Lecture I: (magnetic) dipolar gases. Lecture II: Rydberg Rydberg interaction. Lecture III : Rydberg ground state interaction

Transcription

1 Lecture I: (magnetic) dipolar gases Lecture II: Rydberg Rydberg interaction Lecture III : Rydberg ground state interaction

2 Rydberg atoms - Size quan%ty scaling 100S- state of 87 Rb radius n² ~ 1 µm S 1/2 r R(r) 2 (10 3 a 0-1 ) S 1/2 200S 1/2 Size of Rydberg atom > 1 µm for n > r [µm]

3 Rydberg electron interacting with ground state atoms 2 R 43,0 2 2 rr 43, a0

4 Rydberg electron interacting with ground state atoms 2 R 43,0 2 2 rr 43, a0

5 Ultracold Rydberg Chemistry Giant molecules Two or few-body physics

6 Rydberg electron interacting with ground state atoms 2 R 43,0 2 2 rr 43, a0

7 Ultimately: one electron bound by a charged BEC 0 BEC

8 Single electron in a quantum gas Cooper pairs electron phonon coupling Many-body physics

9 Universität Stuttgart 5. Physikalisches Institut Outline History of Rydberg atoms in dense gases How Rydberg electrons catch atoms Single Rydberg electron in a BEC +

10 The group of Rome Oscar D'Agostino Emilio Segrè, Edoardo Amaldi Franco Rasetti Enrico Fermi

11 History of Rydberg atoms in dense gases E. Amaldi E. Segrè Hilger Ltd., London UK

12 H cm -3 H cm GHz E. Amaldi, E. Segre: Nature 133, 141 (1934), Nuovo Cimento 11, 145 (1934)

13 Interaction between a charge and a polarizable atom e - Rb - r

14 Interaction between a charge and a polarizable atom e - - r Rb V() r r ur = d E 1 ur ur = α E E αq α = = (4 πε ) 2r 2r 0

15 Interaction between a charge and a polarizable atom V () r = 2 π a δ() r pseudo s V() r = α 4 2r

16 Interaction between a charge and a polarizable atom V () r = 2 π a δ() r pseudo s V() r = α 4 2r range of interaction E r E r * * kin( ) = pot( ) h 1 µαq = 2µ r (4 πε ) * 2 2 * 4 0 r r * SI a.u. 2 µαq = = α 18a 2 (4 πhε ) 0 0

17 H cm -3 H cm GHz 2 2π h U = a n m e atom e atom atom e E. Amaldi, E. Segre: Nature 133, 141 (1934), Nuovo Cimento 11, 145 (1934)

18 2 2π h U = a n m e atom e atom atom e Zeitschrift für Physik 90, (1934)

19 interac>ng Rydberg electron ionic core ground state atom electron Effect on ground state atom?

20 PRL 85, 2458 (2000)

21 density/pressure shia ionic core atom effects electron 2 2π h U = a n m e atom e atom atom e electron ground state atom E. Fermi, Nuovo Cimento 11, 157 (1934). E. Amaldi, E. Segrè, Nuovo Cimento 11, 145 (1934) A. Omont, J. Phys. France 38, 1343 (1977) I. Fabrikant, J. Phys. B 19, 1527 (1986).

22 Trilobite molecules ionic core electron effects atom 2 2π h U = a n m e atom e atom e e electron ground state atom E. Fermi, Nuovo Cimento 11, 157 (1934). E. Amaldi, E. Segrè, Nuovo Cimento 11, 145 (1934) A. Omont, J. Phys. France 38, 1343 (1977) I. Fabrikant, J. Phys. B 19, 1527 (1986). C. Greene et al. PRL 85, 2458 (2000)

23 Fermi- Greene Model single channel

24 Trilobite molecules electron effects atom ionic core electron ground state atom 2 2π h U = a n m e atom e atom e e V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, TP, Nature 458, 1005 (2009) 5P Δ 5S

25 rich molecular spectra 36S dimer E B =-19.8(5) MHz? ν=0??? * Atomic line? * * molecule bound by s wave scattering

26 35S Ultralong- range trimers 36S 37S 3 body photoassociation PRL105, (2010)

27 Ultralong- range trimers, and tetramers and

28 Increase l : D state molecules show rovibra>onal states 42 D 5/2 state m J = 5/2 A. Krupp, M. Kurz, P. Schmelcher et al. arxiv: (2014) accepted in PRL

29 Increase l : D state molecules show rovibra>onal states 42 D 5/2 state m J = 1/2 m J = 5/2 A. Krupp, M. Kurz, P. Schmelcher et al. arxiv: (2014) accepted in PRL

30 Increase l : D state molecules show rovibra>onal states 42 D 5/2 state m J = 1/2 m J = 5/2 A. Krupp, M. Kurz, P. Schmelcher et al. arxiv: (2014) PRL 2014

