We demonstrate a fiber-optical switch that operates with a few hundred photons per switching pulse. The light-light interaction is mediated by laser-cooled
atoms. The required strong interaction between atoms and light is achieved by
simultaneously confining photons and atoms inside the microscopic hollow core
of a single-mode photonic-crystal fiber

Bajcsy, Michal

Balic, Vlatko

Hafezi, Mohammad

Hofferberth, Sebastian

Lukin, M. D.

Peyronel, Thibault Michel Max

Vuletic, Vladan

Zibrov, A. S.

Crossref

SWITCHING OF LIGHT WITH LIGHT USING COLD ATOMS INSIDE A HOLLOW OPTICAL FIBER

DSpace@MIT

September 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted11Switching of light with light using cold atoms inside a hollowoptical fiberM. BAJCSY1,2, S. HOFFERBERTH1,2, T. PEYRONEL2, V. BALIC1,2, M.HAFEZI1, A. S. ZIBROV1, M. D. LUKIN1 and V. VULETIC2∗1MIT-Harvard Center for Ultracold Atoms, Physics Department, Harvard University,Cambridge, MA 02138, USA2Department of Physics, MIT-Harvard Center for Ultracold Atoms, and ResearchLaboratory of Electronics, Massachusetts Institute of Technology, Cambridge,Massachusetts 02139, USA∗E-mail: vuletic@mit.eduwww.rle.mit.edu/eap/We demonstrate a fiber-optical switch that operates with a few hundred pho-tons per switching pulse. The light-light interaction is mediated by laser-cooledatoms. The required strong interaction between atoms and light is achieved bysimultaneously confining photons and atoms inside the microscopic hollow coreof a single-mode photonic-crystal fiber.Keywords: quantum optics, nonlinear optics, atom-light interaction, electro-magnetically induced transparency1. Introduction: Strength of atom-light interactionThe implementation of nonlinear optical processes at low light levels is along-standing goal of quantum optics. Since the direct effect of light on lightin vacuum is extremely weak, such light-light interaction must be mediatedby a material system. A gas of cold atoms can serve as a medium that isstrongly coupled to the light field. In particular, cold atoms offer strongoptical transitions that are broadened only by the radiative lifetime of theexcited state, with correspondingly large resonant absorption cross sectionsof order σ ∼ λ2, close to the maximum value σ0 = 3λ2/(2pi) possible for atransition of wavelength λ.In general, large optical nonlinearity is difficult to achieve, and requireslong atom-photon interaction times in combination with low photon loss,and tight transverse confinement of the light. To realize a system meetingSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted12Fig. 1. Hollow-core photonic-bandgap fiber. The diameter of the inner hole, where theatoms are trapped, is 6 µm. The mode waist inside the fiber is 1.9(2)µm. A 3 cm long,vertically mounted piece of fiber is used for the experiments.these requirements, we trap a mesoscopic ensemble of a few hundred cold ru-bidium atoms inside a microscopic hollow-core photonic-crystal fiber (PCF,see Fig. 1).1 The tight transverse confinement of the atoms and of the lightwithin the same one-dimensional waveguide enables strong atom-photoninteractions. Using electromagnetically induced transparency2–6 (EIT) ina mesoscopic regime involving small numbers of atoms and photons, wedemonstrate coherent all-optical switching with a few hundred photons perswitching pulse, and one to two photons per target pulse.For simultaneous transverse confinement of light and atoms on a lengthscale d, the interaction probability between a single atom and a single pho-ton of wavelength λ scales as p ∼ σ/d2 ∼ λ2/d2, and in our system canapproach a few percent. In turn, the atomic medium can be manipulated bypulses containing p−1 ∼ 100 photons. Such a medium enables atom-photon,as well as photon-photon interaction, and exhibits nonlinear optical effectsat power levels corresponding to ∼ p−1 photons per pulse.Experimental implementation of few-photon nonlinear optics has previ-ously only been accomplished in cavity QED systems, where single atomsare situated in narrow-band, high-finesse cavities,7 such that a photon inter-acts multiple times with an atom. Over the last decade, major progress hasbeen made, with several experiments demonstrating nonlinear optical phe-September 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted13nomena with single intracavity photons.8–10 However, these experimentsremain technologically challenging and must compromise between cavitybandwidth, mirror transmission, and atom-photon interaction strength.Recently, hollow-core PCFs filled with a molecular gas have been usedfor significant enhancements of efficiency in processes