Controlling chemical reactions of a single particle

Abstract

Traditionally, chemical reactions have been investigated by tuning thermodynamic parameters, such as temperature or pressure. More recently, laser1 or magnetic field2 control methods have emerged to provide new experimental possibilities, in particular in the realm of cold collisions. The control of reaction pathways is also a critical component to implement molecular quantum information processing3. For these studies, single particles provide a clean and well-controlled experimental system. Here, we report on the experimental tuning of the exchange reaction rates of a single trapped ion with ultracold neutral atoms by exerting control over both their quantum states. We observe the influence of the hyperfine interaction on chemical reaction rates and branching ratios, and monitor the kinematics of the reaction products. These investigations advance chemistry with single trapped particles towards achieving quantum-limited control of chemical reactions and indicate limits for buffer-gas cooling of single-ion clocks.

Main

The full control over all quantum mechanical degrees of freedom of a chemical reaction allows the identification of fundamental interaction processes and the steering of chemical reactions. This task is often complicated in heteronuclear systems by a multitude of possible reaction channels, which make theoretical treatments very challenging. Therefore, focussing on the best-controlled experimental conditions, such as using state-selected single particles and low temperatures, is crucial for the investigation of chemical processes at the most elementary level. The hybrid system of trapped atoms and ions offers key advantages in this undertaking. On the one hand, ion traps offer a large potential well depth to trap the reaction products for precision manipulation and investigation. On the other hand, contrary to pure ionic systems, there is no Coulomb barrier between the particles to fundamentally prevent chemical reactions at low temperatures. Therefore, the efforts to control the motional degrees of freedom of one4,5,6 and both7,8,9,10,11,12,13 reactants in hybrid atom–ion systems have paved new ways towards cold chemistry. The yet missing component is the simultaneous control of the internal degrees of freedom.

The interaction between an ion and a neutral atom at long distances is dominated by the attractive polarization interaction potential V (r), which is of the form

Here, C4 = α0q2/(4π0)2 is proportional to the neutral particle polarizability α0, q is the charge of the ion, 0 is the vacuum permittivity, and r is the internuclear separation. Inelastic collisions take place at short internuclear distances. In the cold, semiclassical regime this requires collision energies above the centrifugal barrier14,15,16. Such processes are referred to as Langevin-type collisions and happen, even for cold collisions7,9, at an energy-independent rate . Here μ is the reduced mass of the collision partners and na is the neutral atom density. More subtle effects, such as the hyperfine interaction, which may lead to atom–ion Feshbach resonances, are not included in the polarization potential and have been investigated only theoretically so far17.

Experimentally, reactive Langevin collisions in the polarization potential have been investigated in ground state collisions7,8,9,10,12,18, which have exhibited relatively low rates for inelastic collisions, except for resonant charge exchange7. Recently, the first steps towards understanding reactive collisions in excited electronic states have been made using large ion crystals11,12,13, suggesting either a dominant contribution from very short-lived electronic states in the Rb + Ca+ system11 or, contrarily, a negligible contribution from excited state collisions in the Ca + Yb+ system12.

Here, we demonstrate how control over the internal electronic state of a single ion and the hyperfine state of neutral atoms can be employed to tune cold exchange reaction processes. We study quenching, charge-exchange and branching ratios, and we use near-resonant laser light to control the rates. Our measurements show a high sensitivity of the charge-exchange reaction rates to the atomic hyperfine state, highlighting the influence of the nuclear spin on atom–ion collisions.

In our experiment we study collisions between ultracold 87Rb atoms and single 174Yb+ ions, for which γLangevin/na = 2.1×10−15 m3 s−1. We start by determining the inelastic collision loss rate coefficients for the long-lived 2D3/2 (radiative lifetime 52 ms) and 2F7/2 (radiative lifetime 10 years) states of the ion (see Fig. 1 and Methods). The collisional stability of these states is of importance in buffer-gas-cooled ion clocks19 and quantum information processing. By optical pumping, both states are prepared as ‘dark’ states (see Methods), to study pure two-body collisions in the absence of light. This approach differs fundamentally from previous experiments in atom–ion11 excited state collisions, which always have been in presence of near-resonant laser light. We measure the inelastic loss rate γ by immersing the ion for a variable time t into the neutral atom cloud and determining the survival probability8,9,20,21 . To understand and model our data, we make three assumptions: first, the atom and the ion can undergo an inelastic process only in a Langevin-type collision. Second, the characteristic collision time is significantly shorter than the radiative lifetime. Third, inelastic collisions can only be exothermic thanks to the very low kinetic energy of the colliding partners and the absence of resonant laser light. We model γ = γLangevin as proportional to the Langevin collision rate using the state-dependent proportionality constant . For the electronic ground state of the ion interacting with the |F = 2,mF = 2〉 hyperfine ground state of Rb we find9S|2,2〉 = 10−5±0.3, and for the excited states we measure D|2,2〉 = 1.0±0.2 and F|2,2〉 = 0.018±0.004 (see Table 1). The constant = 1 corresponds to the largest allowed inelastic collision rate in the semiclassical model, and even in near-resonant charge-exchange between equal elements of atoms and ions7 it was expected and approximately found to be = 1/2. In this regard, our results are unexpected, as the 2D3/2 state of Yb+ combined with the 2S1/2-state of Rb is off-resonant by 0.14 eV to the next available asymptotic state in the Yb + Rb+ manifold (see Fig. 1). In contrast, the 2F7/2-state has nearby asymptotic states but its inelastic collision rate is significantly lower.

