Abstract
Laser cycling of resonances can remove entropy from a system via spontaneously emitted photons, with electronic resonances providing the fastest cooling timescales because of their rapid spontaneous relaxation. Although atoms are routinely lasercooled, even simple molecules pose two interrelated challenges for cooling: every populated rotational–vibrational state requires a different laser frequency, and electronic relaxation generally excites vibrations. Here we cool trapped AlH^{+} molecules to their ground rotational–vibrational quantum state using an electronically exciting broadband laser to simultaneously drive cooling resonances from many different rotational levels. Undesired vibrational excitation is avoided because of vibrational–electronic decoupling in AlH^{+}. We demonstrate rotational cooling on the 140(20) ms timescale from room temperature to , with the groundstate population increasing from ~3 to . This cooling technique could be applied to several other neutral and charged molecular species useful for quantum information processing, ultracold chemistry applications and precision tests of fundamental symmetries.
Introduction
Laser cooling of atomic translational and internal energies has made possible a wide range of applications including creation of novel phases of matter^{1}, atomwave accelerometry^{2} and ultraprecise timekeeping^{3}. Because of their additional internal structure, lasercooled molecules offer possibilities for extending the quantum toolkit in completely new directions. For instance, the large electric dipoles of trapped polar molecules could be used to coherently transfer information between molecules or to electronic circuits for quantum information processing^{4,5}, ultracold molecular dipoles could be oriented by external fields to control chemical reactions^{6} and molecular structure can provide enhanced sensitivity in searches for breakdowns of the Standard Model of particle physics^{7,8,9,10}. However, before the full potential of molecules can be harnessed, methods are needed to prepare and reset their rotational and vibrational quantum states, with laser control offering a promising option.
Translational cooling of molecules initially in a particular rotational–vibrational state has been achieved using narrowband lasers, with unwanted vibrational excitation minimized because of an unusual degree of electronic–vibrational decoupling in the selected species^{11,12,13}. Vibrational cooling of translationally cold molecules has been performed using broadband lasers^{14} and incoherent light sources^{15} with spectral filtering removing light that would lead to vibrational heating, and also by using spectrally tuned multimode diode lasers^{16}. Rotational cooling is particularly critical for many applications because of the relatively small energy of rotational excitations; for instance, while many species are already in their ground vibrational state at room temperature, several to many rotational states are populated for all molecules. Rotational cooling has previously only been accomplished using narrowband lasers optically pumping population from a small number of rotational states at one time. A static narrowband laser was used to transfer population from two excited rotational states to the ground state in a beam experiment^{10}. In an experiment on molecules formed by photoassocation from an ultracold atomic gas, cooling from the few populated rotational states to a single state was achieved by pumping from each level serially using a swept narrowband laser, in conjunction with a broadband laser providing vibrational cooling^{17}. Finally, rotational cooling of trapped molecular ions from room temperature to the ground state was achieved on relatively slow timescales (seconds) by waiting for spontaneous and blackbody radiationdriven rotational transitions to redistribute population to levels pumped by narrowband lasers^{18,19}.
Broadspectrum rotational cooling has previously been proposed^{20,21,22,23}, and here we demonstrate its implementation, using a broadband laser tuned to an electronic resonance to cool rotations of trapped AlH^{+} molecules from room temperature to their ground rotational state. As in the previous molecular translational cooling demonstrations^{11,12,13}, undesired vibrational excitation during electronicresonance cycling is avoided because of vibrational–electronic decoupling in our chosen molecule, AlH^{+}. Because the broadband laser simultaneously cools population from all initially excited states, cooling to the ground rotational state is relatively fast (~100 ms), and our use of a fast electronic resonance offers future possibilities for microsecondtimescale cooling. Broadband rotational cooling will allow rapid quantum state preparation both in molecular beam experiments, in which the time available for laser cooling is limited, and in trappedmolecule experiments where the initial rotational temperature is too high for cooling by a swept narrowband laser. In nondestructive trappedmolecule work such as spectroscopy or quantum information processing, particularly in ion traps where hold times can extend to many hours, broadband rotational cooling could also provide rapid state resets allowing the same molecules to be reused repeatedly, rather than requiring the trap to be dumped and reloaded in each experimental iteration.
