Cooling by quantum pickpocketing

[Nature India Special Issue: Lighting the way in physics]

Quantum physics and its application has dominated the description of physical phenomena since the beginning of the twentieth century. Central to these developments has been the detailed studies of atomic and molecular systems and their ions. In the last decades of the twentieth century, the ability to trap and cool single or few atoms/ions/molecules in a dilute gas ensemble allowed the opportunity to repeatedly interrogate particle quantum systems with unprecedented precision.

Trapping

The trapping of an atom (A), molecule (M) or their ions (I) is accomplished by specifically tailored configurations of electric, magnetic and optical fields. Traps are isolated regions of space where the displaced particle feels a restoring force towards the trap centre. Traps are formed over very small volumes in space – ~ mm3 or less in most cases – and have a maximum potential energy (PE) for particle confinement. When the kinetic energy of the trapped particle exceeds the maximum trap PE, the particle escapes the trap. To keep the particle continuously trapped, cooling of the trapped particles is necessary to bleed away the kinetic energy gained by the particle via uncontrolled fluctuations, imperfections as well as in the act of measurement.

Cooling

Cooling of quantum systems reduces the motional energy spread and requires the removal of kinetic energy from the motion of the particle. It is mediated by interactions that are inherently dissipative or inelastic and is achieved via a scattering process with fields, such as light, or material particles, such as atoms. Trapping, cooling and manipulation of single species of particle have led to tremendous advances in the fields of precision spectroscopy and metrology, quantum many-body physics and more.

Experimental background

In the mid-2000s, my colleagues at the Raman Research Institute (RRI) K. Ravi, Arijit Sharma and I started thinking about studying interactions at the quantum limit. Previous studies were doing a wonderful job of investigating particle-particle interaction with single trapped species, such as atoms or ions. Our aim was to study interspecies interactions between atoms and ions in the quantum regime when they were both trapped and cooled. This would allow us to look at a far wider range of interactions and enable the study of interacting quantum systems, which is fascinating and relevant to the quantum revolution we are in now.

Hybrid traps

We came up with the concept of hybrid traps (as they are now known), which combine the possibilities of simultaneously cooling and trapping distinct species such as atoms, ions and molecules in overlapping traps. Hybrid traps allow the preparation of both the internal states and the motional states of the two species, so that the interaction of interest can be studied with high precision and specificity. In what follows we will refer to the scientific knowledge of the time when we studied the interactions between trapped ions and laser-cooled atoms, rather than what has been discovered since.

Our first hybrid trap was a combined linear Paul trap with a magneto-optical trap (MOT). A Paul trap combines radio frequency voltages on electrodes with DC voltages. The time varying fields dynamically trap ions as static electric fields cannot make an ion trap as explained by Earnshaw’s theorem. The MOT combines laser cooling with gradient magnetic fields to achieve spatially localised cooling and trapping of atoms. In the years that have followed, more versatile hybrid traps have been built at RRI.

Tension with established thought

We first created an MOT of atoms and then ionised a small fraction of laser-cooled rubidium (Rb) atoms using two-photon ionisation. Since the ions were created in the overlapped trap centre of the two traps and the laser-cooled atoms had very low kinetic energy, the daughter ions created by ionisation were trapped in the ion trap. The trapped Rb+ ions can be detected by extraction to a channel electron multiplier (CEM) and identified by the time of flight taken. How long the trapped ions survive in the ion trap is then determined by measuring the loss of ions as a function of trap hold times. The cooling of the ions was determined by the application of the virial theorem to the widths of the time of flight distribution of the extracted ions. The longer the ions are held in the trap, the more efficient the ion cooling is in combatting the heating of the ions from all the uncontrolled processes. The Rb+ ion cannot be laser-cooled as the lowest optical transition is deep in the vacuum ultraviolet regime. The only cooling mechanism available to the Rb+ ion is collisions with the trapped Rb atoms.

We observed very efficient collisional cooling of the ions (Ravi, K., Lee, S., et al. Nat Commun 3, 1126; 2012). This was totally unexpected according to the foundational paper on collisional cooling of trapped ions by Fouad Major and Hans Dehmelt (Phys. Rev. 170, 91; 1968). Simply put, their theory, which a number of experiments had verified, predicted that for equal mass of ion (mI) and atoms (mA) no net heating or cooling could occur. To cool an ion efficiently by collisions, the condition was mA<mI (more practically mA≪ mI) and the condition mA>mI would lead to rapid heating of the ion. Our experimental measurements for which strong cooling was observed was for mA=mI, firmly contradicting the long established paradigm.

Two cooling mechanisms

We showed how cooling by elastic collisions worked quite differently when the coolant atoms were spatially compact and centred at the bottom of the ion trap. However, the observed ion lifetime data suggested there had been highly efficient cooling that had been far greater than could be supported by elastic collisions, since the large majority of collisions would be glancing which, on average, would result in very little momentum transfer. This signalled the presence of another much more effective cooling process. We proposed that the cooling was mediated by resonant charge exchange (RCE). In this mechanism, when the cold parent atom collides with a fast daughter ion without any change in internal energy an electron can hop from atom to ion resulting in a cold ion and a fast atom after the collision. Such an exchange of kinetic state of the ion and atom, resulting from the hop of a single electron from one ion core to an identical core makes resonant charge exchange an effective cooling mechanism. Its exchange-mediated process is quantum in essence and has the light touch of a pickpocket.

Results

To explain the observations, we needed a deep dive into the mechanics of collisional cooling of ions. The trapped ion heats and a collision will reduce its velocity and actually change its post-collision direction, resulting in it shifting from a trapping state to a non-trapping state because the stability of the ion is a function of its velocity vector and the phase of the trap potential. When the direction of the velocity changes after a collision, the ion can become non-trapped and be lost. In our experiment, the collisions happen very close to the bottom of the ion trap where the radiofrequency field is small and therefore the probability of a trap loss collision is very small. So elastic cooling with equal masses works and theory predicts that irrespective of the ratio of masses of the colliding partners, the ions should cool when collisions happen only at the bottom of the ion trap. This was subsequently shown in many theoretical and experimental works.

RCE cooling effects were calculated and its effectiveness in cooling was shown numerically in this study. Subsequent experiments from ours and other groups have confirmed the cooling mechanism. We are now building new experiments at RRI to further investigate this symmetry- and exchange-driven phenomenon.

Conclusion

In summary, in the article we showed unexpected ion cooling and explained it with two different cooling mechanisms and we offered a range of predictions for cooling, which have been subsequently proved. This work was enabled by the invention of a new type of combined trap for ions and atoms, the measurements in which led to an observation that was inconsistent with the canon in the field, encouraging detailed theoretical analysis of collisional cooling and the discovery of the two cooling mechanisms. Needless to say, the key contributions to this and related work in this area at RRI.