such as wavelengthconversion11 and four-wave mixing.12 Several groups have also success-fully loaded an atomic vapor into a PCF, for applications such as atomicguiding.13,14 The recent observations of electromagnetically induced trans-parency in room-temperature rubidium with nanowatt control fields15 hasdemonstrated the promise of these systems for nonlinear optics at very lowlight levels.Fig. 2. Setup for loading the hollow-core photonic-crystal fiber with laser-cooled atoms.A magnetic guide consisting of four wires carrying currents assists the loading of atomsfrom a magneto-optical trap located 6 mm above the end of the fiber. Inside the fiber,the atoms are confined by an off-resonance dipole trap, with the trapping light guidedin the fiber. Light is coupled into and out of the fiber using lenses above and below thefiber.The centerpiece of our experiment is a 3 cm-long piece of hollow-corePCF (Fig. 1), vertically mounted inside an ultra-high vacuum chamber. Alaser-cooled cloud of 87Rb atoms is collected into a magneto-optical trap(MOT), focused with a magnetic guide, and loaded into the hollow core ofthe PCF (see Fig. 2). Inside the fiber, the atoms are radially confined bya far-detuned dipole trap formed by a single beam guided inside the fiber.September 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted14The dipole trap is red detuned from the rubidium D2 line (λ = 780 nm)by typically a few nanometers, such that the atoms are pulled towards theintensity maximum of the trapping light,16 i.e. towards the center of thehollow core. Inside the fiber, the small diameter of the guided mode (waistsize w = 1.9(2)µm) results in strong transverse confinement, with radialtrapping frequencies on the order of 50 kHz, and a deep trapping potentialon the order of 10 mK at guiding-light powers of a few milliwatts.Fig. 3. Absorption of light by atoms inside fiber for continuous trap (red, absorptionminimum shifted), and for modulated trap with probing while trap is off (black, unshiftedminimum). The frequency shift in the absorption is due to the light shift of the 5S1/2 →5P 3/2 transition by the trapping light. The frequency shift that is in agreement withcalculations (solid line) provides evidence that the atoms are trapped in the high-intensityregion inside the fiber.To probe the atoms in the fiber, we monitor the transmission of a very-low-power (∼ 1 pW) probe beam through the PCF (Fig. 3), detected by asingle-photon counter. This probe can be frequency tuned over the D1 orD2 resonance absorption lines of rubidium. The dipole trap light introducesa power dependent, radially varying AC-Stark shift, which results in a char-acteristic inhomogeneous broadening and frequency shift of the absorptionprofile (red data in Fig. 3). Comparison with the absorption profile calcu-lated from the dipole trap parameters verifies that the atoms are trappedinside the fiber. For the optical experiments described below, we avoid theSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted15unwanted perturbation of the absorption profile by synchronously modu-lating the dipole trap and the probe beam out of phase. The modulation ata rate faster than the trapping frequency allows the atoms to interact withthe probe photons only when the dipole trap is off, while the time-averagedoptical trap still prevents them from colliding with the fiber wall. We thenobserve an absorption profile that is completely determined by the naturallinewidth of the transition (black data in Fig. 3). From these data we con-clude that ∼ 100 atoms create an optically dense medium (resonant opticaldepth OD = 1) in the fiber. The absorption profile shown in Fig. 3 corre-sponds to an optical depth OD ≈ 30.17 All optical experiments describedbelow are performed in the modulated dipole trap to avoid inhomogeneousbroadening of atomic transitions.Fig. 4. Lifetime of atoms in hollow-core photonic-bandgap fiber. The figures show themeasured optical depth (linear and logarithmic scales) vs. time. The atomic decay fortimes between 10 ms and 40 ms is exponential with a decay time constant τ = 12 ms. Weinterpret the kink near 40 ms as being due to atoms leaving the lower end of the fiber. Thelifetime increases to 100 ms if the atoms are stopped inside the fiber by one-dimensionalDoppler cooling.The quality of the vacuum inside the fiber is not known, and the gaspressure inside the fiber could substantially exceed that in the main cham-ber since the extreme aspect ratio of the fiber L/d ∼ 500 corresponds tovery poor conductance. This could result in fast loss of the trapped atomsSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted16due