Enhancement of Rydberg atom interactions using dc and ac Stark - - PowerPoint PPT Presentation

University of Virginia, Department of Physics 6/27/2011

Enhancement of Rydberg atom interactions using dc and ac Stark shifts

Parisa Bohlouli-Zanjani

Enhancement of interatomic interactions by electric field induced resonant

energy transfer (RET)

Determining unknown atomic energy levels by dc field induced RET spectra Using ac field induced RET for energy level determination where dc field

can not be used

RET can be utilized in the implementation of dipole blockade 2

Objective Motivations

A + A ! B + C

3

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

4

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

5

Rydberg atoms

• loosely bound electron circling ionic core.

Ionization continuum Infinitely many bound states

• these states have long lifetimes (eg. 17p of Na: 50 µs ).
• properties scale with n and can be exaggerated.

for Na ionization potential quantum defect Rydberg constant (13.5 eV)

6

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

7

Experimental Methodology

• Form cold Rb atoms in a MOT for studies

between stationary atom

1 mm3, 300 µK , Rydberg atoms: 107 cm-3

• Rydberg

atom excitation using 480nm frequency doubled Ti:sapphire laser

• Measurement and compensation of stray E and B fields using mwave transitions

between Rydberg states

• Do experiment …
• Verify excitation using SFI technique
• 10 Hz repetition rate

8

Selective Field Ionization (SFI) detection of Rydberg atoms

400 300 200 100

• 100
• 200

Voltage (V) 12x10

• 6

10 8 6 4 2 Time (s) slowly rising FIP

ion signal (47s1/2 & 47p1/ 2 states)

47p1/2 47s1/2

Field ionization pulse MCP signal

47p1/2 47s1/2

voltage time (µs)

Use SFI to determine state

distribution in the trap.

9

Rydberg Atom Excitation

Energy

6s 5p3/2 ~ 780 nm Cooling & trapping transitions (Diode Laser) ~ 480 nm Frequency doubled Ti:sapphire laser 5s ns np Ionization Continuum Infinitely many bound states 46d nd 5d

10

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

Stabilize lasers at frequencies where direct locking to a

reference line is not possible

High resolution optical spectroscopy for laser cooled

Rydberg atom excitation. Optical Transfer Cavity Stabilization using Tunable Sidebands of RF Current-Modulated Injection-Locked Diode Lasers

Motivation Objective

Review / Alternative approaches

• Absolute frequency reference (Barger 1969)

Beat note locking Practical up to a certain frequency difference

feedback ref. laser PD trgt. laser feedback ref. laser trgt. laser

TC

PC

• Scanning transfer cavity (TC) (Lindsay 1991,

Rossi 2002)

Scanning rate limits the maximum error correction Sensitive to low frequency vibrations Complexity of the fringe comparison

ref. laser trgt. laser TC feedback

AOM (EOM)

• Stabilized TC (Burghardt 1979, Plusquellic 1996)

Frequency shift using EOM or AOM

A general frequency stabilization technique

Fabry--Perot TC stabilized using a tunable sideband

from a current modulated injection locked diode laser.

Frequency shifts without using AOMs or EOMs. Not limited to certain wavelengths Tuning frequency with RF precision.

14

Experimental setup :

piezo

transfer cavity

PD

control circuit

PBS PBS

control circuit

to MOT

doubler 480 nm

λ/2

Ti:Sapphire ring laser- 960 nm

PD

fiber λ/2 master laser 780nm

Rb PS locking

fiber FR λ λ λ λ/2 λ λ λ λ/2

slave laser

fiber PBS λ λ λ λ/2 PBS

RF

+fm

• fm
• R. Kowalski et al.,
• Rev. Sci. Instrum.

72, 2532 (2001).

fm

15

Rydberg atom excitation (85Rb)

Autler –Townes splitting : B. K. Teo et al., Phys. Rev. A. 68, 053407 (2003).

