Rubidium on Helium Droplets: Analysis of an Exotic Rydberg Complex

Letter pubs.acs.org/JPCL

Rubidium on Helium Droplets: Analysis of an Exotic Rydberg Complex for n* < 20 and 0 ≤ l ≤ 3 Florian Lackner, Günter Krois, Markus Koch, and Wolfgang E. Ernst* Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria/EU ABSTRACT: Rubidium atom Rydberg states perturbed by helium droplets of different sizes provide insight into the role of a nanosized dielectric on the Coulomb potential. The observation of droplet size-dependent shifts of excited states with respect to bare atom states is explained by a decreased quantum defect and a lowered ionization threshold. Within the scope of a Rydberg model, we demonstrate that quantum defects and ionization potentials are constant for each specific Rydberg series, which confirms the Rydberg character of excited Rubidium states on helium droplets. A set of six Rydberg series could be identified. Individual Rydberg states are observed with effective principal quantum numbers up to n* ≈ 19 and l ≤ 3, for which the expectation value of the electron orbital radius is about 10 times larger than the droplet radius.

SECTION: Spectroscopy, Photochemistry, and Excited States

R

IT and the QD are lowered due to the presence of the HeN, and both depend on the number of He atoms in the droplet. The droplet size dependence of the QD gives information about the l value of the atomic state from which the observed Rb−HeN states originate. The advantage of the bound 52P1/2 (2Π1/2) Rb−HeN state12 as an intermediate state in a two-step excitation scheme13 is that it enables access to states with high l. High l and n states are of interest because the electron wave function is spread out, and the penetration of the Rydberg electron into the HeN is reduced. Due to the smaller overlap of high-l orbitals with the core of the Rb−HeN complex, one should expect longer lifetimes of the high-l states. Lower electronically excited states of Ak atoms, which reside on the surface of HeN, have been investigated since the early days of helium nanodroplet isolation spectroscopy.14 The D lines of the Ak atoms, from Li15 to Rb16 and Cs,17 are among the best investigated electronic transitions in doped HeN. By contrast, relatively little work has been done on the characterization of higher excited states13,18,19 and Rydberg states.6,8,9 Only Na− HeN8,9 and Cs−HeN6 Rydberg states have been investigated so far. The lack of a bound intermediate state in the Na−HeN system restricts the investigations to Π and Σ states (see below). For the Cs−HeN system, where the use of a two-step excitation scheme is possible,13 no investigation of droplet sizedependent effects was performed, and the experimental detection scheme forbids the complete recording of the 6D state manifold. The Rb−HeN complex provides the ideal Ak− HeN system for following a complete Rydberg series up to the IT.

ydberg state spectroscopy provides important insights into the charge distribution of an ionic core through its interaction with a single outer electron. From the hydrogen atom to small molecules1,2 and clusters,3 Rydberg states are found in a wide variety of systems. Most recently, the Rydberg state concept has been applied to the “heavy Bohr atom”,4 a H+H− ion-pair system, bound by the Coulombic 1/r potential. The extraordinary properties of Rydberg atoms enable the formation of ultralong-range Rydberg molecules where the rubidium (Rb) macrodimer has recently been characterized spectroscopically.5 We report on a comprehensive and systematic investigation of nS, nP, nD, and nF Rydberg series of the Rb-helium nanodroplet (Rb−HeN) complex, which forms a new type of exotic Rydberg system. When an alkali metal (Ak)−HeN cluster is excited into states where the diameter of the valence electron orbital becomes large compared to the droplet diameter, recent experiments indicate that the system consists of an Ak ion immersed inside the HeN surrounded by a Rydberg electron.6,7 This exceptional configuration of Ak−HeN is of fundamental interest, and questions about its properties and stability are of importance.6,8−11 In this Letter we focus on the Rb−HeN system, which exhibits a favorable electronic structure and provides essential advantages in terms of accessibility of states with high orbital angular momentum quantum number l and in terms of the assignment of D and F states. We provide evidence for the excitation of a Ak−HeN system into an nF state. In addition, we present the new application of a method for the assignment of Ak−HeN Rydberg states, which is similar to a method for the assignment of Rydberg states in l-mixed supercomplexes.1,2 Excited states are organized into Rydberg series, allowing the determination of series specific ionization thresholds (ITs) and quantum defects (QDs). We find that the © 2012 American Chemical Society