to collisions with background gas inside the fiber. We have investigatedthe trapping by measuring the optical depth vs. time, and the result for thecloud falling through the fiber is shown in Fig. 4. We observe an exponen-tial decay with a time constant of τ = 12 ms for 30 ms, with subsequentfaster decay. We interpret the latter, in agreement with simple estimates, asbeing due to atoms reaching the lower end of the fiber, and having enoughenergy (supplied by gravity) to leave the fiber in spite of the longitudinalconfinement provided by the dipole trap. The data in Fig. 4 may lead oneto conclude that the background-gas-limited lifetime of the atoms insidethe fiber amounts to 12 ms for our present system.However, when we stop the falling of the atoms inside the fiber byone-dimensional Doppler cooling along the fiber, we observe much longertrapping times, in some measurements as long as 100 ms. The shorter timeconstant of 12 ms for the falling cloud may then indicate that the opticaltrapping potential inside the fiber is not completely smooth, and that itmixes the longitudinal motion (whose kinetic energy is much larger thanthe radial trap depth) with the transverse motion, resulting in radial lossof the atoms when their radial kinetic energy exceeds the depth of thetrapping potential.2. Incoherent switching of light with lightFig. 5. Incoherent switch using optical pumping. 300 photons coupled into the fiberon the |1〉 → |3〉 transition are sufficient to cause 50% reduction of the probe on thetransition |2〉 → |4〉.An incoherent optical switch can be implemented by optical pumpingSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted17(see Fig. 5). A sample is prepared in the state |1〉 with an optical depthOD > 1 on the |1〉 → |3〉 transition. Upon excitation on that transition,atoms decay with probability γ2/(γ1+ γ2) from the state |3〉 into the otherhyperfine level |2〉. When sufficiently many atoms have accumulated in state|2〉, probe light coupled into the fiber, resonant with the |2〉 → |4〉 transition,is extinguished.Fig. 5b shows the extinction of the probe light on the |2〉 → |4〉 tran-sition as a function of the number of photons incident on the |1〉 → |3〉transition. We achieve a 50% reduction of the probe transmission with only300 pump photons coupled into the fiber. This corresponds to ∼ 150 atomsbeing transferred into the |2〉 state, which is sufficient to cause the observedabsorption of the probe beam.3. Coherent switching of light with lightThe incoherent switch relies on optical pumping by spontaneous emission.It is also possible to implement a coherent method based on EIT (see Fig.7). Here a control beam is applied on the |2〉 → |3〉 transition, such that anyincident probe photon on the |1〉 → |3〉 transition is converted into a dark-state polariton,18 with one polariton component being the atomic-spin-waveexcitation to the |2〉 state. When the control beam is sufficiently weak,corresponding to slow light traveling with velocity v ¿ c, each incomingphoton is converted into an atomic excitation populating the |2〉 state.Fig. 6. EIT with weak control field. Left: In the absence of the EIT control beam (blackdata), the sample is opaque with an optical depth OD ∼ 1. In the presence of the controlbeam (red data), a transmission window opens up. Right: Only 104 photons per controlbeam pulse are needed to provide good EIT transmission.Fig. 6 shows EIT in a sample with optical depth OD ∼ 1. In the presentSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted18system the classical control beam itself is quite weak, and as few as 104photons per pulse provide good transparency. For the parameters shownin Figs. 6,7, the pulse is delayed by 30% of its width, or 100 ns. Thiscorresponds to a group velocity of the light on the order of 3 km/s ¿ c,i.e., to a dark-state polariton that is dominated by the atomic excitation.18Fig. 7. All-optical switch based on the Yamamoto-Harris four-level scheme. Left: Leveldiagram with probe, control, and switching field. Right: Transmission of the probe light,normalized to the peak EIT transmission, as a function of the number of photons in theswitching pulse.The coherent switch is based on the four-level scheme proposed by Har-ris and Yamamoto,19 as shown in Fig. 7 on the left. The probe light cou-pling the states |1〉 and |3〉 is transmitted on the EIT resonance, unless theswitching light is applied on the transition |2〉 → |4〉. In the latter case, theswitching light excites the atomic population in state |2〉 and destroys thedark-state polariton, thereby reducing the transmission of the probe light.Fig. 7 (right graph) shows