Coherent control of Rydberg atoms

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Geoffrey Gallagher
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1 Coheret cotrol of Rydberg atoms Haruka Maeda Departmet of Phys. & Math., Aoyama Gakui Uiversity

2 Why Rydberg atom? Multilevel ladder system What ca we study with Rydberg atom? Microwave multiphoto ioizatio of multilevel system Populatio cotrol of quatum ladder system Dyamic autoresoace ad multiphoto adiabatic rapid passage

3 Eergy Why Rydberg atom? simple multilevel ladder system resoace frequecies microwave (RF) regio Rydberg atom (H-like atom) A + e - Large orbital radius r = r.5 m (Bohr radius) = r.5 m Multilevel couplig Resoace ~7.3GHz Iterestig properties (simple -scalig law) 7 E E etc. / / 3 3, ( low l ), Excellet testig groud for coheret cotrol of oliear system

4 Why Rydberg atom? Multilevel ladder system What ca we study with Rydberg atom? Microwave multiphoto ioizatio of multilevel system Populatio cotrol of quatum ladder system Dyamic autoresoace ad multiphoto adiabatic rapid passage

5 -Typical experimet- (a) Dye laser pulses MW e - Sigal out MCP WR-6 Wave guide Dye laser pulses Atomic beam Septum Dye laser pulses Timig diagram MW pulse s Negative field pulse t MW hor Atomic beam Pair of field plates e - Sigal MCP Dye laser pulses MW Atomic beam MW Field ramp

6 -Typical experimetal method ad results- Experimetal results Excitatio scheme of Sr E (ev) 5.7 MW pulse Sr II 5s 5sd Rydberg state MW amplitude F (V/cm) l = 4 ~ 46 m 5s5p P l = 46.9 m Sr I 5s H.M. ad T.F. Gallagher, PRL 93, 93 (4)

7 -Scaled frequecy - 3 = : microwave frequecy / 3 :Kepler frequecy i atomic uits (a.u.) = H + e - +

8 -MW ioizatio at several frequecy regimes- Photoelectric effect Rich physics 4 3 Radom detuig Localizatio High frequecy regime (Quatum mechaical) Pricipal resoace Resoace Chaotic ioizatio Low frequecy regime (classical dyamics) Quatum chaos study Tuel ioizatio DC field ioizatio see, for example, P.M. Koch ad K.A.H. va Leeuwe, Phys. Rep. 55, 89 (995)

9 -MW ioizatio at photoelectric effect regime- photoelectric effect Li = 3 ω 7 GHz J.H. Guria, K.R. Overstreet, H. Maeda, T.F. Gallagher, PPA 8, 4345 ()

10 -MW ioizatio at several frequecy regimes- Photoelectric effect Localizatio High frequecy regime (Quatum mechaical) Pricipal resoace Resoace Chaotic ioizatio Low frequecy regime (classical dyamics) Quatum chaos study Tuel ioizatio DC field ioizatio see, for example, P.M. Koch ad K.A.H. va Leeuwe, Phys. Rep. 55, 89 (995)

11 Eergy HCP ioizatio probability Nodispersig wave packets (NDWP) Li : s s 7 = ~ ~ = (GHz) Li 7p Rydberg atom + F = V/cm, 7.5 GHz, liearly polarized MW pulse oliear iteractio electro motio is phase locked to the MW field (NDWP) Li + s e - F(t) ear resoat ~ 57 ps Extremely log lifetime Electro motio ca be detected with fs laser pulse Li =7, MW 7.5 GHz, F ~ 3 V/cm ~ 57 ps. 5 Relative time delay (ps) +HCP polarity local potetial well (bucket) r Kepler orbital period of 7p state Kep 58 ps

12 HCP ioizatio probability How to detect NDWP with fs laser pulse? THz half cycle field pulse (HCP). ps Delay stage High voltage ~.5 ps D. You, R.R. Joes, P.H. Bucksbaum, ad D.R. Dykaar, Opt. Lett. 8, 9 (993) 57 ps fs, 8 m Ti:sapphire laser pulse (< ~4J/cm ) GaAs THz HCP microwave is phase locked to the harmoics of 8 MHz fs pulse trai Ioizatio of phase-locked electro by impulsive mometum kick 57 ps NDWP!! small ioizatio probability HCP + large ioizatio probability HCP ( ~.5 ps ) Kep (~ 57 =7) x Relative time delay (ps)