Figure 1: Level scheme and inelastic processes of the ion-neutral system.
figure1

a, Left: Yb+ level scheme with the transitions used for optically pumping the ion (to scale). Middle: level scheme of a rubidium atom. Right: asymptotic level schemes of the two channels Yb++Rb and Yb + Rb+. The collision is initiated in the Yb++Rb manifold and the Yb + Rb+ manifold can be populated by charge-exchange processes. b, Pictorial representation of the charge exchange reaction, and, c, quenching from an excited state. Shown are the filled core electronic shells and the relevant valence electrons. Yb+* refers to an electronically excited state of Yb+.

Table 1 Measured proportionality constant and branching ratios.

We now compare these results with inelastic collisions in the absolute lowest hyperfine state |F = 1,mF = 1〉 of the neutral atom. The hyperfine energy difference between the |F = 1,mF = 1〉 and |F = 2,mF = 2〉 states of Rb is 30 μeV, which is larger than the collision energy but negligible on the scale of the molecular potentials or the trap depth (250 meV). We find a significantly enhanced probability for inelastic collisions with the ion in the electronic ground state S|1,1〉 = (35±11)×S|2,2〉, which demonstrates the important role of the hyperfine interaction. For collisions with the ion in the D3/2 state, the value of remains unchanged.

For collisions in the electronic ground state of the ion, exothermic inelastic collisions are inevitably associated with a chemical reaction, leading to charge exchange or possibly the radiative association of molecules. The excess energy is converted into photons and/or kinetic energy of the reaction products. Depending on the amount of kinetic energy released, the reaction products are ejected from the ion trap or kept and detected by in-trap mass spectrometry9,22. A partial conversion of internal energy into kinetic energy in the predominantly predicted16 case of radiative charge exchange could be caused by the energy-dependent Franck–Condon overlap of the wave function of the entrance channels (A1Σ+ and a3Σ+) and the exit channel X1Σ+ of the (RbYb)+ potentials, owing to a 70% smaller polarizability of the X1Σ+ state (assuming negligible momentum transfer by the photon and constant orbital angular momentum). We control the distribution of the kinetic energy release in the charge exchange reaction by employing the hyperfine state of the neutral atoms; for atoms in |F = 1,mF = 1〉 we retain Rb+ with (48±3)% probability in the ion trap and for atoms in |F = 2,mF = 2〉 we find it with (35±3)% probability. We also study inelastic collisions in the excited dark D- and F-states, where the probabilities for observing Rb+ are quite similar to each other (see Table 1). We do not observe the formation of (YbRb)+ or Rb2+ molecules. The search for the latter was performed with the isotope 176Yb+ to achieve the required mass resolution.

With regards to collisional quenching between different electronic levels of the ion, we are principally able to detect two different quenching scenarios: 2F7/2→ 2S1/2 and 2D3/2→ 2F7/2. We directly observe quenching of 2F7/2→ 2S1/2 as shown in Fig. 2, where we exemplarily show two different experimental runs, with and without quenching (see also Methods). After the quenching, we observe an increased temperature of the ions, which indicates a release of kinetic energy smaller than the depth of our trap, despite the large energy gap between the 2S1/2 and 2F7/2states. The quenching rate from 2D3/2→ 2F7/2 was observed not to be detectable above our background rate.

