Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency

0.3 MB·English

by  A. K. Mohapatra

Coherent optical detection of highly excited Rydberg states using electromagnetically
induced transparency
A. K. Mohapatra, T. R. Jackson and C. S. Adams
Department of Physics, Durham University, Rochester Building, South Road, Durham DH1 3LE, England.
(Dated: February 1, 2008)
Weobserveelectromagnetically inducedtransparency (EIT) onthe5s→5p transition in aroom
temperaturerubidiumvapourcellbycouplingthe5pstatetoaRydbergstate(nsorndwithn=26
to 124). We demonstrate that the narrow line–width of the EIT resonance (2 MHz) allows precise
measurementofthedstatefinestructuresplitting,andtogetherwiththesensitivityoftheRydberg
state to electric fields, we are able to detect transient electric fields produced by the dynamics
of charges within the cell. Coherent coupling of Rydberg states via EIT could also be used for
cross–phase modulation and photon entanglement.
7
0 PACSnumbers: 03.67.Lx,32.80.Rm,42.50.Gy
0
2
In comparison to low energy atomic states, highly ex- bergexcitationregion. Asionscanbeproducedbyeither
n
a cited Rydberg states (with principal quantum n > 25) interactions[8] or the laser fields used to excite and trap
J display rich many–body behavior due to their enhanced Rydberg atoms [13], knowledge of the role of ions is es-

0 two–bodyinteractions[1,2]. Forexample,agasofultra– sential to the success of quantum gate schemes. As we
1 coldRydbergatomsisfoundtoevolvespontaneouslyinto show Rydberg EIT provides an useful diagnostic of the
a plasma [3] and back [4]. There is considerable interest presence of charges.

2
v inthepotentialtoexploitthestrongdipole–dipoleinter- The energy levels of 85Rb relevant to this work and
action between Rydberg atoms [5] to realise fast quan-
0 the experimental set-up are shown in Fig. 1. The EIT
tum gates [6, 7]. The dipole – dipole interactions also
0 ladder system consists of a weak probe beam resonant
2 leads to ionization if the ions are not separately con- with 5s 2S (F = 3) → 5p 2P (F′) transition and an
1/2 3/2
2 fined [8]. Inaddition, electromagneticallyinducedtrans- intensecouplingbeamresonantwiththe5p2P (F′)→
1 parency (EIT) involving a Rydberg transition could be nd 2D or 5p 2P (F′) → nd 2D as ind3/ic2ated in
6 usedtodeviseaphotonicphasegateforopticalquantum 3/2 3/2 5/2
0 Fig. 1(a). The d state hyperfine splitting is negligi-
computing [9].
h/ Experimentally,Rydbergatomsaredetectedindirectly ble. The probe beam with wavelength λp =780.24 nm,
power 1 µW and beam size 0.4 mm (1/e2 radius) propa-
p via the ions orelectrons produced by anionizationpulse
gatesthrougharoomtemperaturerubidiumvaporcellof
-
[1]. Thisdetectiontechniqueprovideshighefficiencybut
t length 75 mm, Fig. 1(b). The transmission through the
n isdestructiveandtheatomcannotbere–used. Forquan-
a cellasthe probebeamis scannedis monitoredona pho-
tum information applications a non–destructive detec-
u todiode. The probe laser polarization is varied between
tion of the Rydberg state is preferable. One possibility
q linear (vertical or horizontal) and circular using appro-
: iselectromagneticallyinducedtransparency(EIT)which
v priate waveplates. The coupling beam with wavelength
is manifest as an absence of absorption or an associated
i λc =479.2−483.9 nmisproducedbyacommercialdou-
X rapidvariationinthedispersionallowingdissipationfree
bleddiodelasersystem(TopticaTA-SHG).Thecoupling
sensing of the desired atomic resonance. EIT has been
r beam counter–propagates through the cell with a power
a widely studied in atomic vapors [10], frequently using a
up to 200 mW, a spot size of 0.8 mm (1/e2 radius), and
Λ – scheme where a coherence is induced between two
linear polarization in the vertical direction. The vapor
ground states. Alternatively, in the ladder scheme the
cell is placed inside a µ-metal shield to reduce the effect
coherence is induced between a ground state and an ex-
of stray magnetic fields.