Received: March 28, 2012 Accepted: May 3, 2012 Published: May 3, 2012 1404

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Figure 1. Excitation spectra of Rb−HeN recorded with R3PI-TOF spectroscopy for droplet sizes of N̂ 60,20 = 2000 (black), N̂ 60,18 = 3200 (green), N̂ 60,16 = 5000 (red), and N̂ 60,14 = 7500 (blue) as a function of the laser L2 wavenumber. Laser L1 excites the 52P1/2 (2Π1/2) intermediate state (fixed at 12600 cm−1). From this state, the second laser L2 is scanned across Rydberg states. A third photon ionizes the complex. The signal is obtained by monitoring the ion yield of the most abundant Rb+−Hem (m = 1−6) complexes with a TOF mass spectrometer. The states are grouped into Rydberg series as indicated on top. The vertical dashed line marks the IT of the bare atom, and the top scale shows the effective principal quantum number n* of the bare atom.

and activated 2 μs afterward in order to avoid distortions (Stark-effect). Rb−HeN excitation spectra obtained with different droplet sizes are presented in Figure 1. The spectra are plotted as a function of the laser L2 wavenumber. They begin at the 5D state manifold and continue to the IT. The highest resolved Rydberg state has an effective principal quantum number of n* ≈ 19 (the effective principal quantum number is defined as the difference between the principal quantum number and the QD). The recorded spectrum clearly shows a regular pattern of states, which repeats with integer steps of n*. Thus we organize the observed states into Rydberg series, as indicated on top in Figure 1. Considering Rb−HeN substates arising from Rb nS, nP, nD, and nF bare atom states, nine allowed transitions into the molecular sublevels S(Σ), P(Π, Σ), D(Δ, Π, Σ), and F(Δ, Π, Σ) are expected. The assignment is helped by a procedure that was applied by the Field group for the identification of CaF1 and BaF2 Rydberg states. The effective principal quantum number n* of each of the nine subseries should differ by approximately 1 for consecutive members. With this condition, six sequences could be assigned without prior knowledge of absolute quantum numbers. Assuming a constant QD and IT for the higher members, absolute quantum numbers could be determined. These values were confirmed by following a series down to its lowest members that agree well with the experimental results in ref 13 (5D state manifold) and with the calculations (states up to the 7P manifold) in ref 23. The D(Δ)-features appear close to the bare atom nD lines, which is important for the confirmation of F states (see below). Table 1 shows the dependence of the D(Δ)-feature on the droplet size and the principal quantum number. The peak shift and the line width for lower states increases with the droplet size. The lower states are strongly blueshifted. For n ≥ 8, the D(Δ)-peak shift is negative, which corresponds to a redshift of the Rb−HeN below the bare atom state. The D(Π) and D(Σ) peaks merge to one peak for n* > 6, hence we refer to this series as the D(Π/Σ) series. Similarly we assign the P(Π), P(Σ), S(Σ), and F series. For the F series it was not possible to

For characterization of the observed Rydberg states, we use the well-established pseudodiatomic model for the Ak−HeN system,15 where the HeN is treated as one atom in a diatomic molecule, and the molecular axis is defined by the connection between the center of the droplet and the Ak nucleus. In this picture, the projection Λ of the valence electron’s angular orbital momentum onto the molecular axis is a conserved quantity, and the diatomic selection rules for electronic transitions apply (ΔΛ = 0, ± 1). A detailed description of the experimental setup and the excitation scheme can be found elsewhere.6,20,21 In brief, helium droplets are produced in a supersonic jet expansion of highpurity helium gas through a cold 5 μm nozzle (p0 = 60 bar, T0 = 14−20 K) into vacuum. The droplet sizes follow a log-normal distribution, and the distribution maxima N̂ P0,T0 are N̂ 60,20 = 2000, N̂ 60,18 = 3200, N̂ 60,16 = 5000, and N̂ 60,14 = 7500, corresponding to droplet radii of 28, 33, 38, and 44 Å, respectively.22 The HeN are doped by means of a resistively heated pickup cell, containing a small amount of Rb metal. A resonant three-photon-ionization (R3PI) scheme is applied. The ion yield is monitored with a time-of-flight (TOF) mass spectrometer (Jordan D-850 AREF). A pulsed Ti:Sapphire laser L1 (Coherent Indigo-S, 30 ns pulse duration, 0.15 mJ pulse energy) excites the Rb−HeN system into the 52P1/2 (2Π1/2) intermediate state (first step). L1 is spatially overlapped and synchronized with a tunable pulsed dye laser L2 (Lambda Physik FL 3002, 26 ns, ∼ 6 mJ), which induces a transition to Rb−HeN Rydberg states (second step). A third photon of either L1 or L2 ionizes the complex, and the resulting ions are counted while L2 is scanned. The counter is set to a time window, corresponding to the mass range of Rb+−Hem (m = 1−6). This mass range was found to not be influenced by parasitic signals arising from, e.g., fragmented Rb dimers or bare Rb atoms. The obtained ion signal is smoothed, and the spectra obtained with different dyes are scaled to match each other. Thus intensities of different peaks can not be compared. For the investigation of high Rydberg states (ν̃L2 > 20250 cm−1), the TOF extraction field was turned off during the laser pulse 1405