13 Eergy (GHz) QM represetatio of NDWP Periodically drive quatum system Floquet (dressed-atom) state D Rydberg atom i a liearly polarized microwave (MW) field H Floquet-state eergy vs. MW amplitude F MW xf cos( t ) x = Rotatig frame ()& Rotatig-wave approximatio (a.u.) (a) Bluest state=troja wave packet Spatially well defied (b) Red state = Ati-Troja WP Phase reversed MW amplitude F (V/cm) MW NDWP cosists of a few states

14 Eergy (GHz) HCP ioizatio sigal (arb. uits) Typical ioizatio sigal of MW MW amplitude F (V/cm) Relative time delay (ps)

15 Eergy Eergy Eergies of two coupled states by a resoat coheret field plotted i a rotatig frame (with agular freq. ) dressed-atom or Floquet picture + - correspodig classical picture electric dipole aliged opposite to a static field + - dipole aliged to the field Rabi frequecy oscillatig dipole

16 Ioizatio probability Ioizatio probability Ioizatio probability Ioizatio probability Ioizatio probability Ioizatio probability Excitatio of circular NDWP (a) MW cavity e - Sigal MCP X-microwave X-HCP. Y directio X directio (a) (b) Liear polarizatio alog Y.5.5. Y-HCP Dye-laser pulses (b) Li beam Y-microwave Field ramp (c) t (ps) (d) t (ps) Circular polarizatio Dye-laser Y-MW pulse X-MW pulse pulses.5.5 y (c) () () (3) (4) () () (3) (4) t Field-ioizatio ramp (e) t (ps) (f) t (ps) Liear polarizatio alog X Li + e - x.5.5 HM, J.H. Guria, T.F. Gallagher, PRL, 3 (9) t (ps). 5 5

17 I Classical iterpretatio of NDWP D atom : H = p x xf cos( t) (i atomic uits) Noliear phase lockig....9 p p q + q x t = t = p/ t = p t = 3p/ Motio of pricipal resoace islad

18 I I p -Resoace islads ad chaotic sea i Poicaré surface of sectios - D atom: H = H xf cos t H p = x x global chaos=ioizatio t Larger F p p q q x.9 65 p p q stable agaist ioizatio

19 I q p p 3.76V/cm 47.9GHz.88V/cm 3.96GHz = = = = F F I (c) MW I q p p (d) MW I (b) CR =7 MW& ) cos( ) cos( t xf t xf x p H = -Commo resoaces (CR) i bichromatic field- = =

20 What is Rydberg atom? Multilevel ladder system What ca we study with Rydberg atom? Microwave multiphoto ioizatio of multilevel system Populatio cotrol of quatum ladder system Dyamic autoresoace ad multiphoto adiabatic rapid passage

21 Eergy Ituitive ad couterituitive populatio trasfer : Multiphoto adiabatic rapid passage(marp) f Three-level ladder ladder climbig (g to f) (a) Dressed-state eergy vs. wavelegth g i A C B i f f i i Populatio trasfer (b) f g i f A C B g f i g g oe-photo avoided crossigs g Positive chirp pulse CIPT (c) Negative chirp pulse Ituitive populatio trasfer (IPT) t g f i A B C wavelegth f i g -photo avoided crossig

22 Eergy (GHz) Eergy (GHz) Eergy (GHz) 5 Multi-level Rydberg ladder system i dressed-atom picture (, =74 +, = + ( = ), =76 -, ) V/cm Two- zero level couplig zero couplig 5 V/cm MW field F MW = V/cm Ladder climbig (dyamic autoresoace) Multiphoto ARP (GHz) (GHz) =79 5 = (GHz) MW field F MW =.5 V/cm.5V/cm (GHz) 7 3 =7 =73 =77 =78 ~ Ladder climbig/ climbig dow = = (GHz)

23 I I Phase-lockig of the electro motio throughout the chirp Dyamic autoresoace B. Meerso ad L. Friedlad, PRA 4, 533 (99) F=.V/cm, /p =9.GHz F =. V/cm =7 = = q 3GHz 9GHz Frequecy (GHz) t 3GHz Phase-lockig throughout the chirp q Z + + E MW 9GHz