cited state via an intermediate state [11]. Previously,
excited d states with principal quantum number up to A typical spectrum corresponding to the 85Rb
n=8 havebeen observedvia opticalprobing ofa ladder 5s 2S1/2(F = 3) → 5p 2P3/2 → 45d ladder system is
system [12]. shown in Fig. 2. In (a) we show the probe absorption
with the coupling laser tuned close to and far way from
Inourwork,wepresentexperimentalresultsonanEIT
the 5p 2P (F = 4) → 45d 2D resonance. The fre-
ladder system involving highly excited Rydberg states 3/2 5/2
quency axis is calibrated using the known splittings be-
with n = 26−124. We show that the non–destructive
tween the 5p 2P hyperfine states [14]. Note that due
probing of a Rydberg level opens up an wide range of 3/2
to the Doppler mismatch between the probe and cou-
possible experiments. In particular we focus on two ap-
pling lasers, the hyperfine splitting of the 5p 2P state
plications: Firstly we exploit the narrow line–width of 3/2
is scaled by a factor of 1−λ /λ , and the fine structure
the EIT spectra to extend measurement of the nd series c p
splitting of the nd state by λ /λ .
fine structure splitting up to n = 96. Secondly, we il- c p
lustrate the potential of Rydberg EIT for detecting the In Fig. 2(b) we show the difference between the reso-
dynamics of ions or electrons in the vicinity of the Ryd- nant and far–detuned traces. The spectrum contains six
2
(a) (b) a change in the probe transmission of 5%. This peak
nd 2D5/2 Probe beam height is reduced and the width is increased by about a
2D3/2 factor of two if we remove the magnetic shield. The ob-
Electrode
served spectra are not strongly dependent on the probe
Coupling +V -V
479-484 nm laser polarization.
The line–width of the EIT resonanceis between 2 and
Rb
4 MHz depending on the laser power and the transi-
F=4 tion. The EIT line–width is considerably narrower than
5p 2P3/2F=3
F=2 Magnetic shield the natural width of the intermediate 5p states (6 MHz)
but much larger than the natural width of the Rydberg
Probe 780 nm Photodiode
states. At low probe laser power, the line–width is lim-
F=3 ited by the line–width of the probe and coupling lasers
5s2S1/2 Coupling beam
and incomplete cancellation of the Doppler shifts due to
F=2
the wavelengthmismatch. The line–widthcanbe broad-
FIG. 1: (a) Energy level diagram of the 85Rb ladder sys- ened to of order 10 MHz by increasing the probe inten-
tem. A probe beam at 780 nm measures the absorption on sity above saturation providing a convenient signal for
the 5s 2S1/2 →5p 2P3/2 transition while an intense coupling frequency stabilization of the 480 nm laser.
beam at 480 nm dresses the 5p 2P3/2 →nd 2D3/2,5/2 transi- Also apparent in Fig. 2(b) is that the lineshape of the
tionwithn=26−124. Thefineandhyperfinesplittingofthe EITfeaturedisplaysenhancedabsorptionjustbelowand
ndand5p2P3/2statesrespectivelygiverisetosixtwo–photon above the two–photon resonance. This effect arises due
resonancelines. TheRydbergstatehyperfinesplittingisneg- to the wavelength mismatch between the coupling and
ligible. (b) A schematic of the experimental set-up. The 480
probelasers. Althoughtheeffectisknown[15],ithasnot
and 780 nm beams counter-propagate through a room tem-
been observed in previous experiments. One can obtain
perature Rb vapour cell. The transmission of the 780 nm
a theoretical prediction for the EIT lineshape using an
light is detected on a photodiode. The vapour cell is placed
approximate expression for the susceptibility derived in
between two electrodes inside a magnetic shield.