0.6 0.4 0.2 0.0 Averaged MCP signal (V) 100 80 60 40 20 Target laser (960nm) frequency + offset (MHz) (a) (b) (c) (d) 59.5 MHz

3/2

46d

5/2

46d

(a) (b) (c) (d) 119 MHz 385 THz 46d 5/2

1/2

5s

3/2

5p

3/2

46d cooling laser 780nm

16

Frequency stability

• Frequency fluctuation of the

target laser (Ti:sapphire, 960 nm)

(a) unlocked 140 MHz (b) locked < 0.25 MHz

140 120 100 80 60 40 20

• 20

MBR freq drift (MHz) 3000 2000 1000 time(s)

• 1.0

0.0 1.0

drift (MHz)

30 00

time(s)

(b) locked

(a) unlocked

(a) unlocked

Not limited to certain wavelengths Tuning frequency with RF

precision.

Frequency shifts without using

AOMs or EOMs.

17

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

• P. Filipovicz et al., Optica Acta, 32, 1105 (1985)

Properties of Rydberg atoms

• 3

n¤ = n ¡ ±

l

dipole-dipole interaction strong for Rydberg states -- even

• ver long distances.

atoms temporarily excited to Rydberg states strongly interact

due to dipole-dipole interaction -- but don’t interact when in ground state.

^ Vdd = ~ ¹ A ¢~ ¹ B ¡ 3 (~ ¹ A ¢~ n)(~ ¹ B ¢~ n) R3

A B

RA B ^ n

~ ¹ B ~ ¹ A

Electric Dipole-Dipole Interactions between Rydberg Atoms

Resonant Energy Transfer (RET) through dipole-dipole interactions

A + A ! B + C A + A ! B + C

21

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

22

Resonance condition may be achieved using Stark effect:

Electric field (V/cm) Energy (cm-1) 100 300 200 20p 20s 19p

• 316
• 332
• 334
• 330
• 314
• 300
• 298

After excitation of 20s states:

Electric field (V/cm) 200 20p signal 210 220 240

23

Achieving resonance condition in Rb

Rb Stark map - energies relative to 44d5/2

44d5=2 + 44d5=2 ! 42f 5=2 + 46p3=2

24

Mismatch as a function of n

Consider the process:

Energies determined using quantum defects from:

• J. N. Han et al., PRA 74, 054502 (2006); W. H. Li et al., PRA 67, 052502 (2003)

Energy shifts of this magnitude can be easily

• btained using the

ac or dc Stark effect

¢ Em i sm at ch = Ef ¡ Ei

¢ Em i sm at ch

nd5=2 + nd5=2 ! (n + 2)p3=2 + (n ¡ 2)f

25

Observation of dc field induced RET at n = 44

44d5=2 + 44d5=2 ! 46p3=2 + 42f

Observation of dc field induced RET at n = 32

32d5=2 + 32d5=2 ! 34p5=2 + 30g

27

Resonant electric fields can be used to determine energy levels

known energies unknown!!

32d5=2 + 32d5=2 ! 34p5=2 + 30g

±

g(n = 30) = 0:00405(6)

28

Lower n by 1 and process cannot be tuned into resonance

nd5=2 + nd5=2 ! (n + 2)p3=2 + (n ¡ 2)f 5=2;7=2

n = 43 n = 44

ω !"#

• s

! > Ens ! < Ens

• $
• s

(") Ens = En ¡ Es

Can an ac field be used?

Perturbative dc Stark effect Perturbative ac Stark effect

¢ En = 1 2"2

z

X

s

En sj < nj ¹ zjs> j2 E 2

n s ¡ (~! )2

¢ En = " 2

z

X

s

j < nj ¹ zjs> j2 En s " z " z

30

Summary of the materials to be discussed

Rydberg atoms Experimental methodology

Magneto-Optical Trap (MOT), Selective Field Ionization (SFI) Laser frequency stabilization

Dipole-Dipole interactions, RET dc electric-field-induced RET

Estimation of g series quantum defect

Observation of ac electric-field-induced RET

31

Observation of ac field induced RET at n = 43

%&'() %&*()

• 43d5=2 + 43d5=2 !