Results
Choice of molecular species
AlH^{+} is a favourable species for broadband rotational optical cooling (BROC)^{23} because its A^{2}Π−X^{2}Σ^{+} electronic resonance is fairly decoupled from vibrations, supporting ~30 excitation/spontaneous emission cycles before vibrational excitation occurs^{22} (Fig. 1). It is also important to consider the complexity of the spectral filtering required to ensure that the broadband laser drives only rotational cooling transitions^{20}. For AlH^{+} and similar species, only simple spectral filtering is needed because vibrational–electronic decoupling implies matched rotational constants in the two electronic states, and thus wellseparated rotationally deexciting (Pbranch) and exciting (Rbranch) bands (Fig. 2).
Trapping and rotational analysis apparatus
Our experiment is performed in a room temperature linear Paul trap integrated with equipment for timeofflight mass spectrometry (TOFMS). In each experimental run, laser ablation is used to load lasercooled Ba^{+} ions along with typically 50 Al^{+} ions, with the Al^{+} numbers kept small to maintain sufficient TOFMS resolution. We operate with an intentionally degraded vacuum (3 × 10^{−10}mbar) so that AlH^{+} is formed on a 1min timescale by reaction of Al^{+} with background gas. Coulomb repulsion keeps ions several microns apart, preventing ion–ion chemical reactions and allowing the lasercooled Ba^{+} ions to sympathetically cool AlH^{+} ions into a socalled Coulomb crystal^{24} with a translational temperature <1 K. The large interion separation and ultrahigh vacuum conditions result in decoupling of the AlH^{+} translational, rotational and vibrational temperatures. Optical rotational cooling could also be performed on translationally warmer samples; however, crystallization is advantageous because it localizes the molecules, allowing for higher laser intensity and improving TOFMS resolution.
After loading the trap, AlH^{+} rotations and vibrations equilibrate to room temperature via blackbody radiation before cooling lasers are applied (Fig. 3). At room temperature, 99.9% of the AlH^{+} population is in the lowest vibrational state v=0, with significant population distributed among the first 10 rotational levels, N=0–9, and 4% in N≥10. The rotational population distribution is destructively probed by stateselective (1+1′) resonanceenhanced multiphoton dissociation (REMPD)^{25,26}, which converts AlH^{+} only in a target rotational–vibrational state into Al^{+}, and is analysed with TOFMS. In each experimental iteration the REMPD probe is tuned to a single rotational level, and Al^{+} and AlH^{+} populations are counted. We do not attempt to independently analyse the number of AlH^{+} loaded into the trap, but rather determine the degree of rotational cooling by TOFMS measurements of the Al^{+} to AlH^{+} ratios after REMPD. The trap is reloaded and the same experiment repeated typically 10 times to gather statistics for each rotational level. Further details of the apparatus and state readout can be found in ref. 26.
Spectral filtering of the broadband laser
The light source for BROC is a frequencydoubled femtosecond laser (SpectraPhysics Mai Tai) yielding 900 mW at the 360 nm A^{2}Π_{1/2}X^{2}Σ^{+} transition. The laser is spectrally filtered after the doubling stage. Spectral filtering is accomplished using a homebuilt device, consisting of diffraction gratings and cylindrical lenses in the 4f Fouriertransform optical layout^{27} and a razor blade mask to block the highfrequency part of the spectrum. The broadband spectral filtering apparatus and its application to rotational cooling is described in detail in ref. 23.
We achieve a spectral filtering cutoff sharper than observable in the commercial spectrometer data shown in Fig. 2. Two independent characterizations described in Methods yield a cutoff resolution of 2 cm^{−1} at the 10dB extinction point. The ultimately achievable spectral resolution is set by the diffraction limit; for our grating (3,600 lines mm^{−1}) and beam waist (16 mm), this limit is 0.1 cm^{−1} at fullwidth at half maximum^{23}. The dominant effect making our current resolution far from the diffraction limit is expected to be the large spherical aberration in our offtheshelf lenses; commercially available optics are readily available to bring the cutoff resolution near the diffraction limit. The spectral separation between rotationally heating and cooling transitions is approximately 2B_{e} (4B_{e}) for species with (without) allowed Qbranch (rotationally nonchanging) transitions, where B_{e} is the rotational constant for the molecule. For AlH^{+}, 2B_{e}=13 cm^{−1}, so even the currently achieved filtering resolution is sufficient for efficient cooling.