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Table 1. D(Δ) Peak Positions, Peak Shifts Compared to the n2D3/2 State and Peak Width for Different Droplet Sizes N̂ and Principal Quantum Numbers n N̂

n

position/cm−1

shift/cm−1

width/cm−1

7500 7500 7500 7500 7500 7500 3200 3200 3200 3200 3200 3200

5 6 7 8 9 10 5 6 7 8 9 10

13181 ± 5 16174 ± 10 17725 ± 15 18636 ± 6 19218 ± 3 19615 ± 3 13166 ± 5 16152 ± 5 17719 ± 10 18631 ± 5 19216 ± 5 19617 ± 5

60 ± 5 66 ± 10 24 ± 15 −7 ± 6 −25 ± 3 −34 ± 3 44 ± 5 44 ± 5 18 ± 10 −12 ± 5 −27 ± 5 −32 ± 5

80 ± 10 78 ± 7 52 ± 15 38 ± 6 29 ± 7 24 ± 7 62 ± 7 57 ± 5 40 ± 10 31 ± 6 19 ± 7 22 ± 7

Figure 3. Excitation spectrum monitored on the masses of Rb+−Hem (m = 1, 2, 3) for droplet sizes of N̂ 60,14 = 7500. Bare Rb atom line positions are marked by vertical bars. Exciplex formation is strongly enhanced for high Λ states (e.g., 5D(Δ), close to the bare atom line13). Increased exciplex formation is also monitored close to the 4F state, indicating the high-Λ character of this state.

resolve different Λ substates because the F states have very small QDs. For higher n, l-coupling to the pseudomolecular axis becomes weaker, and molecular states merge to one single peak and form a hydrogen-like Rydberg series converging to the attractive potential curve of the ion in/on the droplet. The Rydberg potentials are very similar to the potential curve of the ion and an attractive force acts on the ionic core of the Rb atom.7 Figure 2 shows a portion of the spectrum at the highest

7500. Most striking is the difference between Rb+−He and Rb+−He2/3 signals. The 5D(Δ) state is known to be closer to the bare atom line than the 5D(Π) and 5D(Σ) state.13 We thus conclude that for lower states, an increased Rb+−He2/3 signal indicates high Λ(l) states. The Rb+−He signal on the blue side of the bare atom 7S state is due to a combination of 7S(Σ) and 4F(Δ, Π, Σ). We interpret the Rb+−He2/3 peak at 14240 cm−1 as being due to the high Λ component, i.e., 4F(Δ). This demonstrates that high l states are accessible with our two-step excitation scheme. We can identify higher S and F states by comparing the Rb+ and Rb+−Hem signals for lower states. For n*≳ 8.5, this Λ dependence vanishes, and Rb+−Hem complexes are detected regardless of the intermediate state. In order to model the droplet size dependence of the spectral features in Figure 1, we use a Rydberg approach. The Rb−HeN energy levels EΛ,N̂ (IT,n*) are represented by the Rydberg formula:24 R∞ EΛ, N̂ (IT, n*) = ITΛ, N̂ − (n*Λ, N̂ )2 (1)

Figure 2. Excitation spectrum of high Rydberg states monitored on the masses of Rb+−Hem (m = 1−6) for droplet sizes of N̂ 60,14 = 7500 and N̂ 60,18 = 3200. Lines are broader and the red shift is stronger for larger droplets. The vertical dashed line at 21017 cm−1 marks the fieldcorrected IT. Bare atom nD line positions are indicated as vertical lines.

n*Λ, N̂ = n − dΛ, N̂

(2)

