Collective Interaction Between a. Bose-Einstein Condensate and a Coherent. Few-Photon Field

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1 Diss. ETH No Collective Interaction Between a Bose-Einstein Condensate and a Coherent Few-Photon Field A dissertation submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Sciences presented by Claudius Ferdinand Brennecke Dipl.-Phys., University of Hamburg, Germany born in Starnberg, Germany citizen of Germany accepted on the recommendation of Prof. Dr. Tilman Esslinger, examiner Prof. Dr. Atac Imamoglu, co-examiner 2009

2 Zusammenfassung Im Rahmen dieser Doktorarbeit wurde die kollektive Wechselwirkung zwischen einem Bose-Einstein Kondensat und dem Feld eines optischen Resonators mit kleinem Modenvolumen und exzellenter Güte experimentell realisiert und erforscht. Dieses System erönet ein neues Forschungsgebiet innerhalb der Resonator-Quantenelektrodynamik, in welchem eine makroskopische Materiewelle eine starke Wechselwirkung mit wenigen Photonen eingeht. Kernstück des experimentellen Aufbaus bildet ein optischer Transportmechanismus, der es erlaubt, mehrere hunderttausend ultrakalte Atome in einen optische Resonator zu transferieren, welcher bereits für einzelne Atome im stark-koppelnden Regime operiert. Erstmals können damit unter Beteiligung weniger Photonen in der Resonatormode kollektive Phänomene in den internen und externen Freiheitsgraden eines Bose-Einstein Kondensates experimentell untersucht werden. Wie unsere Messungen und theoretischen Überlegungen belegen, lassen sich damit zwei zentrale Modellsysteme im Bereich der Quantenoptik und der Resonator-Optomechanik realisieren. Im Bereich der Resonator-Quantenelektrodynamik stellt unser System eine ideale Realisierung des Tavis-Cummings Modells dar, welches die kollektive Wechselwirkung zwischen N gleichartig gekoppelten zwei-niveau Systemen und einem harmonischen Oszillator beschreibt. Einzelne atomare Anregungen des gekoppelten Systems verteilen sich in Form einer kohärenten Quantenüberlagerung auf alle Atome, und wechselwirken deshalb, im Gegensatz zum einzelnen Atom, mit der N-fachen Kopplungsstärke mit dem Resonatorfeld. Zur Charakterisierung des gekoppelten Systems messen wir das Energiespektrum aus, und weisen das vorhergesagte Skalierungsverhalten der kollektiven Kopplungsstärke nach. Die Messungen benden sich in sehr guter Übereinstimmung mit unserer theoretischen Modellbeschreibung, welche die nicht-resonante Kopplung an höhere Resonatormoden mit einbezieht. Im dispersiven Limes erfährt die kohärente Materiewelle ein optisches Gitterpotential, welches durch Resonator-Lichtkräfte hervorgerufen wird und i

3 bereits in der Anwesenheit einzelner Photonen einen signikanten Einuss auf die atomare Bewegung hat. Im Gegensatz zu klassischen optische Gitterpotentialen hängt die Tiefe dieses Gitterpotentials aufgrund der dispersiven Rückkopplung der Atome auf das Resonatorfeld entscheidend davon ab, wie sich die Atome innerhalb der Modenstruktur des Resonators anordnen. Dies bewirkt eine hochgradig nichtlineare Kopplung zwischen kollektiver atomarer Bewegung und dem Resonatorfeld. Wie in der vorliegenden Doktorarbeit erstmals erkannt wurde, lässt sich dieses System im Rahmen der Resonator-Optomechanik beschreiben, wobei kollektive Oszillationen der Kondensatsdichte die Rolle des mechanischen Freiheitsgrades spielen. Die auÿerordentliche Kontrolle über die atomaren Bewegungsfreiheitsgrade ultrakalter Gase ermöglicht es prinzipiell, mit diesem System in das Quantenregime der Resonator-Optomechanik vorzustossen. Wir beobachten eine ausgeprägte optische Bistabilität in Anwesenheit einzelner Photonen, hervorgerufen durch die kollektive Verschiebung der Atome innerhalb der Modenstruktur des Resonators. Anhand des Lichtfeldes welches den Resonator verlässt, sind wir erstmals in der Lage, kohärente Dichteoszillationen kleiner Amplitude innerhalb eines Bose-Einstein Kondensates in Echtzeit zu beobachten. Ferner untersuchen wir den Einuss eines zusätzlichen statischen Gitterpotentials auf die kollektive atomare Bewegung, und demonstrieren eine weitere mögliche Realisierung eines optomechanischen Systems mit stark lokalisierten ultrakalten Atomen. Unsere Beobachtungen lassen sich quantitativ im Rahmen einer Mean-Field-Theorie erklären. ii

4 Abstract Collective coupling between a Bose-Einstein condensate and the eld of a small-volume ultrahigh-nesse optical cavity is experimentally achieved and investigated for the rst time. This system opens access to a conceptually new regime of cavity quantum electrodynamics where a macroscopic matter wave strongly couples to few optical photons. The core of the experimental setup is given by an optical-transport scheme, that allows to transfer several hundred thousands of ultracold atoms into an optical resonator, which operates in the single-atom strong coupling regime. With few photons occupying the cavity mode, we explore collective phenomena both in the internal and motional degrees of freedom of a Bose-Einstein condensate. Our measurements and theoretical investigations conrm that our system realizes two fundamental model systems in quantum optics as well as cavity optomechanics. In the context of cavity quantum electrodynamics, our system constitutes an ideal realization of the Tavis-Cummings model, which describes the coherent interaction between a single harmonic oscillator and N two-level systems, all coupling identically. Single excitations are coherently shared among all atoms, and exchanged with the cavity eld at a rate which is enhanced by a factor of N, compared to the single atom case. To characterize the coupled system, we map out its eigenenergy spectrum, and conrm the predicted scaling behavior of the collective coupling strength. These measurements are in very good agreement with our theoretical model description which additionally takes into account the o-resonant coupling to higher-order cavity modes. In the dispersive regime, the cavity-induced dipole forces provide an optical lattice potential which is collectively sensed by the coherent matter-wave. Furthermore, due to dispersive retroaction on the cavity eld, the lattice depth dynamically depends on the atomic density distribution within the cavity mode. This causes highly nonlinear dynamics of the collective atomic motion and the cavity eld intensity. Within the scope of this thesis, it iii

5 was established for the rst time that the system can be described within the framework of cavity optomechanics, where the role of the mechanical oscillator is played by a collective density excitation of the condensate. The tremendous control over the external degrees of freedom of ultracold gases provides in principle a direct access to the quantum regime of cavity optomechanics. Here, we report on the observation of optical bistability at the single photon level, caused by the collective displacement of the atoms within the cavity mode structure. By detecting the light which leaks out of the optical resonator, we are able to in-situ observe coherent small-amplitude density oscillations in a Bose-Einstein condensate. We investigate the inuence of an additional static lattice potential on the collective atomic motion, and demonstrate yet another realization of cavity optomechanics with tightly conned ultracold atoms. Our measurements are in very good agreement with a quantitative mean-eld model. iv

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