the limit of a weak probe [11]
3λ2
0.58 15 χ(v)dv = −i pγ N(v)dv γ −i(∆ −k ·v)+
(a) (b) 4π 2 2 p p
h
0.56 10 (Ωc/2)2 −1
, (1)
n γ −i(∆ +∆ −(k +k )·v)(cid:21)
sio0.54 −3) 3 p c p c
s 0
mi x1 5 where Ω , ∆ , and k = 2π/λ are the probe or
Trans0.52 ∆ T ( 0 ctoorusp,lriensgppel,accsteivrepRly,ca,bainfdreNqu(pve,)cnicsietsh,edneutump,ncbinergsdeannsditywoafve85vRecb-
0.5 atoms with velocity v. The decay rates γ are the nat-
2,3
ural widths of the intermediate and upper state in the
−5
0.48 ladder system. Additional line broadening mechanisms
−200 −100 0 −200 −100 0
Detuning (MHz) Detuning (MHz) such as laser line–width can be included in γ3. By sum-
ming the contributions from the different hyperfine lines
FIG.2: (a)Probetransmissionasafunctionofprobelaserde- in the 5p 2P state (with appropriate weightings) and
3/2
tuning near the 85Rb 5s 2S1/2(F =3)→5p 2P3/2 resonance integrating the imaginary part of (1) over the velocity
withthecouplinglaserdetunednearlyon–resonance(redline) distribution for a room temperature vapor one obtains
and far above resonance (blue line) with the 5p 2P3/2(F = the absolute absorption coefficient, and hence the trans-
4) → 45d 2D5/2 trnasition. (b) The change in the transmis- missionthroughthe vaporcellasafunction ofthe probe
sion, ∆T, due to the coupling beam given by the difference
detuning. Multiplelevelsintheupperstateoftheladder
between the two curves in (a). Six EIT resonances are ob-
system can be included by adding extra coupling terms
served.
in Eq. (1) [16]. Fig. 3 shows the prediction of Eq. (1)
in comparison to the experimental data for (a) n = 45
and (b) n = 80. The only fit parameters are the Rabi
lines corresponding to transitions between the F =2, 3, frequency and detuning of the coupling laser, the rate
and4hyperfinestatesinthe 5p2P3/2 stateandboththe γ3, and the fine structure splitting of the d state. The
fine structure components 2D and 2D of the 45d enhanced absorptionobservedat higher Ω , Fig. 3(a), is
3/2 5/2 c
state as indicated in Fig. 1(a). The position of the EIT accurately predicted by Eq. (1).
peak within the Doppler broadened absorption profile is For the 80d state, Fig. 3(b), the change in the probe
determined by the coupling laser detuning. For a cou- transmission is reduced to about 1%. This is consistent
pling power of 180 mW, the largest peak corresponding with the expected 1/n3/2 scaling of the coupling beam
tothe5p2P (F =4)→45d2D resonance,produces Rabi frequency. We can still observe the EIT resonance
3/2 5/2
3
0.55

0.6 (a) (b) z)
H100
0.59 0.545 M
n g (
o0.58 n
missi0.57 0.54 plitti 50
ans0.56 e s 40
Tr ur 30
0.55 0.535 uct
0.54 str 20
e
0.53 0.53 Fin
−100 −50 0 50 −100 −80 −60 −40 −20 12
Detuning (MHz) Detuning (MHz)
50 60 70 80 90
n
FIG. 3: Probe transmission as a function of detuning (thick
redline)comparedtoEq. (1)(thinblackline)for(a)then=
FIG.4: Theobservedfinestructuresplitting(filledcircles)of
45dstatewithΩc =2π(3.5MHz)andγ3 =2π(0.3MHz),and thedstateasafunctionoftheprincipalquantumnumbern.
(b) n=80 with Ωc =2π(1.5 MHz) and γ3=2π(0.3 MHz). The open diamonds are data from Ref. [17]. The line is a fit
of the form A/n∗3 with A=11.5(4)×103 GHz.
uptothe101dstateandusinglock-indetectionuptothe
124dstate. TheEITspectragiveadirectmeasureofthe 700 -30) 0
1
d state fine structure splittings. Previous measurements x -5
using two–photon absorption and a thermionic diode to s) 600 T ((cid:39)-10
(cid:80)
detecttheionisedRydbergstateshavereportedvaluesup e ( 500 cm) 2
to n=65 [17]. We are able to resolvethe splitting up to m V/ 0
n=96. InFig. 4weplotthe finestructuresplittingasa nt ti 400 E ( -2-100 0 100 200
afufintctaiossnuomfinngtoagefothrmerAw/itnh∗d3awtaithfroAm=[1171]..5T(4h)e×lin1e03shGoHwzs nsie 300 Time ((cid:80)s)
a
and n∗ = n−δ, where δ = 1.35 is the quantum defect. Tr
200
The n = 75 spectrum displays an asymmetric lineshape
which leads to a systematic error. Our measured split- 100
tings are typically larger than those observed in [17] by
0 20 40 60 80 100 120 140 160 180
up to 10 MHz.