the measured transmission of the probe lightas a function of the number of photons per switch pulse. For the oscillatorstrengths of the transitions used, ∼ 700 switch photons result in a 50%reduction of the probe transmission. A contrast of over 90% between the”on” and ”off” states of the switch can be achieved with a modest increasein the number of switch photons.174. Outlook: Towards switching light with a single photonThe number of photons required for the all-optical switch is set by theratio of mode area to wavelength squared, in combination with the oscil-lator strengths of the transitions used. To reduce the required switchingpower further, it should be possible to use a hollow-core PCF with smallerhole diameter. However, the attractive Casimir-Polder force between atomsSeptember 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted19and fiber walls sets a limit on the hole diameter that lies probably some-where between 2 and 3 µm.20 This implies that by reducing the fiber andelectromagnetic-mode diameters alone, it will not be possible to reach thelimit where a single switch photon can extinguish the probe light.Further reduction in switch power then requires some form of repeatedinteraction between the light and the atoms. While in principle externalmirrors can be added, such a system will not achieve high finesse due therelatively low efficiency (∼ 60%) of coupling into and out of the fiber. Itmay be more promising to attempt to integrate some form of Bragg mirrorsinto the fiber itself.An alternative is to use quantum optics techniques to realize effec-tive multiple interactions between light and atoms. For instance, it shouldbe possible to build a Bragg grating into the atomic system itself usingstationary-light EIT techniques, as demonstrates by Bajcsy et al. in freespace.21 Another possibility to enhance the light-light interaction is to setup a double-EIT scheme where both the probe and the switch light are trav-eling slowly.22 Both schemes require optical depths OD & 100,18,22 which iswithin reach with modest and incremental improvements of the fiber load-ing procedure. With such optical depth, it may also be possible to realizea gas of strongly-interacting photons in this one-dimensional system.23References1. R. Cregan, B. Mangan, J. Knight, T. Birks, P. Russell, P. Roberts and D. Al-lan, Science 285, 1537 (1999).2. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).3. S. Harris, Phys. Today 50, 36 (1997).4. S. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).5. M. Fleischhauer, A. Imamoglu and J. Marangos, Rev. Mod. Phys. 77, p. 633(2005).6. L. Hau, S. Harris, Z. Dutton and C. Behroozi, Nature 397, 594 (1999).7. B. Dayan, A. S. Parkins, T. Aok, E. Ostby, K. Vahala and H. Kimble, Science319, 1062 (2008).8. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup and H. J.Kimble, Nature 436, p. 87 (2005).9. T. Wilk, S. C. Webster, A. Kuhn and G. Rempe, Science 317, 488 (2007).10. I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff and J. Vuckovic,Science 320, 769 (2008).11. F. Benabid, G. Bouwmans, J. C. Knight, P. S. J. Russell and F. Couny, Phys.Rev. Lett. 93, p. 123903 (2004).12. S. O. Konorov, A. B. Fedotov and A. M. Zheltikov, Opt. Lett. 28, 1448 (2003).13. T. Takekoshi and R. J. Knize, Phys. Rev. Lett. 98, p. 210404 (2007).September 10, 2009 17:29 WSPC - Proceedings Trim Size: 9in x 6in ICOLS09vuletic˙submitted11014. C. A. Christensen, S. Will, M. Saba, G.-B. Jo, Y.-I. Shin, W. Ketterle andD. Pritchard, Phys. Rev. A 78, p. 033429 (2008).15. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta and B. J.Kirby, Phys. Rev. Lett. 97, p. 023603 (2006).16. R. Grimm, M. Weidemu¨ller and Y. B. Ovchinnikov, Adv. Atom. Mol. Opt.Phys. 42, p. 95 (2000).17. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov,V. Vuletic and M. D. Lukin, Phys. Rev. Lett. 102, p. 203902 (2009).18. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).19. S. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, p. 3611 (1998).20. Y. Lin, I. Teper, C. Chin and V. Vuletic´, Phys. Rev. Lett. 92, p. 050404(2003).21. M. Bajcsy, A. S. Zibrov and M. D. Lukin, Nature 426, 638 (2003).22. A. Andre´, M. Bajcsy, A. S. Zibrov and M. D. Lukin, Phys. Rev. Lett. 94, p.063902 (2005).23. D. Chang, V. Gritsev, G. Morigi, V. Vuletic, M. Lukin and E. Demler, NaturePhysics 4, 884 (2008).

Switching of light with light using cold atoms inside a hollow optical fiber

http://dspace.mit.edu/bitstream/1721.1/64684/1/Vuletic.pdf

Switching of light with light using cold atoms inside a hollow optical fiber

Abstract

Similar works

Full text

Available Versions

Crossref

DSpace@MIT