45p3=2 + 41f 5=2;7=2

32

Observation of ac field induced RET at high frequency

+""," -./

+0

• "

43d5=2 + 43d5=2 ! 45p3=2 + 41f 5=2;7=2

33

Summary

Developed a general technique for laser frequency stabilization at

arbitrary wavelengths

Determined unknown energy levels using dc field induced RET Demonstrated ac field induced RET at two different frequencies in Rb

ac fields can be used in some situations where dc fields cannot

Using a microwave, one could turn interactions on and off quickly

(due to modulation capabilities of the source)

Acknowledgment : J. D. D. Martin, J. Petrus, D. Vagale, M. Fedorov, A. Mogford,

• K. Afrousheh, J. Carter, Owen Cherry.

Funding: NSERC, CFI, OIT, AECL, University of Waterloo

Thank you!

35

ac field induced RET vs. dc field induced RET

Ec + Ed ¡ Ea ¡ Eb = 0 Consider this process: RET condition:

En = En 0 + " 2

zkn

zero field energy Stark shift ¢ En = 1 2"2

z

X

s

En sj < nj ¹ zjs> j2 E 2

ns ¡ (~! )2

ac Stark shift

¢ En = "2

z

X

s

j < nj ¹ zjs> j2 Ens

dc Stark shift (EC0 + ED 0 ¡ EA 0 ¡ EB 0 ) + " 2(kc + kd ¡ kA ¡ kB ) = 0

¢ Em i sm at ch + " 2k = 0

a + b! c+ d

36 Study the interaction and dynamics of the transitionally cold Rydberg

atoms, by controlling and minimizing the dephasing processes.

Identify reversible and irreversible dephasing processes in the study of

electric dipole-dipole interactions between cold Rydberg atoms(1).

Diagnose electric field inhomogeneity in Rydberg atoms’ surface

interactions due to patch fields.

Maintain the internal coherence of a single trapped Rydberg atom(2).

Motivations Objectives

1) K. Afrousheh, et al, Phys. Rev. Lett., 93, pp. 233001 (2004). 2) P. Hyafil, et al, Phys. Rev. Lett., 93, 103001 (2004)

Observation of Echo effect using cold Rydberg atoms in a magnetic field inhomogeneity

37

Geometrical representation of the Spin echo:

(E) (F) (A) (B) (C) (D) (F) (E) π / 2 time π τ τ (A) (B) (C) (D) x x x x x x z y z y z y z y z y z y

Initial state (0,0, Mz) ) ( } , , { γ × = = dt d M M M

z y x

H M M M

Magnetization Total magnetic field T=0

38

• Spin Echo technique in NMR

Magnetization

• Rydberg atoms Echo effect

Cold Rydberg atoms’ echo effect in correspondence to Spin echo technique

) ( } , , { γ × = = dt d M M M

z y x

H M M M

3 * 3 2 * 2 1 * 1 3 2 1

/ ) ( ) ( / ) ( } , , { ω ω ω ω ω = − ≡ − = − ≡ + = + ≡ × = =

∗ ∗ ∗

bb aa r V V i ba ab i r V V ba ab r dt d r r r

ba ab ba ab

• r

r r

1 ) ( ) ( ) ( t b t a t + = ψ

With perturbation V

(48s1/2) (48p1/2)

39

Geometrical representation of the Spin echo:

(E) (F) (A) (B) (C) (D) (F) (E) π / 2 time π τ τ (A) (B) (C) (D) x x x x x x z y z y z y z y z y z y (G) π / 2 (G) x z y

Initial state (0,0, 1)

T=0

Rabi Oscillation on 34s5/2-34p 5/2 one-Photon Microwave Transition

41

• Two-photon transitions between Rydberg states with the same gJ factors show

negligible broadening in a MOT.

• E.g.,

Rabi Oscillation on 32d5/2-33d 5/2 Two-Photon Microwave Transition

1.2 1.0 0.8 0.6 0.4 0.2 0.0

FIP Signal (normalized)

6.0 5.0 4.0 3.0 2.0 1.0 0.0

microwave pulse length (us)

33d 32d

2 / 5 2 / 5

) 1 ( d n nd + →

42

Can an ac field be used?