Figure 2: Collisional quenching from 2F7/2 to 2S1/2.
figure2

A two-ion Coulomb crystal is prepared in the 2F7/2 dark state by optical pumping, then interacts with the neutral atoms, and is subsequently probed by laser fluorescence (see Methods). An early appearance of laser fluorescence indicates collisional quenching (black curve) as compared to no quenching (grey curve). The large fluorescence dips indicate a high temperature of the ion crystal.

Having established the inelastic collision parameters of the metastable D- and F-states without resonant laser light, we now turn our attention to inelastic collisions in the presence of laser light for both the 2S1/2– 2P1/2 (369 nm) and the 2D3/2– 3D[3/2]1/2 (935 nm) transitions. The purpose of the light is to experimentally tune the rates and to observe the occurrence of inelastic collisions in real time. The radiative lifetime of the 2P1/2 state (8 ns) is too short compared with the collision rate to provide pure P-state measurements. Here and in the following, we assume that the F-state is unoccupied, because the 411-nm light is turned off and collisional quenching into the F-state has been measured to be negligible. Therefore, the overall inelastic collision rate is determined by a mixture of S-, P-, D-, and D[3/2]-states

Here, px is the occupation probability of state x, which we determine experimentally for different settings of laser intensities and detunings (see Methods). In Fig. 3a we show the state populations of the S, P, D and 3D[3/2]1/2 states as we vary the frequency of the laser at 935 nm on the 2D3/2– 3D[3/2]1/2 transition. Figure 3b shows the associated change in the inelastic collision rate in the presence of the neutral atoms. We demonstrate tuning by one order of magnitude and we find it closely follows the model of equation (1) indicating a dominant contribution from the D-state. From these data we also extract P = 0.1±0.2, which is small and consistent with zero. Figure 3c shows the linear scaling of the inelastic collision rate with neutral atom density, confirming the picture of binary collisions.

Figure 3: Inelastic collision control by laser light.
figure3

a, State population measurement of the ion in the absence of neutral atoms as a function of the detuning of the repump laser at 935 nm. b, Inelastic collision rate for the same detuning data in the presence of neutral atoms at na = 1×1018 m−3. The solid line shows the theoretical result of equation (1). c, Density dependence of the inelastic collision rate with the repump laser on resonance. The exponent of the power-law fit (solid line) is 0.98±0.02.

Finally, we turn our attention to the observation of the kinematics of the collision products. In Fig. 4 we show the fluorescence at 369 nm during the interaction, with the 935-nm light on. Figure 4a–c shows individual experimental runs, in which the initial sharp loss of fluorescence results from an inelastic collision. If some kinetic energy is released in this process, the ion is on a large trajectory in the trap (much larger than the size of the atom cloud), but can be re-cooled, which is signalled by the relatively slow increase of the reoccurring fluorescence, from which we determine a lower bound for the release energy of 8 meV. We observe in 4% of our events that the fluorescence of the ion reoccurs after a certain time, before it undergoes a second inelastic collision and is dark again. As we keep the Yb+ ion in the trap, these processes are not charge-exchange reactions but quenching processes with a kinetic energy release less than ≈250 meV. Because the ion is colliding in highly excited electronic states, such as P1/2 and D3/2 with internal energies of ≈3 eV, this suggests a mostly radiative decay into the ground state S1/2. We have ruled out that the reoccurrence events are linked to the dissociation of a potential molecular ion in a secondary collision with neutral atoms12. To this end, we have performed this measurement also with extremely short interaction times between neutral atoms and the ion (on the order of a few collision times) and performed mass spectrometry on the dark ion after the collision, confirming the absence of a molecular ion.

Figure 4: Monitoring of inelastic atom–ion collisions.
figure4

ac, Recorded fluorescence for selected events. After a quick initial loss, the fluorescence reoccurs after random times when the kinetic energy released in the inelastic collision has been removed by cooling. Then, a second collision occurs and the ion disappears again. The curves are vertically offset for clarity. d, Sum of 343 repetitions of the experiment, which is fitted with an exponential decay for short times. Inset, zoom-in on the initial decay of plot d. The solid line is an exponential fit to the data.

Methods

Preparation of ultracold atoms and ions.

