Selective population of dressed states by rapid adiabatic passage

12 January 1996

ELSEVIER

CHEMICAL PHYSICS LETTERS Chemical Physics Letters 248 (1996)244-248

ii

Selective population of dressed states by rapid adiabatic passage A.F. Linskens, N. Dam*, B. Sartakov 1, j. Reuss Department of Molecular and Laser Physics, Catholic University of Nijmegen, 6605 MB Nijmegen, Netherlands

Received 17 July 1995; in final form 1 November 1995

Abstract

We report the direct observation of the dressed state which is populated during adiabatic passage of a molecule through the curved wavefronts of a strong nominally resonant pump laser. The dressed system is probed by a weak probe laser halfway during its passage through the pump field. Adiabaticity is demonstrated to break down at high probe intensity.

1. I n t r o d u c t i o n

Excitation schemes which efficiently transfer population from a molecular ground state to an excited state are of interest to many fields of atomic and molecular physics, where the use of vibrationally or electronically excited atoms or molecules provides an additional degree of freedom. Examples include (reactive) molecular scattering [ 1-3 ], surface scattering [4], hot band spectroscopy [5,6], etc. An efficient way of selective population transfer by optical excitation is provided by the rapid adiabatic passage (RAP) technique (see, for example, Ref. [7] ). For a two-level system this involves exposing molecules to a monochromatic laser pulse with a smooth intensity profile which is chirped through resonance during the interaction time. Such a pulse can lead to 100% inversion on the selected transition, almost independent of the experimental parameters, as has been demonstrated using cw [ 8 - 1 1 ] and pulsed [12,13] lasers. Using two different lasers, both of them resonant and not chirped in * Corresponding author. E-mail: [email protected] l General Physics Institute, Moscow, Russian Federation.

frequency but slightly delayed in time with respect to each other, essentially the same phenomenon has been shown to occur in three-level systems [ 13-16]. The common feature of all level schemes to which RAP has been applied is that the whole system of molecule and laser field(s) is prepared in an eigenstate, the so-called dressed state (see e.g. Refs. [ 17,18] ), in which it remains during the whole interaction time (adiabatic passage). During the interaction, however, the laser parameters change in such a way that this eigenstate, initially corresponding to the molecular ground state, corresponds to the molecular excited state after the interaction (see also Fig. 2). In a sense, it is thus possible to make a transition without changing state! Usually, only the final result of the interaction is reported [ 8 - 1 6 ] . Here, we focus on R A P in a twolevel system using a weak second laser to probe the system during its passage. We show that the population is indeed confined to a single dressed state. For increasing probe power, the perturbation it introduces to the dressed states destroys the adiabaticity o f the interaction, which results in the redistribution of the

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A.F. Linskens et al./ Chemical Physics Letters 248 (1996) 244-248

245

population over both available dressed states. It should be noted that dressed states can also be prepared nonadiabatically, by carefully controlling the phase o f the excitation laser, as has been demonstrated by Mossberg and co-workers [ 19]. In Fig. 1a the molecular energy level scheme pertinent to our experiments is represented schematically. A strong laser ( p u m p laser) couples the molecular ground state, which initially carries all the population, to an excited state. The influence this pump laser exerts on both the energy levels themselves as well as on the population thereof can be probed by another much weaker laser ( p r o b e laser), either on the same transition or on a transition to a third level which is unaffected by the p u m p laser. As long as the probe laser is much weaker than the pump laser, this allows a treatment o f only the pump laser in the dressed atom picture and to consider the probe laser semi-classically, as a weak perturbation. Following the notation o f Cohen-Tannoudji et al. [ 17 ], the dressed states can be expressed in terms o f the uncoupled states o f molecule and field as

pump laser and the detuning, zl, which can be summarized as

11) = s i n e l a ; N) + cos e l b ; N - 1),

(1)

¢

12) = cos e l a ; N) - sin e l b ; N - 1),

(2)

with R ( z ) the radius o f curvature o f the wavefronts at a distance z from the focus. In our case sr < 0. The behaviour o f the dressed states ]1) and t2) during the passage through the laser beam is depicted schematically in Fig. 2; this figure also serves to illustrate the way R A P proceeds, and how this phenomenon can be monitored by a second laser on the same or another transition.

where by convention, dressed state I1) has the higher energy (Fig. I b). Here, the quantized field is described in terms o f photon number states IN) [ 18,20]. In the semi-classical limit, the mixing coefficients are a function o f the Rabi frequency, OR, associated with the

@

@ C

A J' A

fT

/

l

In our case, the molecules in a molecular beam pass through the curved wavefronts and the Gaussian intensity profile o f a single mode laser beam, which is focused close to but not on the molecular beam [ 10] (see also Fig. 3). Thus, both OR and A become timedependent, in such a way that adiabatic passage is achieved [ 21 ]. Their functional time dependences are given by OR(l) = ,OR(0) e x p [ - ( l / T ) 2 ] and

d ( t ) = srt.