Laser power (mW)
Finally, we investigated the effect of an external elec-
tricfieldontheRydbergenergylevelsbyapplyingavolt-
agebetweenthecopperbarelectrodesshowninFig.1(b). FIG. 5: The width of the EIT transient as the electric field
is switched between ±10 V/cm as a function of the coupling
We observe no effect on the EIT spectra for dc elec-
tric fields up to 100 Vcm−1 regardless of the probe and laser power. The transient time decays exponentially to a
fixedvalueat high power. Inset: Thetransient EITresponse
coupling laser polarizationssuggestingthat the Rydberg
as thefield is switched between ±2V/cm.
atoms are being screened. The main source of charge
within the cell appears to be ions and electrons pro-
duced by photo – desorption induced by the coupling
laser at the surface of the cell [18]. For example, by to a time varying field we lock the probe laser to the
retro–reflecting the 480 nm laser with a glancing angle 5s 2S (F =3)→5p 2P (F =4) transition using po-
1/2 3/2
at the cell wall we can generate an asymmetric charge larization spectroscopy [19], and tune the coupling laser
distribution which creates a field of order 50 mV/cm in to resonance with the 5p 2P (F = 4) → 45d 2D
3/2 5/2
theEITinteractionregion. Wecandetectthissmallfield transition. The change in transmission(∆T) as the field
as a 2.5 MHz splitting of the 70d line. is switched is shown in Fig. 5(inset). Eachtime the field
To further investigate the screening effect and charge direction changes the EIT peak is suppressed due to the
dynamics within the cell, we studied the effect switch- transient penetration of the applied field. The duration
ing the electric field direction in a time of order 1 µs. ofthistransientdependslinearlyontheamplitudeofthe
Foradcfield, thechargesdriftwithadistributionwhich field,anddecreasesexponentiallywiththecouplinglaser
exactly compensates the applied field. However, if the power, see Fig. 5. The dependence on the coupling laser
field is switched in a time less than the relaxation time power arises because at higher power the charge density
of the charge distribution there is incomplete cancella- isincreasedandthedistributioncanrelaxfastertowards
tion of the applied field leading to a perturbation of the the steady–state fully–screened distribution. There is a
EIT signal. To monitor the response of the EIT peak smallasymmetrybetweentheresponsetoincreasingand
4
3 (a) (b) corresponding to their respective |mJ| components, as
shown in Fig. 6. Similar spectra have recently been ob-
2 served by ionizing ultra–cold Rydberg atoms [20]. In a
time varying field, one may not expect to observe nar-
1
row lines, however, due to the quadratic dependence on
)
2
− the electric field, the time dependence of the resonance
0 0
(x1 3 (c) (d) lines hasarectifiedsin2–dependence whichisalmostlike
T a dc field. The distortion of the lineshape due to the
∆ 2 time–dependence of the field is most apparent in the
2D (|m | = 1/2) line (at −120 MHz in Fig. 6(d)) as
5/2 J
1
it has the highest field sensitivity. These results indicate
that Rydberg EIT could provide a useful optical probe
0
−200 −100 0 −200 −100 0 of photo–ionization processes and plasma dynamics.
In summary, we have demonstrated the coherent op-
Detuning (MHz)
tical detection of highly excited Rydberg states (up to
n = 124) using EIT, providing a direct non–destructive
FIG. 6: EIT spectra observed by scanning the coupling laser
across the 5p 2P3/2(F = 4) → 45d 2D resonance with the probe of Rydberg energy levels. The observed spectra,
probelaserlockedtothe5s2S1/2(F =3)→5p2P3/2(F =4) display enhanced absorption below and above the Ryd-
transition. Ahigherprobepowerisusedsothelinesarepower berg resonance, and can be accurately predicted by the
broadened and the enhanced absoprtion effect is lost. An rf optical Bloch equations. The narrow line–width of the
field with frequency 90 MHz and amplitude (a) 0; (b) 180; EIT resonance allows us to extend measurements of the
(c)320;and(d)480mV/cmisapplied. Thelargest andnext fine structuresplitting of the ndseries up to n=96. We
largestpeakin(a)arethe2D5/2and2D3/2lines,respectively. also show that the EIT spectra are sensitive to charge
Asthefieldisincreasedtheselinesaresplitinto3and2|mJ| dynamics within the cell. In our experiment the density
states. In (d) the 2D3/2(|mJ| = 1/2) states have moved out ofatomsparticipatingintheEITresonanceismorethan
of frame to theleft.