31 Scaled rovibra>onal probability densi>es 0a a a a 0 0a a 0 ν=0;j=0 2000a a 0 ν=0;j=0 Axial states: Toroidal states:

32 Going higher in n: dimers, trimers, tetramers, pentamers Binding energy scales with principal quantum number n=62 1 MHz n=71

33 Even higher n: from molecules to mean shia n A. Gaj, A. T. Krupp, J. B. Balewski, R. Löw, S. Hofferberth, and T. Pfau Nature Comm. In press 62 51

34 In situ Rydberg spectroscopy setup

35 Increase density: Rydberg spectroscopy in a BEC BEC Spectra 62S T>T c T<<T c

36 Increase density: Rydberg spectroscopy in a BEC BEC Spectra 62S T>T c T<<T c T>T c T<<T c

37 Length scales Many body physics probability to find an atom inside Rydberg electron wavefunc>on small, but finite! r Ryd >d Few body physics d: mean particle distance r B : blockade radius r Ryd : size of electron orbit r B >d>r Ryd

38 Rydberg atoms - Blockade quan%ty scaling 100S- state of 87 Rb life>me n³ 1.24 ms Polarizability n GHz (V/cm) - 2 Van der Waals C 6 n x a.u. M. Saffman et al., Rev. Mod. Phys. 82, 2313 (2010)

39 probability to find an atom inside Rydberg electron wavefunc>on small, but finite! Few body physics Rydberg atoms in dense gases Many body physics r Ryd >d d: mean particle distance r B : blockade radius r Ryd : size of electron orbit r B >d>r Ryd

40 System Rydberg: 1.2 µm radius / 4.2 µm radius BEC: atoms, 5 / 18 µm radial / axial TF-radius 700 / atoms inside Rydberg atom

41 Effect of BEC on single Rydberg electron effect on Rydberg: lineshift ~10 MHz

42 Effect of single electron on BEC 110S ~ 700 atoms inside ~ 50 atoms lost pp effect on Rydberg: lineshift ~10 MHz 202S ~ atoms inside ~ 7 atoms lost pp

43 Rydberg electron sets BEC in motion 110S

44 Effect of single electron on BEC 110S ~ 700 atoms inside ~ 50 atoms lost pp strong mechanical effects 202S ~ atoms inside ~ 7 atoms lost pp no mechanical effects

45 Effect of single electron on BEC 110S ~ 700 atoms inside ~ 50 atoms lost pp strong mechanical effects 202S ~ atoms inside ~ 7 atoms lost pp no mechanical effects J.B. Balewski, A.T. Krupp, A.Gaj, D. Peter, H. P. Büchler, R. Löw, S. Hofferberth and T. Pfau, Nature, 502, 664 (2013)

46 Line shia line shift depending only on mean density n: (cf. Amaldi, Segrè, 1934) density not homogeneous (Thomas-Fermi) Amaldi Segrè

47 Solving GP equation for our parameters T. Karpiuk, M. Brewczyk, K. Rzążewski

48 Loss aaer ToF numerics collaboration with Tomasz Karpiuk, Mirosław Brewczyk and Kazimierz Rzążewski (Warsaw, Poland) arxiv: Methods: Monte-Carlo simulation of excitation process time evolution of Gross-Pitaevskii equation for BEC Classical field approximation to extract atom loss PRA 81, (2010)

49 Combining high Rydberg states and BEC Rydberg core serves as e - - trap Rydberg blockade allows only one single electron quasifree electron in pure state atoms within wavefunction strong coupling of charged impurity to BEC excitations

50 Wavefunc>on 2 imaging of single electrons r 2 Ψ( ) dz 182S m=0 110S m=0 Excite single Rydberg atom 180D m=0 106D m=0 BEC as contrast agent (GP simulation) 180D m=2 106D m=2 T. Karpiuk, M. Brewczyk, K. Rzążewski, J. B. Balewski, A. T. Krupp, A. Gaj, M. Schlagmüller, R. Löw, S. Hofferberth, and T. Pfau "Detecting and imaging single Rydberg electrons in a Bose-Einstein condensate" arxiv:

51 Ion BEC interac>on? new approach to prepare a single ion in a BEC? Idea 1: high n circular (l>>0) state Idea 2: hold ion in optical trap electron outside the BEC shields ion magic wavelength (430nm) ODT for ion

52 The COLD Rydberg team W Li, T Pohl, JM Rost ST Rittenhouse, HR Sadeghpour, D Peter, HP Büchler, K Rzążewski, M Brewczyk M. Kurz, P. Schmelcher Robert Löw Sebastian Hofferberth: Rydberg quantum optics SFB/TRR 21