Cavity-QED and Single Atom Maser and Laser

1. Cavity-QED and Single Atom Maser and Laser Herbert Walther Max-Planck-Institut für Quantenoptik 85748 Garching bei München, Germany http://www.laser.physik.uni-muenchen.de Herbert.Walther@mpq.mpg.de Sino-GermanSymposium on Quantum Engineering, Beijing, Nov. 23-27, 2005

2. 1896 Einstein & Co. Schottenhamelzelt

3. „Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us closer to the secret of the ‚Old One.‘ I, at any rate, am convinced that He is not playing at dice.“

4. Outline of the Talk Deterministic photon generation (by cavity- quantum electrodynamics) One-atom maser Trapped single ions

5. ~ ~ Free Atom versus Atom in Cavity CavityQuantumElectrodynamics Free Atom Atom in Cavity Mode density distribution near resonance wc 1 rcavity (w) = 2p VcQ (w-wc)2 + (wc/2Q)2 ρ /ρ = (3l3/4p Vc).Q Q cavity free Nc: Mode volume wc Q: Quality factor Q = Dwc

6. Free Atom versus Atom in Cavity Consequencesfortheatom: Modification of spontaneous emission rate Level shifts Oscillatory energy exchange (determined by photon statistics) (E.T. Jaynes, F.W. Cummings, Proc. IEEE 51 , 89 (1963))

7. Steady state field is generated: In most of the parameter regions sub-Poissonian statistics is obtained i.e. nonclassical fields Atom in excited state Interaction-Hamiltonian s+ HI= hg [s+a + a+s-] Pauli operators for atomic system - (a, a+) annihilation and creation operators of radiation field One-Atom Maser Single atom-Single mode of a cavity Resonant superconducting cavity Atom coupling constant g (Rabi-frequency) Cavity field w =k coupling constant Q Cavity walls g Atomic decay: > > (k, g) g Strong coupling

8. Dn Velocity selected atoms = 1 - 4 % n w Q -1 » Single photon Rabi frequency: g 40 000 s g > > t . 10 Quality factor of cavity Q = 4 10 = 0.3 s ¬ cav » Temperature of the cavity 140 mK One-Atom Maser Scheme Levels n = 63 Atomic beam oven Maser transition 21GHz Cavity n = 61 Field ionisation Laser excitation Laser excitation Ground state

9. . Q = 3 1010 T = 0.5 K g-1 = 0.2 s Maser Resonance H. Walther, Phys. Rep. 219, 263 (1992) Rb85 63p3/2 – 61 d5/2 Resonanzfrequenz: 21.456 GHz

10. Rubidium oven Superconducting niobium cavity State selective field ionisation of Rydberg atoms Velocity selective angle tuned UV laser One-Atom Maser Atoms leaving the cavity are entangled with the generated field , n cos (f n+1) , n i sin (f n+1) , n+1 ñ Ö Ö ñ ñ

11. Pump parameter (Q/p) ñ á á ñ n /Nex q parameter Nex = 40 Normalized photon number n /Nex q parameter Interaction time (µs) Puming Curve and Photon Statistics of the One-Atom Maser n2 - n á ñ á ñ 2 Theory: P. Meystre et al. - 1 q = n á ñ

12. = = = = ~ ~ Photon Statistics in the One-Atom Maser Filipowicz, Javanainen, Meystre, Optics Comm. 58, 327 (1986) q parameter q parameter Poissonian photon statistics . gtint Nex = 1 threshold for maser N • 2p corresponds to quantum • non-demolition situation N k

13. Low Temperature Behaviour of the Micromaser

14. Low Temperature Behaviour of the One-Atom-Maser Normalised Photon Number <n>/Nex Fano Mandel q Parameter

15. Low Temperature Behaviour of the One-Atom-Maser Thermal photon number = 0.1 Nex = 50 g= 39 kHz Thermal photon number = 10-4 Nex = 50 g= 39 kHz P.Meystre, G.Rempe, H.Walther, Opt. Lett. 13, 1078 (1988)

16. Low Temperature Behaviour of the One-Atom-Maser PHOTON NUMBERSTATES are directly diplayed Normalised photon number Interaction time (µs) Trapping states are characterised by the pair of numbers (nq, k) that satisfies the relation: nq+1 gtint = kp Ö

17. The Micromaser Pump Curve at Low Temperatures Trapping states appear as valleys in the Nex direction they correspond to PHOTON NUMBER STATES Trapping states are characterised by the pair of numbers (nq, k) that satisfies the rela- tion: nq+1 gtint = kp Ö M. Weidinger, B.T.H. Varcoe, R. Heerlein, H. Walther, Phys. Rev. Lett. 82, 3795-3798 (1999)

18. t = 58 int interaction time for the (1, 1) trapping state S. Brattke, B.T.H. Varcoe, H. Walther, Phys. Rev. Lett. 86, 3534-3537 (2001) Photon-Fock-States on Demand T T t = 45 µs int deviates from trapping con- dition

19. Other Cavity QED Systems

20. Summary Cavity QED Experiments Microwave Atomic beam oven Cavity Field ionisation Laser excitation Walther et al. Haroche et al. Visible single photon pulse 2 P 1/2 pump- pulse 2 D 3/2 2 40Ca+ S 1/2 Lange et al., Nature 414, 49 (2001) and Nature 431, 1075, (2004) Kimble et al. Nature 425, 268 (2003) Rempe et al.