(4)

Here, the parameter 7-depends on the width o f the laser focus and the flow velocity o f the molecular beam, vf; the (constant) tuning rate ~" also depends on the degree o f focussing and the position o f the focus relative to the molecular beam, as =

---v0,

(5)

cR(z)

la;N+O

l a;N> a

(3)

A

[\b,'

C ............................

Probe ~ b

Pump

OR

tan 2~9 = - - -

~,A

Ib;N-l> f

I1> .... 12>

Bare Dressed Fig. 1. (a) Relevant part of the SF6 energy level scheme. The transition b ~-- a is the p3P(4)E transition, induced by the pump laser (fat arrow, with detuning zl). The probe laser (thin arrow) monitors the 2t-'3 +-- p 3 Q ( 3 ) E transition (c ~-- b). (b) Bare states (left) and dressed states (right) used to describe the coupling of the molecule with the pump laser field. Only pump photons are used in the dressed state description.

h,

Ib;N>

Ic>

1 Ib;N-l>

'="

la:N>

I b ~ N )

Fig. 2. Probing of the dressed states by a weakly driven transition between the pumped levels (a) or to a third level (b). The molecule is prepared in the bare state containing la) (populated state indicated by solid dot), which corresponds to the dressed state I1) when the molecule enters the pump laser focus. Transitions which can be observed under these conditions are indicated.

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A.F. Linskens et a l . / Chemical Physics Letters 248 (1996) 244-248

A weak probe laser can be introduced to probe the dressed states during adiabatic passage. When this probe laser acts on the same transition as does the pump laser, it couples the bare states la; N) and Ib; N), i.e. it couples adjacent rungs of the dressed state energy ladder (Fig. 2a). In principle, this implies that four transitions should be possible. Only two of these will be observed under conditions of adiabatic passage, because of the specific population distribution; both of these leave the molecule unexcited (see again Fig. 2a; the state which carries the population is marked by a solid dot). When the probe laser operates on another transition, the upper level is not affected by the pump laser. Two transitions are possible in this case, only one of which is expected to be seen under conditions of RAP (Fig. 2b).

2. Experimental

zT PUMP LASER

MOLECULAR BEAM

13tlmr'}

y

m probe

MOLECULAR BEAM

The heart of the experimental apparatus is formed by a molecular beam machine equipped with a liquid He cooled bolometer [22] and two home-built, cw waveguide CO2 lasers. An extensive description of the apparatus can be found elsewhere [23], so we will limit ourselves to those details pertinent to the present experiments. The molecular beam is produced by expanding a 2% SF6 in He mixture at 200 kPa ( 1500 Torr) through a room temperature 30/~m nozzle. Its total internal energy is detected by a liquid He cooled semiconductor bolometer, which is pumped down to 1.5 K. The molecular beam is crossed perpendicularly by two counterpropagating CO2 laser beams (both slightly tilted in order to avoid mutual cavity perturbations). Both lasers have a tuning range of 1 GHz around the laser line centers (by using acousto-optic modulators) and a linewidth of less than I00 kHz. Using cylindrical optics the pump beam is focused to an elliptical spot, elongated along the direction of the molecular beam (interaction length of 10 mm). It is focused close to, but not on, the molecular beam, so that the molecules 'see' curved wavefronts. This is illustrated in Fig. 3. The probe laser is focused to a ¢ = 0.5 mm circular spot in the centre of the pump laser. This configuration probes the molecules in a region of virtually constant pump laser intensity [24]. SF 6 is pumped on the P ( 4 ) E transition of the fun-

Fig. 3. Experimental configurationof pump and probe laser foci where they overlapwith the molecularbeam (not to scale). Cylindrical optics are used to create an elongated pump laser focus, so that the probe laser 'sees' moleculeswhich are immersed in a virtually homogeneouspump field. damental 93 band (b ~-- a in Fig. la) and probed either on the same transition or on the Q ( 3 ) E of the 293 ~-93 hot band [ 11,25]. These transitions are 250 MHz and 98 MHz, respectively, detuned from the 10P16 CO2 laser line centre (at 947.7420 cm -1 [26] ) (c b in Fig. la). In the experiments the pump laser is intensity modulated by a mechanical chopper, while its frequency is kept fixed. The probe laser is scanned in frequency and the bolometer signal is lock-in detected at the chopper reference frequency. Thus, all spectral features observed are due to the combined interaction of both lasers.