All states of a given series can be described by two parameters, the IT (ITΛ,N̂ ) and the effective principal quantum number n*Λ,N̂ (which is related to the QD dΛ,N̂ ). Note that IT and d depend on the droplet size N̂ . R∞ denotes the Rydberg constant, and in good approximation we can treat the QD as independent of n. The EΛ,N̂ (IT,n*) are obtained from the spectra as maxima of Gaussian fits to the spectral peaks, neglecting the shallow minimum (≈5 cm −1 ) 7 of the 52P1/2(2Π1/2) potential. A nonlinear least-squares fit is used to determine ITΛ,N̂ and n*Λ,N̂ from eq 1. Only peaks with n* > 5.2 are included in the fit because, for lower states, the peak positions deviate from the model.6 The strength of our method is that it is not based on an initial correspondence with bare atom states. Conclusions about the IT and the QD include only n*. For bare atoms, the QD for series of nl states is approximately constant. From eq 2 it is evident that the remainder of n*, which is obtained by the modular arithmetic

resolved Rydberg states (TOF E-field 240 V/cm). The E-field influences only the position of the IT and not the position of the resolvable peaks up to n* = 19. All Λ-substates have merged, and for large droplets the high Rydberg states are broader and the redshift is stronger than for small droplets. Additional information is extracted from our observation that the probability for exciplex formation upon excitation into a Rb−HeN Rydberg state increases with Λ, at least for lower n. Consequently, the amount of observed Rb+−Hem (m = 1, 2, 3) allows one to draw a conclusion about the Λ (and thus l) character of the Rb−HeN state. The Rb+−Hem (m = 1, 2, 3) ion yields in the section of the spectrum containing the 5D, 7S, and 4F manifolds are shown in Figure 3 for droplets of N̂ 60,14 = 1406

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operation “n* mod 1”, is constant for each nl series. For Cs− HeN6 and Na−HeN,8 the QDs are smaller than the bare atom values. In Figure 4b it is shown that the Rb−HeN QD is also

IT is presented for various droplet sizes. The highest resolved states have an orbital radius, which is approximately 10 times larger than the HeN. Within a Rydberg model we analyze the observed droplet size-dependent effects of peak shift, line broadening, and red shift of IT. In addition, we show evidence for the excitation of previously unobserved nF states, demonstrating the possibility of transitions into high l states. Our findings support a qualitative picture in which the helium nanodroplet forms a dielectric around the Ak+ reducing the binding energy and the interaction of the outer electron with the Ak+ core orbitals, thus resulting in a lower IT and a smaller QD. In a more refined model, the Pauli exclusion due to the helium should lead to a reduced core penetration of the Rydberg electron. In this limit, the helium may be modeled as a dielectric around the Ak+ ionic core.10

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

Figure 4. Decrease of the ITs (a) and effective principal quantum number n* mod 1 (b) as a function of droplet size. Both parameters show a trend toward atomic values.25 The solid line in (a) represents the mean value of the IT shift for each droplet size and the uncertainties of the IT values are smaller than ±10 cm−1.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the Austrian Science Fund (FWF) under Grant FWF-E-P19759 and the EFRE Program of the European Union and the Region of Styria.

lowered by the droplet; additionally we validated here that the QD is droplet size dependent. The bare atom QDs are indicated as horizontal lines, and the Rb−HeN QDs are plotted in colors. For example, for dD = 1.35, it follows from eq 2 that n* mod 1 = 0.65 (horizontal line in Figure 4b). The 1 − (n* mod 1) = 0.35 operation (right scale) provides the remainder of the QD. For the D(Δ) series, 1 − (n* mod 1) ≈ 0.27, which corresponds to a decreased QD dD(Δ) = 1.27 (ΔdD(Δ) = −0.08) if one assumes that the Rb−HeN QD lies in the range of the free atom. All QDs are lowered by the influence of the HeN and show a trend toward the related bare atom values with decreasing N̂ . This demonstrates that our method allows the allocation of transitions according to their l(Λ) character. The observed decrease of the QD may be due to a shielding of the Rb+ ionic core from the Rydberg electron. This corresponds to an increase in energy, which is manifested in the spectra as a blue shift of lines for low n*, where the influence of the QD is most pronounced. The IT of the Rb−HeN system is found to be droplet size dependent and lowered in comparison to bare Rb (Figure 4a). This is in agreement with previous experiments.7,8 The lowered IT is explained by the attractive interaction of the HeN and the positive alkali core due to polarization.7 Our values (Figure 4a) are in good agreement with ref 7, where an IT lowering of 37− 55 cm−1 for droplet sizes in a similar range as here is reported. The ITs show no significant l and Λ dependence and show a trend toward the bare atom value for decreasing N̂ . In light of this discussion, we can describe the droplet size-dependent line broadening effect by the log-normal distribution of the droplet size. Each size has its specific ITΛ,N̂ and dΛ,N̂ and thus necessarily a different spectral position. The breadth of the distribution at low nozzle temperature is reflected by broad spectral peaks. In conclusion, we have demonstrated the Rydberg character of excited states of Rb atoms on helium nanodroplets. A complete excitation spectrum from the 5D state manifold to the

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REFERENCES

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