We prepare 4×105 neutral 87Rb atoms in the |F = 2,mF = 2〉 hyperfine state of the electronic ground state at temperatures down to T≈200 nK in a harmonic magnetic trap of characteristic frequencies23 (ωx,ωy,ωz) = 2π×(8,26,27) Hz. By changing atom number and temperature, we tune the atomic density by two orders of magnitude. The atoms can be transferred into an optical dipole trap formed by two crossed laser beams at 1,064 nm. Here, the atoms can be transferred into the ground hyperfine state |F = 1,mF = 1〉 using a resonant microwave pulse. At the same location, we trap single Yb+ ions in a radio-frequency Paul trap with secular trap frequencies of radially and ωax = 2π×42 kHz axially8,9. We use standard techniques to cool and detect single ions or small ion crystals on the cycling transition 2S1/2– 2P1/2 near 369 nm wavelength (see Fig. 1). From the excited 2P1/2state, radiative decay populates the 2D3/2 state with a probability24 of ≈1/200. For efficient laser cooling and detection, a laser at 935 nm pumps the population via the 3D[3/2]1/2 state back into the cooling cycle. Preparation in 2D3/2 (radiative lifetime 52 ms) is achieved by optical pumping from the S1/2 state using laser light at 369 nm in less than 10 μs in the absence of light at 935 nm, which is significantly faster than the inverse of the Langevin collision rate of a few 103 s−1. Alternatively, the 2F7/2 state (radiative lifetime 10 years) is populated by optical pumping on the 2S1/2– 2D5/2line with spontaneous decay on the 2D5/2– 2F7/2 transition25. The ion is spatially overlapped with the centre of the ultracold neutral atom cloud by displacing the two independent trapping potentials. The typical collision energies26, due to residual micromotion, are on the order of 0.004 meV.

Detection of collisional quenching.

We prepare two ions in a small Coulomb crystal at time t = 0 in the 2S1/2 ground state, which we detect by near-resonant laser fluorescence at 369 nm (together with repumping at 935 nm). The optical pumping into the 2F7/2 state using light at 411 nm is switched on at t = 500 ms for 500 ms and, typically within 100 ms, the ion is pumped into the desired state (see Fig. 2). As a result, the fluorescence counts on the 369nm transition drop to zero. After the interaction with the neutral atoms (effective duration typically 16 ms) and the subsequent removal of the neutral atom cloud, the fluorescence on the 2S1/2– 2P1/2 transition (together with repumping at 935 nm) is probed from t = 5,000 msonwards. If the ion is still in the 2F7/2 state it will not scatter photons; however, if it has been quenched to 2S1/2, we observe fluorescence. At t = 6,000 ms, the ions are optically pumped from the F-state back into the S-state to ensure that no ions have been lost. The fluorescence count rate during the preparation part of the sequence is lower owing to the presence of an offset field from the magnetic atom trap, which is turned off when the atoms are released.

Experimental determination of the ion electronic state occupation.

Owing to the experimental situation of a multilevel system in the presence of a magnetic field and imperfect polarization of the laser beams, we determine the state populations px = τx/τc experimentally rather than relying on theoretical modelling. Here, τc is the average time between two spontaneous decays on the 2P1/2– 2D3/2 transition, τx is the average time spent in state x{S,P,D,D[3/2]} during τc, and . The time τP is given by the decay rate Γ of the P1/2 state and the branching ratio of the P-state into S- and D-states as τP = 200/Γ. A sequence of alternating pulses from the 369 nm and 935 nm lasers are used to determine τS and τD. τP + τS is observed as the exponential decay constant of fluorescence after the 369 nm laser is pulsed on. The pulse length is set to get complete depletion of the SP system into the D-state. For a given setting of intensity and detuning of the 935-nm laser, the average number of photons N369 per 369 nm pulse depends on the duration t935 of the preceding repump pulse. Varying the length t935 allows us to retrieve τD and the photon detection efficiency η from the fit of 200η[1−exp(−t935/τD)] = N369 to the counted photon number. We find η = (2.1±0.1)×10−3, in accordance with the numerical aperture of the imaging system and the quantum efficiency of the single-photon counter. The lifetime of the excited 3D[3/2]1/2 state is τD[3/2] = 40ns and the branching ratio is 98% into S1/2 and 2% into D3/2. Decay into P1/2 is not dipole-allowed owing to parity27 and therefore we do not have to consider a cascade through intermediate levels.

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Acknowledgements

We thank D. Sigle for experimental assistance, Engineering and Physical Sciences Research Council (EP/H005676/1), European Research Council (Grant number 240335), and the Leverhulme Trust (C.S.) for support.

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The experimental protocols were devised by all authors. Data taking and data analysis was performed by L.R., C.Z. and C.S. The manuscript was written by M.K. with contributions from all authors.

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Correspondence to Carlo Sias.

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Ratschbacher, L., Zipkes, C., Sias, C. et al. Controlling chemical reactions of a single particle. Nature Phys 8, 649–652 (2012). https://doi.org/10.1038/nphys2373

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