Spectroscopy of trapped HD+ molecular ions at millikelvin temperatures



Stored ensembles of molecules at sub-Kelvin temperatures form a promising starting point for a variety of applications. One wide-ranging application is high-resolution spectroscopy, which is possible because usual line-shifting and broadening effects due to collisions, high thermal velocities, and finite transit time are strongly suppressed. Spectroscopy of rovibrational transitions in the electronic ground state can take advantage of these special conditions because the lifetime of vibrational levels of molecules is typically long (~ms or longer), and thus lifetime broadening is not an important limitation. The low translational temperature also increases the absorption rate significantly, making spectroscopy on weak overtone transitions possible even with moderate laser power.

In our lab we have realized such conditions by storing HD+ molecules in an ion trap together with laser-cooled Be+ ions, which leads to sympathetic cooling of the HD+ molecules to temperatures in the millikelvin range[1]. The choice for HD+ is motivated by the fact that it is the simplest molecule after H2+, and as such is of interest as a fundamental three-body quantum system. HD+ is also of importance for astrochemistry. In particular, a comparison between measured vibrational transition frequencies and high-precision ab initio calculations could lead to the first identification of QED effects in a molecular system, and to a spectroscopic measurement of the fundamental constant me/mp and of the deuteron quadrupole moment. High-precision spectroscopy of HD+ might also be employed to test the constancy of me/mp[2]. The combination of long storage times and low temperatures of the molecular ions distinguishes our method from previous spectroscopic studies of HD+ and other isotopomers, which were performed on warm ensembles or on ion beams.


Fig. 1. Linear radiofrequency trap used for storage of cold Be+/HD+ ensembles




Our setup consists of an ultrahigh vacuum chamber which houses the ion trap, and the laser systems necessary for laser cooling of Be+[3] and laser spectroscopy of HD+. We use a linear radiofrequency (rf) trap (see Fig. 1). A rapidly time-varying quadrupole potential applied to the four rods gives rise to ponderomotive, harmonic confinement of the ions in the radial directions, whereas movement along the axial direction is restricted by static voltages applied to the end segments of the trap. Typical harmonic trapping frequencies for an Be+ ion are 280 kHz for the radial dimensions, and 70 kHz for the axial dimension.

Fig. 2. Typical Be+ Coulomb crystal containing HD+. Individual Be+ ions are visible through the 313 nm fluorescence they emit, whereas the HD+ ions reside in the dark cylindrical core of the crystal. The cooling laser beam propagates from right to left, exerting a light pressure onto the Be ions, but not on the molecules; therefore, the molecules cluster on the right side of the crystal.


Loading Be+ and HD+ ions into the trap

Be+ ions are loaded into the trap by electron-impact ionization of neutral Be atoms from an effusive beam traversing the trap. A laser beam at 313 nm is directed along the trap axis and provides Doppler laser cooling at the 2s 2S1/2 (F=2) « 2p 2P3/2 (F=3) transition in Be+. Typically ~1000 Be+ are loaded and their secular motion is cooled down to several millikelvin, as deduced from molecular dynamics simulations. This leads to the formation of ellipsoidal ion crystals[4], see Fig. 2, in which the 3D Coulomb interaction between the ions ensures that the cooling effect by the 313 nm laser beam on the axial motion is transferred to the radial directions as well. The presence of Be+ ions is obvious from the 313 nm fluorescence, which is monitored by a CCD camera and a photomultiplier tube (PMT). HD+ is identified by driving its oscillatory (secular) motion in the trap with a resonant electric field, which sympathetically heats the Be+ ions and therefore leads to an increased fluorescence rate. The rise in the fluorescence signal is proportional to the number of HD+ ions present in the trap.

Detection of rovibrational transitions in HD+

Spectroscopy on (v'=4, J') ¬ (v"=0, J") overtone transitions in the X 2S+ electronic ground state of HD+ is done using a 1.4 mm tunable diode laser system. To detect the transition, excited-state (v'=4) molecules are selectively dissociated using 266 nm light ((1+1') REMPD). The consequent loss of HD+ is recorded by comparing the number of HD+ ions before and after the spectroscopic step using the secular excitation method described above.