two orders of magnitude lower than the density used in
the observation of dipole blockade [5]. In future work
we will apply the technique to higher density vapors to
decreasingfieldthatdependsonthealignmentoftheEIT investigatedipoleblockadeeffectsandtheirpotentialap-
probe relative to the center axis of the cell. plication in photon entanglement [9].
If we apply an rf frequency to the electrodes then We are grateful to S. L. Cornish, I. G. Hughes, M. P.
the time variation of the field is too fast for either the A. Jonesand R.M. Potvliegefor stimulating discussions
ions or electrons to screen the field. In this case, the and A. P. Monkman for the loan of equipment. We also
2D and 2D resonances are split into 3 and 2 lines thank the EPSRC for financial support.
5/2 3/2
[1] T. F. Gallagher, Rydberg atoms (Cambridge University Mod. Phys.77, 633 (2005).
Press, Cambridge 1994). [11] M. Xiao, Y. Q. Li, S. Z. Jin and J. Gea–Banacloche,
[2] I.Mourachko,D.Comparat,F.deTomasi,A.Fioretti,P. Phys. Rev.Lett. 74, 666 (1995).
Nosbaum, V. M. Akulin, and P. Pillet, Phys. Rev. Lett. [12] J. Clarke, H. Chen and W. A. van Wijngaarden, Appl.
97, 083003 (2006). Opt. 40, 2047 (2001).
[3] M. P. Robinson, B. Laburthe Tolra, M. W. Noel, T. [13] R. M. Potvliege and C. S. Adams New J. Phys. 8, 163
F. Gallagher, and P. Pillet, Phys. Rev. Lett. 85, 4466 (2006).
(2000). [14] U. D. Rapol, A. Krishna and V. Natarajan, Eur. Phys.
[4] T. C. Killian, M. J. Lim, S. Kulin, R. Dumke, S. D. J. D 23, 185 (2003).
Bergeson and S. L. Rolston, Phys. Rev. Lett. 86, 3759 [15] A. Krishna, K. Pandey, A. Wasan and V. Natarajan,
(2001). Europhys. Lett. 72, 211 (2005).
[5] T. Vogt, M. Viteau, J. Zhao, A. Chotia, D. Comparat, [16] S.D.Badger, I.G.HughesandC.S.Adams,J.Phys.B
and P. Pillet, Phys. Rev.Lett. 97, 083003 (2006). 34, L749 (2001).
[6] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cˆot´e [17] K. C. Harvey and B. P. Stoicheff, Phys. Rev. Lett. 38,
and M. D. Lukin,Phys. Rev.Lett. 85, 2208 (2000). 537 (1977).
[7] M. D. Lukin, M. Fleischhauer, R. Cˆot´e, L. M. Duan, D. [18] J. H. Xu, A. Gozzini, F. Mango, G. Alzetta and R. A.
Jaksch, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 87, Bernheim, Phys.Rev.A 54, 3146 (1996).
037901 (2001). [19] C.P.Pearman,C.S.Adams,S.G.Cox,P.F.Griffin,D.
[8] W.Li,P.J.TannerandT.F.Gallagher,Phys.Rev.Lett. A. Smith,and I.G. HughesJ. Phys. B 35, 5141 (2002).
94, 173001 (2005). [20] A.Grabowski, R.Heidemann,R.L¨ow,J.StuhlerandT.
[9] I. Friedler, D. Petrosyan, M. Fleischhauer, and G. Kur- Pfau, Fortschr. Phys. 54, 765 (2006).
izki, Phys.Rev. A 72, 043803 (2005).
[10] M.Fleischhauer,A.Imamoglu andJ.P.Marangos, Rev.