the beauty2 we see is mediated to us as light. The stars and the planets unveil their presence and further out galaxies, clusters of galaxies and super clusters of galaxies, as photons travelling for ages, to meet our eyes. Light is an electromagnetic disturbance that travels at a high speed from a source. It can be absorbed, re-emitted, reflected and refracted. Human beings, sometimes clever, learn about light and create eye-glasses to improve vision, light sources to light up the darkness, binoculars to observe greater distances and the camera to preserve an image.