Presentation on theme: "Quantum Theory of Collective Atomic Recoil in Ring Cavities"— Presentation transcript:
1 Quantum Theory of Collective Atomic Recoil in Ring Cavities Università degli Studi di MilanoDipartimento di Fisica via Celoria 16, Milano, ItalyPhD School in Physics, Astrophysics and Applied PhysicsQuantum Theory of Collective Atomic Recoil in Ring CavitiesMarina SamoylovaThesis advisor:Dr. Nicola Piovella16th October 2012“Mini Workshop ”, Milano
2 OutlineThe advantages of studying a Bose-Einstein Condensate (BEC) in a ring cavityA possible experimental realization of such a systemThe semi-classical and quantum models of the systemThe numerical analysis of the exact solutionThe summary of the resultsFuture doctoral research
3 Introduction Superradiant Rayleigh Scattering in free space (SRyS) [ Collective Atomic Recoil Lasing in free space (CARL) ]incident laser beam
4 Introduction SRyS in free space CARL in a ring cavity Scattered photons can be recycled many timesCoherence time is enhancedBEC + thermal clouds (100μK)Scattered photons rapidly leavethe interaction regionBose-Einstein Condensate (BEC) only
5 2D CARL configuration X Z System: a BEC in a high-finesse ring cavity XZpump fieldΦ
6 Experimental setupΦA Bose-Einstein condensate is prepared in an Ioffe-Pritchard type magnetic trap in a high-finesse ring cavity (F=135000).The BEC is illuminated by s-polarized pump light incident under the angle Φ=37˚. The pump beam is provided by a Ti:sapphire laser.The condensate scatters the light superradiantly into two counter-propagating cavity modes.The atomic momentum distribution is taken via absorption imaging.A single-photon counter records the photons transmitted through one of the cavity mirrors. S. Bux, C. Gnahm, R. Maier, C. Zimmermann and Ph. Courteille, Phys. Rew. Lett. 106, (2011). S.Bux, H.Tomczyk, D.Schmidt, C.Zimmermann, N.Piovella, Ph.Courteille, New J. Phys., submitted (2012).
7 Results of the experiment N=80000 is the number of atoms,t= 200μs is the duration of the pump laser pulseindividual momentum stateAt certain conditions only 4 momentum states can be populated
8 The semi-classical model We are interested in a 4-level systemclosed systems of equations !In the semi-classical limit the four states configuration can be solved in termsof two independent two-level systems for the left and right cavity modes.
9 The Quantum ModelThe Hamiltonian of the system in the interaction picture:where and are constants of motion representing the sum of excitations for the systems 1 and 2, respectively.ttThe general state of the system: , whereand
12 Summarywe consider CARL-type dynamicswe investigate 4-level systemIn the semi classical limit the four states configuration can be represented in terms of two independent two-level systems.The quantum problem can be solved exactly where its full quantum properties are determined.
13 Future Plans BEC in optical lattice Why is it so interesting? Easy to realizeLarge variety of optical latticesFascinating optical effects2D3DPhotonic band gaps (PBG)
14 Future Plans What is PBG? Why? We consider propagation of light through an optical lattice loaded with cold atomsrange of frequencies whereno propagation modes existin any directionsa-π/aπ/aThe goal is to study photonic band gaps in cold atomic structuresAccess to real time manipulationsPerfect long range orderWhy?