Rovibrational spectra of HD+

The above spectroscopic method has led to the observation of spectra such as those depicted in Figs. 3(a) and 3(b) [5]. Broadening to ~40 MHz is observed, which is much wider than the ~20 MHz Doppler width expected from the secular temperature of the HD+ ions. We have verified that micromotion due to axially directed AC fields at the trap drive frequency (14 MHz) is responsible for the broadening. This micromotion generates sidebands in the spectrum, which are barely resolved, resulting in the observed linewidths.

Fig. 3. Experimental spectra (data points), fitted theoretical spectra (solid curve), and theoretical stick spectra. (a) Spectrum of (v'=4, J'=1) ¬ (v"=0, J"=2). (b) Spectrum of (v'=4, J'=3) ¬ (v"=0, J"=2). The insets show typical error bars. The frequency-axis calibration is done using a water absorption cell and is accurate to within ~40 MHz [5].

Comparison with theory

Figures 3(a) and 3(b) also show "stick spectra", which are obtained by evaluating the electric dipole matrix elements between HD+ hyperfine states within (v", J") and (v', J'). The hyperfine state vectors are found by diagonalization of an effective spin Hamiltonian, which describes the coupling between the nuclear, electronic and rotational spins. To within the experimental resolution, the agreement with the theoretical spectra is good.

Absolute frequency measurement

Recently we have measured the (v'=4, J'=3) ¬ (v"=0, J"=2) spectrum using a grating-enhanced external cavity diode laser, developed in the group of Prof. Andreas Wicht at our institute. The laser is frequency-locked to a self-referenced frequency comb, which in turn is stabilized to a GPS-disciplined hydrogen maser. This system allows continuous tuning of the laser with better than 25 kHz absolute accuracy, leading to the spectrum depicted in Fig.4. An analysis of possible systematic shifts, including Zeeman and Stark shifts, allowed to determine  the deperturbed ("zero") rovibrational frequency from the measured spectrum with 0.5 MHz accuracy [7]. This result is in excellent agreement with the latest theoretical calculations.

With this result, we have demonstrated a new method for measuring the electron-to-proton mass ratio. Our accuracy is about 5 parts in 109, not as good as with other methods (via the g-factor of the electron in a hydrogenic ion), but with potential for significant improvement.


Fig. 4. Experimental spectrum (data points), fitted theoretical spectrum (solid curve), and theoretical stick spectrum of the (v'=4, J'=3) ¬ (v"=0, J"=2) transition in HD+The frequency values are accurate to < 25 kHz [6].


Several developments towards higher spectroscopic resolution are in progress. To overcome both the micromotion and Doppler broadening, a new ion trap is under construction. Special care is taken to avoid AC electric fields which may cause micromotion.  Doppler broadening is eliminated by a trap design which allows confinement of the HD+ ions in the Lamb-Dicke regime, in which first-order Doppler shifts are absent.

Current team members

HD+ spectroscopy and ion trap development:

Bernhard Roth, T. Schneider

Frequency comb and IR diode laser development:

Ingo Ernsting, A. Nevsky

IR laser development:

U. Bressel, M. Hansen, Sergey Vasilyev, Alexander Nevsky, H. Duncker


·      Deutsche Forschungsgemeinschaft

·      EC network ‘‘Cold Molecules’’ No. HPRN-CT-2002-00290

·      Alexander von Humboldt Foundation

·      Forschungsfonds Universität Düsseldorf

(see our Publication list for an up-to-date list)

[1] - P. Blythe, B. Roth, B. Roth, U. Fröhlich, H. Wenz, and S. Schiller, Phys. Rev. Lett. 95, 183002 (2005).

[2] - S. Schiller. and V. Korobov, Phys. Rev. A 71, 032505 (2005).

[3] - H. Schnitzler, U. Fröhlich, T. K. W. Boley, A. E. M. Clemen, J. Mlynek, A. Peters, and S. Schiller, Appl. Opt. 41, 7000-5 (2002).

[4] - U. Fröhlich, B. Roth, and S. Schiller, Physics of Plasmas, 12, 073506 (2005).

[5] - B. Roth, J.C.J. Koelemeij, H. Daerr, and S. Schiller, Phys. Rev. A 74, 040501 (2006).

[6] - V. Korobov, Phys. Rev. A 74, 052506 (2006).

[7] - J.C.J. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, Phys. Rev. Lett. 98, 173002 (2007).