The spectrum of the femtosecond laser is actually a series of ‘comb teeth’ spaced by 80 MHz; therefore, a mechanism is needed to guarantee that cooling transitions do not accidentally fall between the teeth. In our case, ion translational heating occurs for the radially extended Coulomb crystal because of coupling to the radiofrequency trapping voltage^{28}, yielding sufficient Doppler broadening to ensure spectral overlap^{23}. Alternately, frequency modulation of the cooling laser could be used to modify its tooth structure, eliminating the need for Doppler broadening.
Rotational cooling schemes
The angular momentum selection rules for the A^{2}Π_{1/2}−X^{2}Σ^{+} rotational cooling transition are ΔJ=0, ±1, where J=N+S+L is the total angular momentum including molecular rotation N, electron spin S and electronic orbital angular momentum L. Spectral filtering removes all but rotationally deexciting Pbranch transitions (Fig. 2), driving rotational cooling. Each electronic excitation and spontaneous emission cycle conserves molecular parity; therefore, in the simplest BROC spectral filtering configuration, population is cooled to the lowest rotational–vibrational state of each parity, X^{2}Σ^{+}, υ=0, N=0› and X^{2}Σ^{+}, υ=0, N=1› (Fig. 3a). Because of imperfect electronicvibration decoupling in AlH^{+}, some undesirable vibrational excitation (14% at the fasttimescale equilibrium) also occurs during this cooling process. On the longer timescales (~100 ms) of vibrational spontaneous emission, all population is pumped to the two lowest states of each parity with no residual vibrational excitation.
In order to cool all population into the positiveparity X^{2}Σ^{+}, υ=0, N=0› level, we employ a modified vibrationally assisted BROC scheme (VABROC); here parity conservation of BROC is destroyed by forcing a vibrationally exciting electronic decay to occur only for the negative parity. The spectral cutoff frequency is shifted slightly (Fig. 2b) to additionally drive the X^{2}Σ^{+}, υ=0, N=1›→A^{2}Π_{1/2}, υ′=0, (N′)=0› transition, which has no alternate channel for spontaneous relaxation within the υ=0 manifold, resulting in electronic cycling, until spontaneous electronic relaxation to υ=1 and subsequent spontaneous vibrational relaxation flips the parity. Population immediately afterwards is entirely in the positive parity X^{2}Σ^{+}, υ=0, N=0› or X^{2}Σ^{+}, υ=0, N=2› levels, with population in the latter quickly pumped to the ground state (Fig. 3a). Note that only a single spectral filtering configuration is needed for VABROC cooling from room temperature to the ground state, since the previously discussed BROC process is included within VABROC.
Since the upper state degeneracy is smaller than that of the lower state when driving Pbranch transitions, dark states must also be considered. The unpaired electron spin in the X^{2}Σ^{+} state allows modest magnetic fields to cause sufficient Larmor precession rates and prevent a slowdown of rotational cooling. In our experiment, we use an ~2 Gauss magnetic field perpendicular to the cooling laser polarization.
Rotational cooling results
Figure 3 shows the measured rotational distributions before and after 5 s of BROC or VABROC illumination. The initial rotational populations are well represented by a thermal distribution, given by a Boltzman exponential times a degeneracy factor, validating the analysis techniques. A ‘toy’ Monte Carlo simulation described in Methods is used for statistical analysis.