3. Results and discussion The main result of this Letter is contained in the spectra presented in Fig. 4. These spectra are recorded with the fixed frequency pump laser on resonance with the 93P(4)E transition in SF6. The probe laser is tuned over the concatenated Q ( 3 ) E transition (see Fig. la), and probes the molecules dressed by the pump field;

A.F. Linskens et a l . / Chemical Physics Letters 248 (1996) 2 4 4 - 2 4 8

247

~R (MHz)

~R ( i Hz)

0.5 0.5 2.6 t~ v t~ e-

2.6

v

5.2

5.2

E

10

0 m

10

O

m

20

20 i

;08'0

i

i 100

i ' 110

120

Probe laser detuning (MHz)

,

,

,

,

80

90

100

110

Probe laser detuning [MHz]

Fig. 4. (a) Three-level pump-probe experiment, with a weak probe laser. The configuration is such that the molecules pass adiabatically through the elongated pump laser focus, and are probed in its centre. The pump laser Rabi frequency at the position of the probe laser is indicated to the right of each trace. The dashed curves are calculated iineshapes, taking into account the residual Doppler width, transverse variations of the pump laser intensity and the M-degeneracy of the rotational levels involved. Only one dressed state is seen to carry the population, a feature characteristic of adiabatic passage. (b) As in (a), but using high probe laser intensity. Adiabaticity breaks down due to the perturbation induced by the probe laser, and the population is spread out over both dressed states available.

the (local) pump laser Rabi frequency is indicated for each trace. Fig. 4a is recorded with as low probe laser power as possible while still retaining a reasonable signal-to-noise ratio (2 mW, corresponding to ~Rr°be ,~ 4 MHz in the centre of the focus). All traces essentially show one single peak, which shifts to the red with increasing pump laser power. In the ideal case, the shift should be equal to half the local pump laser Rabi frequency. The experimental data deviate slightly from this ideal case (see Fig. 5). The most important reason for this deviation is probably geometrical, arising from the fact that the observed signal is an average over contributions from the whole probe laser focus. Although longitudinal (~direction in Fig. 3) variations in pump laser intensity have been minimized, lateral (~9-direction) variations are not. Thus, even though each individual molecule will be embedded in an almost unchanging pump laser field while traversing the probe laser focus, different molecules will experience different field strengths. This implies that the effective pump laser Rabi frequency will be lower than the maximum one, which

.(D ~~t'O~.t3 "'.~.. ~
o?,

o

-4"2

-I0

i 5

i 10

i 15

i 20

Pump laser Rabi frequency [MHz] Fig. 5. Observedac-Stark shift of the high energy dressed state as a function of pump laser Rabi frequency.The dash-dotted line represents the expectedbehaviour for the ideal case. occurs in the centre of the probe laser focus. Besides this, a less important contribution will arise from the M-quantum number dependence of the transition strength for transitions between different M-sublevels 'hidden' below the rotational transitions that we observe (see also Refs. [24,27] ). This dependence will

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A.F. Linskens et al. / Chemical Physics Letters 248 (1996) 244-248

result in a s o m e w h a t reduced a c - S t a r k shift at higher (average) Rabi frequencies, and is also responsible for the increasing linewidth at higher p u m p power. The dashed curves in Fig. 4a are calculated taking these two effects into account. M o r e importantly, the appearance o f o n l y one single peak in the probe laser spectrum of Fig. 4a shows that o n l y o n e of the two dressed states (Fig. 2b) is populated d u r i n g the passage of the SF6 molecules through the p u m p laser beam. The existence o f the other dressed state, which is not populated d u r i n g the passage through the p u m p laser alone, can be demonstrated by increasing the probe laser intensity, as shown in Fig. 4b. A large probe laser intensity introduces a significant perturbation o f the dressed states (Eqs. (1) and ( 2 ) , which incorporate o n l y p u m p laser p h o t o n s ) . As a result, the dressed states I1) and 12) mix up with states from adjacent r u n g s in the energy ladder, their population is redistributed a n d adiabaticity breaks down. Thus, the high intensity probe laser spectrum should consist o f two peaks, which is clearly b o r n e out by Fig. 4b. A n interesting aspect o f the shift demonstrated in Fig. 4a is that its direction is a purely experimentally d e t e r m i n e d parameter, related to the position of the p u m p laser focus with respect to the molecular beam. As can be seen from Fig. I b, the sign of the initial det u n i n g determines which o f the dressed states [1) or 12) is prepared initially (see also Eq. ( 3 ) , in c o m b i nation with ( 1 ) and ( 2 ) ) , since it determines whether the p o p u l a t i o n - c a r r y i n g bare state la; N) is the lower or higher energy state in a doublet. In our experiments, the higher energy dressed state I1 ) was prepared, and Figs. 1-3 have been drawn accordingly.

Acknowledgement We w o u l d like to thank C. Sikkens for expert technical assistance. This research was sustained by grants from the E u r o p e a n C o m m u n i t y and a fellowship to N. D a m o f the Royal Netherlands A c a d e m y o f Arts and Sciences.

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