21. g = (m2 w0 /2h e0 V) = Optical Experiments – Atoms in Cavities Coupling constant is increased by reducing mode volume of cavity mode 1/2

22. Strong Coupling Experiments with atoms Rth (atoms/s) g > (k,g) > g/2p k/2p g/2p Walther et al. 1985,1990 7 kHz 0.4 Hz 500 Hz 1.5 Haroche et al.1994 48 kHz 400 Hz 5 Hz 3 . 104 Kimble et al. 1994 7.2 MHz 0.6 MHz 5 MHz5 . 106 Rempe et al.* 2005 5 MHz 5.0 MHz 3 MHz Kimble et al. 2003 16 MHz 4.2 MHz 2.6 MHz Lange et al.** 2004 1 MHz 0.9 MHz 1.7 MHz Feld et al. 1994 340 kHz 190 kHz 50 kHz8 . 106 g: atom-field coupling constant k: decay rate of cavity field g: spontaneous decay of atomic polarization Rth: pumping rate at threshold ) * Trapped atom experiment; trapping time 17 s Trapped ion experiment; trapping time many hours ) * *

23. Single-IonCavity Quantum Electrodynamics

24. Single mode cavity QED Single ion trapping • sub-wavelengthposition control • unlimited observation time strong atom-field coupling Single-Ion Cavity QED Combine the technologies: • deterministic ion-field interaction • single-photon gun • single-ion laser

25. Setup: ion trap and optical cavity How to place the ion between the mirrors? Nature 414,49 (2001) Trap design: • Linear RF trap with open electrode configuration • separate loading region • Ion transfer by DC fields no coating or charging of the dielectric mirrors even at small cavity length

26. Ion Transfer from Loading Region to Cavity trap-axis Region 1 Region 2 (Cavity) Loading • transfer distance: 25 mm • transfer time: 4 ms Shuttling Potential (a. u.) Trap axis position (mm)

27. A Single Ion in a Cavity

28. Single-Ion Mode Mapping (SIMM) single 40Ca+ ion as a nanometric probe of the electromagnetic field: longitudinal scan transversal scan Test of the deterministic interaction of ion and cavity field 397 nm scan position of ion or cavity and ob- serve fluorescence • resolution down to 10 nm • first step towards single-ion cavity QED PMT

29. Two-Dimensional Images of the Cavity Field TEM00 Vertical position (µm) TEM01 Horizontal ion position (µm)

30. z Longitudinal Cavity-Mode Mapping Translation of the cavity along its axis: image of the standing wave structure 1,5 Visibility 40 % 1,0 Count rate (kHz) 0,5 2a l = 397 nm 0 1 2 3 4 Longitudinal cavity position (in units of l) Resolution determined by wavefunction or residual motion of ion Related work by R. Blatt et al., Innsbruck

31. 1 photon Deterministic Single Photon Gun C. K. Law, H. J. Kimble, J. Mod. Opt. 44, 2067 (97) pulse with one single photon single photon pulse • Single ion at a node of the cavity • external pump pulse • cavity with one leaky output mirror 2 P 1/2 2 D 3/2 pump- pulse 40Ca+ 2 S Single-photon pulse at pre-determined time 1/2

32. Single Photon Pulse Shapes Nature,431,1075 ( 2004 ) • Strong Gaussian pump • Weak Gaussian pump c) Square-wave pump d) Double peaked pump Dotted lines indicate pump profiles (not to scale)

33. Photon Correlation Nature 431, 1075, (2004)

34. Summary Deterministic photon generation: One-atom maser- controlled by internal feedback mechanism Trapped ions- single photon wavepacket controlled by pumping pulse

35. Summary Deterministic photon generation: Applications: Quantum phenomena in radiation- atom interaction ( one- atom maser ) Quantum communication; quantum repeaters and single photon sources (ion )

36. Cavity QED with Ions Many thanks to….. One-Atom Maser Matthias Keller Birgit Lange Wolfgang Lange Thomas Becker Theory: M.O. Scully W. Schleich P. Meystre B.G. Englert Michael Klembovsky Linas Urbonas Gabriele Marchi Pierre Thoumany Michael Gorodetsky