BROC cools each parity independently and yields 48(4)% population in X^{2}Σ^{+}, υ=0, N=0› and 46(3)% in X^{2}Σ^{+}, υ=0, N=1›. These data are statistically consistent with fully efficient BROC cooling, as are REMPD probes finding no population in higher rotational states. Figure 3 does include data from an anomalous run yielding nonzero N=3 population; however, as discussed in Methods, this signal is most likely from detector noise. As the spacing between consecutive states of the same parity is large, 50 K (90 K) between the lowest two states of positive (negative) parity, only relatively weak constraints can be set on the temperature achieved by BROC. The 90% CL temperature upper limits are 13 K for positive parity and 19 K for negative parity. The negativeparity limit is obtained when the suspect N=3 signal is neglected; if that signal is attributed to imperfect BROC cooling, then the corresponding measured temperature for negative parity would be 19 K (where the numerical correspondence to the limit value is coincidence).
After VABROC, the population measured in X^{2}Σ^{+}, υ=0, N=0› is %; probing X^{2}Σ^{+}, υ=0, N=1›, we measure a population of %, and we observe no population in N=2 or N=3. These results are consistent with all population after VABROC being in the two lowest rotational states, with the population ratio corresponding to a rotational temperature of .
Although simulation^{23} predicts that the BROC phase of cooling occurs as fast as 8 μs with our current laser intensity, population dynamics measurements were limited by the 10ms speed of a mechanical shutter gating the cooling light. Nonetheless, this timing resolution allows us to analyse the slower of the two VABROC phases associated with a vibrational spontaneous relaxation event. Figure 3b (inset) shows data taken for various cooling times with the population measurement occurring 1 s (several vibrational relaxation lifetimes) later. Similarly to the approach used in ref. 29, the vibrational lifetime τ can be extracted from the timedependent population. The fit described in Methods yields τ=140 (20) ms, in good agreement with the theory value of 127 ms (ref. 22). Blackbody radiation induced rotational and vibrational transitions from lowlying rotational states occur on an ~100s timescale; therefore, these processes do not significantly affect cooling efficiency or analysis.
Discussion
We expect that our rotational temperature after VABROC could in the future be reduced by improved spectral filtering. Regarding improvements in timescale, we note that BROC already cools to the lowest two rotational states in as fast as microseconds, potentially an acceptable starting point for some applications requiring cooling faster than the ~100ms VA timescale. Cooling to a single rotational state could also be achieved in a few microseconds by performing parity cooling without a vibrational relaxation event. For instance, population pumped by BROC into X^{2}Σ^{+}, υ=0, N=1› could be driven by a twophoton excitation to A^{2}Π, with subsequent electronic spontaneous relaxation accomplishing a parity flip in less than a microsecond. An additional femtosecond laser providing vibrational cooling could reduce or effectively eliminate transient vibrational population buildup during BROC due to imperfect vibrational–electronic decoupling. Unremediated vibrational excitations during BROC will be more of a concern in heavier reducedmass species, both because of slower vibrational spontaneous relaxation rates and because of the larger number of rotational cooling steps needed to cool from a given temperature. Further details of these improvements are discussed in Methods.
It is instructive to compare the performance of BROC with a few other approaches for rotational cooling of trapped molecules. The only previous laser cooling of rotations from room temperature used narrowband excitation of vibrational resonances, yielding groundstate population of 36.7% (20 K) for MgH^{+} (ref. 18) and 78% (27 K) for HD^{+} (ref. 19); the processlimiting timescale of several seconds was associated with rotational transitions. In comparison, VABROC cooling of AlH^{+} achieves 95% groundstate population and a temperature of 3.8 K, with a processlimiting timescale of ~100 ms associated with a vibrational transition. Comparing generality of the approaches, the narrowband technique is readily applicable to any polar hydride but has limited utility for species with larger reduced mass (that is, fluorides or chlorides) because of their slower vibrational and rotational transition rates^{19}. BROC is most readily applicable to specialized molecules with decoupled vibrational and electronic modes; however, they can be heavier reducedmass species. Finally, compared with direct cryogenic buffer gas cooling of molecular ions in a 4K apparatus^{30}, we obtain in our room temperature apparatus a temperature a few times colder for a single molecule (and many times colder for larger collections of molecules) on a similar ~100ms timescale.