?

$0 12 1"2 0 3""0 .#

¢ En = · n (! )F 2

z

42f 7=2 ¡ 42g9=2 41f 7=2 ¡ 41g9=2

43d5=2 + 43d5=2 ! 45p3=2 + 41f 5=2;7=2

43

Field strength at this frequency is calibrated using 2-photon probe shifts

43d 44d probe

0.6 0.5 0.4 0.3 0.2 0.1 0.0 44d5/2 fraction 43.9328 43.9324 43.9320 43.9316 43.9312 Probe Frequency (GHz) with dressing without dressing

Assume Stark shifts given by: to determine field strengths.

44

AC dressing field power calibration

0.6 0.5 0.4 0.3 0.2 0.1 0.0 45p signal fraction

• 14
• 12
• 10
• 8
• 6
• 4
• 2

Dressing Input Power (dBm) Power scan: dressing at 28.5 GHz 43d5/2 + 43d5/2 -> 41f5/2 + 45p3/2 8 4

• 4

Mismatch (MHz) 6 5 4 3 2 1 Field Amplitude (V/m) Mismatch: 43d5/2 + 43d5/2 -> 41f5/2 + 45p3/2 Calculated Experimental

Using 2-photon probe shifts calibration

Comparison with theory

Calculated and experimental field amplitude agree well at ~ 3.7V/m!

45

vdW and resonant dipole-dipole interaction strengths

plot thresholds for observation of shifts of 1 and 10 MHz

between 1 and 10 mm, threshold n differs by factor of 3. advantages of lower n (resonant interaction): easier to make transitions from ground state (n -3). less sensitivity to external perturbations (n 7). disadvantages of van der Waals (higher n): 1/R3 is longer range -- multi-body effects more important.

ground state

• Ryd. state

1 Ryd. atom 2 Ryd. atoms Dipole-dipole interaction ‘blocks’ excitation

• f 2 or more Rydberg atoms

dipole blockade

47

Verify the stability of the target laser

Energy

5d 6s 5p3/2

~ 780 nm Cooling & trapping transitions (Diode Laser) ~ 480 nm (MBD)

5s 46d3/2 46d5/2

Rydberg atom excitation (85Rb)

• The tuning accuracy and the drift

behavior of the frequency locked target laser is characterized using Rydberg atom excitation in a 85Rb magneto-optical trap (MOT)

Target laser stability depends on the stability of reference laser

• Polarization Spectroscopy

locking [1]

• Reference laser stability is

characterized by another laser which is locked using sauturated absorption locking by dither/third harmonic lock- in detection [2]

[1] C.P. Pearman et al., J. Phys. B., 35, 5141 (2002) [2] Jun Ye, Steve Swartz, Peter Jungner,* and John L. Hall , Opt. Lett. 21, 1280 (1996).

• 0.4
• 0.2

0.0 0.2 0.4 Beat frequency + offset (MHz) 6000 5000 4000 3000 2000 1000 time(s) 0.23 MHz

Saturated absorption spectrum Polarization spectrum

Summary and Future work

• A general technique for laser frequency stabilization at an arbitrary wavelength

with frequency stability on the order of 1MHz/hr.

• Involves equipment and techniques commonly used in laser cooling and

trapping laboratories.

• Does not require special modulators and drivers.
• The frequency of the target laser can be tuned with RF precision.

……….

• Evacuate the cavity to minimize environmental effects.
• Improve the stability of the reference laser.

Ti:Sapphire Ring Laser – MBR110

Reference Cavity Pump

PZT

Photodiodes Etalon Brewster Plates BRF OD

Control Box

Doubler – MBD

Photo- diodes λ/2 λ/4 Resonant Cavity

Rydberg atom excitation laser, target laser

To MOT

• 960nm commercial ring

Ti:sapphire laser.

• Frequency doubler,

external ring resonator