24 MW field F MW (V/cm) Ladder-climbig experimet (ex.) =7 to =8 populatio trasfer Time-resolved electro sigal Resoace frequecy / 3 ~3 GHz 8 = 8 7 t Li s p 3s 7p ~9 GHz 7 Laser pulses 9GHz Chirped MW pulse 3GHz State-selective field ioizatio 4 F ~ /6 (a.u.) Eergy levels Li 7p ~ 5 s F MW F 8 F 7 t Field ramp (a). Cotour plot darker area : larger populatio. =8 =7 -% MW ioizatio threshold t (s)

25 Detectig odispersig wave packets durig the chirp (Experimet) Li 7p 9GHz HCP 3GHz (Voltage cotrolled oscillator) t raw data S( ) A Boxcar gate pulsed field 3 4 Laser shots Ioizatio sigal t 7.5GHz 5.5GHz 3.5GHz Fast samplig scope # Istataeous MW field # Its derivative #3 HCP ioizatio sigal sorted data S( ) MW Phase retrieval -p p -p p -p p The electro remai phase-locked as the frequecy is chirped!! ( robust )

26 Eergy (GHz) MW field F MW (V/cm) Populatio trasfer by a sequece of oe-photo adiabatic rapid passages (ARP) Fial Rydberg-state populatio () = (GHz) ~ (a) =7 =8 = = = t (s) Radiatio frequecy must cover the etire iteral frequecies of the ladder system (9 to 3 GHz for = 7 to 8 Rydberg atom) large chirp is required!! Atomic iteral frequecy adiabatically follows the radiatio frequecy (phase-locked) (GHz)

27 Eergy-level structures of Li ad Na Li Na (+)s s l (-) l (+)s p s l (-) l (-)s (-) l (l ) (-)p (-)s (-) l (l ) Quatum defect : d s ~.4 d p ~.5 d d ~. Quatum defect : d s ~.35 d p ~.85 d d ~.6

28 Dressed Na s & p states ad a series of ARP s 3 3. V/cm 6s 59p 3.6 V/cm 6s 59p 5.5 V/cm 59s 58p 58s 58s 59s 58p 58s 5 Dyamic Autoresoace (No-dispersig wave packet) 6s 6p 6s p Frequecy (GHz) 57p Frequecy (GHz) 57p s 5 58p No p-state populatio!? 58s Frequecy (GHz)

29 Experimetal results of Na populatio trasfer through sp ladder Microwave field (V/cm) Eergy (GHz) (a) 58s.. (d) 3 5 (c).5 V/cm. (b) ~65s. (e) ~6s 5 6s 6p 6s 59p 59s. (c) ~63s ~6s t(s) Frequecy (GHz) 58p 58s 3 ~6s t(s)

30 Eergy (GHz) Populatio trasfer via a sigle multiphoto ARP 5 V/cm 5.9V/cm (GHz) We wat to kow if this is true.. (GHz)

31 Multiphoto ARP experimet (ex.) =7 to =8 populatio trasfer Time-resolved electro sigal Li s p 3s p = j i t State-selective field ioizatio 4 F ~ /6 (a.u.) Laser pulses Chirped MW pulse 9GHz 3GHz Li p > 5 s F MW F j F i t Field ramp gate (Gaussia/ Square ) t Frequecy, pulse width t, shape, chirp (width, rate, directio), ad F MW of the MW pulse are cotrollable (MW pulse shapig is easy...)

32 Eergy (GHz) MW amplitude F MW (V/cm) Populatio trasfer a sigle multiphoto ARP (MARP) 7 7 = ~ 78 ~6.4 ~6.4 ~6.4 ~ ~6.4 =8 ~6.4 ~6.4 ~6.4 ~6.4 (GHz).. Fial Rydberg-state populatio () GHz =8 =7 =8 t (s) = Oly a small frequecy chirp is required!! Good for optical pulse shapig (GHz) Selective excitatio of the target avoided crossig!!

33 Doble-pulse experimet : trasitio via a sequetial drive of two MARPs Ca we trasfer the populatio largely with a sequece of multiphto ARPs? Li s p 3s p Laser pulses Li p Two Chirped MW pulses (GHz) t Field ramp 5-5 For example, V/cm Two gates t

34 Double-pulse experimets (=85 ~78 ~ 74) :85->78->scaed 4.8 GHz =85 ~78? :79->scaed 4.8 GHz =79 3

35 Summary NDWP plays a importat role i MW ioizatio aroud = regio Populatio cotrol of Rydberg ladder system has bee demostrated both by meas of dyamic autoresoace ad by drivig MARP ackowledgemet T.F. Gallagher@UVa

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