Several other neutral and ionic candidate species for the simplest implementation of BROC have been identified^{21,22,31}. It is interesting to consider the spectral filtering resolution required to rotationally cool diatomic species with heavier reduced mass and correspondingly smaller rotational constants and more congested spectra. Working with the same beam size but near the diffraction limit, we could expect to achieve enough resolution for efficient cooling of fluorides to their ground state and partial cooling of chlorides. Further resolution improvements could be obtained by using a finer grating and possibly by utilizing interference filters to handle transmission of the spectrum around the cutoff (D. Comparat, personal communication). Another option for rotational cooling of species with very small rotational constants would be to use a swept CW laser to cool population near the ground state, as used in ref. 17, but adding to their technique a BROC laser to cool higherlying population.
In analogy with the numerous applications arising from translational laser cooling of only a handful of atomic species, we envision many new possibilities coming from rotational laser cooling of select molecular species with vibrational–electronic decoupling. In additional, the combination of BROC with broadband vibrational cooling^{14} could make possible optical rotational cooling of a still larger class of molecules. Building upon the current work, AlH^{+} is a good candidate for many currently unrealized goals for trapped molecules, including statetostate ultracold chemistry, alloptical cooling of all internal and external molecular degrees of freedom, singlemolecule fluorescence detection, coherent transfer of quantum information between molecular rotations and external circuits^{5} and singlemolecule spectroscopy^{32,33,34} including laboratory searches for timevarying fundamental constants^{7}.
Methods
Spectral filtering characterization
Using a similar femtosecond laser and spectral filtering apparatus operating at a slightly different wavelength (385 nm), we use two different analysis techniques to more precisely characterize the spectral filtering resolution. First, we create a homebuilt spectrometer by inserting a lineCCD (chargecoupled device) camera at the Fourier plane. A continuouswave laser is used to calibrate the spectrometer’s frequency reading and resolution. Second, the narrowband laser is beat against the filtered broadband light on a photodetector. The lowestfrequency beat note occurs between the narrowband laser and the nearest comb tooth from the femtosecond laser. From this beat note intensity, we determine the spectral density of the filtered broadband light at the narrowband reference laser’s frequency. We then map the filtering behaviour as we scan the cutoff across the reference. Both techniques yield a consistent result of 2 cm^{−1} filtering cutoff sharpness at 10 dB extinction.
Anomalous point in BROC data set
In one REMPD–TOFMS probe of N=3 population after BROC, for which there should be no Al^{+} signal if BROC worked perfectly, we observed a structureless peak in the Al^{+} bin of the TOFMS. The peak had a total charge consistent with a twoion Al^{+} signal, which occur in our TOFMS data both with and without structure. However, the peak was also consistent with structureless detector noise spikes observed occasionally at random times. Given our overall sample size and typical TOFMS timing distribution, it is very unlikely that the only observed signal from a residual population in N≥2 occurs as a single twoion event rather than as a small number of oneion events. Nonetheless, we take the conservative approach of treating this point as N=3 population resulting from imperfect BROC; we include it as such in Fig. 3b and in all analyses, except where otherwise noted.
Statistical analysis techniques and results
A ‘toy’ Monte Carlo technique was used to perform statistical error analysis. The method determines statistical properties by simulating repetition of a given experiment a large number of times, each time with the same total AlH^{+} number but with statistical fluctuations creating a distribution of simulated observations. An ntuple array using binomialdistribution random number generation is created; each row in the array represents a set of independent measurements, for example, N=0 and N=1 population fractions. Using variations of this analysis, experimental consistency with our model can be verified, and we can determine statistical bounds without relying on binomial confidence intervals far from the central limit approximation. Example simulation results are shown in Fig. 4.
Perfect BROC cooling would result in 100% population in N=0 and N=1. In our experiment, the combined population measured to be missing from these two states 6(5)%, consistent with the expectation of fully efficient cooling and no loss from molecular dissociation^{22}. Apart from the suspect N=3 data point discussed above, no REMPD probes after BROC detected population in N>1, which is also consistent with fully efficient BROC cooling. Finally, to verify agreement of the BROC measurements with our rateequation simulation^{23}, an ntuple was generated that uses the experimental total ion numbers for our N=0 and N=1 BROC data sets, along with the BROC population fractions of f_{0}=48.3% in N=0 and f_{1}=51.7% in N=1 predicted from simulation. For each of 100,000 entries in the ntuple, the population fraction ratio, defined as f_{0}/f_{1}, is calculated and histogrammed (Fig. 4a). For this sample size, the data are well described by a Gaussian distribution; the experimentally observed ratio is consistent with the simulation, differing by 1.3σ.
The energetically allowed process of predissociation, in which AlH^{+} in the A^{2}Π state dissociates into Al^{+} and H, is expected to be rare^{22}. Predissociation during BROC would yield a signal of excess population in all rotational states, since it would provide an additional channel besides REMPD for conversion of AlH^{+} to Al^{+}. To set an upper limit on the predissociation fraction, the BROC total ion number detected in N≥2 was used, discarding the data set with suspect N=3 signal discussed above. Using five ntuples of 100,000 entries, an additional nonzero predissociation population was added to the toy Monte Carlo simulation; this parameter was varied by hand until only 10% of ntuple entries resulted in the observed value of 0 predissociated ions, from which we conclude at the 90% confidence level (CL) that less than 0.2% of the population predissociated during BROC. We estimate from the rateequation simulation that there are on average five excitations to A^{2}Π for BROC cooling from a room temperature distribution. Combining these results, we conclude at the 90% CL that the branching ratio of predissociation from A^{2}Π relative to spontaneous emission is <0.04%, corresponding to a 90% CL upper limit on the predissociating decay rate of 2π × 800 Hz.
A similar method was used to set the BROC temperature upper limit for each parity state, described in Results. An input temperature was used to calculate the thermal probabilities for being in the first excited state of each parity. This probability was then used to generate five 100,000entry ntuples for the experimental sample size. The temperature was increased until 10% of the ntuple entries contained one molecule in the secondlowest rotational state.
To determine the limits on possible population loss to unprobed states during VABROC, we consider the statistics of the population successfully cooled to N=0, and we ask whether it is consistent with the observed population remaining in N=1. We define a loss fraction f_{x} as the population in any state other than N=0 and insert this loss term into the Monte Carlo simulation. The 68% CL limits on f_{x} were found by adjusting f_{x} until only 16% of the simulated distribution fell on either side of the observed value of 4.6% missing from N=0; a sample ntuple distribution at one of these limits is shown in Fig. 4b. The resulting value for VABROC loss is 4.6_{−1.3}^{+2.1}%. A separate analysis using a similar technique for the population in N=1 yields 2.0_{−1.4}^{+3.3}%. We conclude that our results are consistent with all population after VABROC being in either N=0 or N=1, with no evidence for loss to other states.
The population ratio between N=1 and N=0 was used to determine the VABROC experimental temperature. The 68% CL limits, determined similarly to the VABROC loss and using five ntuples of 100,000 entries, yields a VABROC temperature of 3.8_{−0.3}^{+0.9}K. An alternative analysis technique would be to use the populations rather than the ratio to determine a temperature. For example, using the measured groundstate population of 95% would yield a rotational temperature of 4.4 K. However, since extraction of the temperature from the population ratio makes no assumptions about detection efficiency, we consider it to be the more reliable technique.
Efficiency of VABROC cooling
Apart from the suspect data point discussed above, there is no other evidence that imperfect BROC performance leaves population in N≥2. However, we observe a clear signal of population not fully cooled to N=0 by VABROC (Fig. 3b). This type of asymmetry between BROC and VABROC performance is expected because the spectral cutoff of the latter is necessarily closer to the Qbranch heating transition frequencies. A rateequation simulation predicts that for operation below saturation on all transitions, if 1% of the intensity pumping P(1) leaks through the filter to pump Q(0), the result will be 6% population in N=1, similar to the measured quantities discussed below.
We have not attempted to make a serious model for spectral leakage; however, a simple analysis suggests plausibility for the presence of percentlevel leakage intensity at Q(0). The separation between the P(1) and Q(0) transitions is 13 cm^{−1}, which is smaller than the accuracy of our absolute spectral calibration. The 2cm^{−1} width of this cutoff is large enough compared with the P(1)−Q(0) separation that percentlevel leakage at Q(0) for nonoptimized mask placement would be unsurprising. Further investigation is required to confirm expectations that improved frequency tuning and cutoff resolution of the filter will lead to lower rotational temperatures after VABROC.
VABROC coolingtime model
The detected population P_{0}^{d} in N=0 is expected to obey P_{0}^{d}=P_{0}^{f}−P_{1}^{i}B_{2}e^{−T/τ}, where P_{0}^{f} is the measured asymptotic population in N=0, P_{1}^{i} is the initial population in N=1 following the faster BROC phase of cooling, taken here from simulation, B_{2}≈2/3 is the calculated branching fraction for spontaneous emission from X^{2}Σ^{+}, υ=1, N=1› to X^{2}Σ^{+}, υ=0, N=2›, 1/τ is the overall vibrational spontaneous relaxation rate from υ=1, and T is the duration of the VAPROC pulse. Note that the N=0 population at the shortest times probed is expected to be elevated from ~50% from BROC because VABROC quickly pumps population from υ=0, N=1› into υ=1, N=0›, which then relaxes to either υ=0, N=0› or υ=0, N=2› before analysis.
Upgrades for faster cooling
Driving a single twophoton transition from X^{2}Σ^{+} to A^{2}Π would allow parity to be cooled without needing to resort to the relatively slow vibrational spontaneous relaxation event used in VABROC. Driving this transition in microseconds could be accomplished with a single commercially available pulsed laser, using two photons of the same wavelength, far from any resonance. If continuous parity cooling is desired, CW or quasiCW lasers nearresonant with an intermediate state would be required. Using one of the first few vibrational levels of X^{2}Σ^{+} as an intermediate state, commercially available lasers could drive the transition on microsecond timescales even if detuned from resonance by ~100 MHz. Although the hyperfine structure of AlH^{+} relevant for such narrowband excitation is not yet known, all hyperfine states should be addressable with powerbroadening^{35}.
Reducing vibrational excitation during BROC
The problem of imperfect electronicvibrational decoupling leading to ~14% transient population excited to the υ>0 on the BROC timescale is discussed in Results, as is the importance of this issue for BROC on heavier reducedmass species. To achieve nearunity efficiency cooling on the BROC timescale, a second femtosecond laser can be added to drive some number of Δυ=−1 vibrational cooling transitions. This laser need not be spectrally filtered for typical hydrides and fluorides, since vibrational heating and cooling transitions are generally separated by more than the femtosecond laser bandwidth. Although this is not the case for AlH^{+}, other BROCcandidate molecules such as SiO^{+} (ref. 21) have structure permitting a single laser to simultaneously drive vibrational cooling transitions from several excited vibrational levels. We note that including a vibrationally cooling femtosecond laser might also be desirable for heavier reducedmass species in order to deal with their higher thermally excited vibrational population at room temperature.
Additional information
How to cite this article: Lien, C.Y. et al. Broadband optical cooling of molecular rotors from room temperature to the ground state. Nat. Commun. 5:4783 doi: 10.1038/ncomms5783 (2014).
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Acknowledgements
We thank Michael Schmitt for generous help with uncertainty analysis and Michael Drewsen and Stephan Schiller for useful conversations. This work was supported by AFOSR grant no. FA95501310116, NSF grant nos. PHY1309701 and 0801685, and the David and Lucile Packard Foundation grant no. 200934713.
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C.Y.L. and C.M.S. designed and carried out the experiment. Y.W.L., J.H.V.N. and D.A.T. aided with the spectral filtering characterization, and J.H.V.N. developed the rateequation simulation code. B.C.O. conceived the study and participated in all stages.
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Lien, CY., Seck, C., Lin, YW. et al. Broadband optical cooling of molecular rotors from room temperature to the ground state. Nat Commun 5, 4783 (2014). https://doi.org/10.1038/ncomms5783
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DOI: https://doi.org/10.1038/ncomms5783
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