Studying fundamental physics using quantum enabled technologies with trapped molecular ions

Abstract

The text below was written during two visits that Daniel Segal made at Université Paris 13. Danny stayed at Laboratoire de Physique des Lasers the summers of 2008 and 2009 to participate in the exploration of a novel lead in the field of ultra-high resolution spectroscopy. Our idea was to probe trapped molecular ions using Quantum Logic Spectroscopy (QLS) in order to advance our understanding of a variety of fundamental processes in nature. At that time, QLS, a ground-breaking spectroscopic technique, had only been demonstrated with atomic ions. Our ultimate goals were new approaches to the observation of parity violation in chiral molecules and tests of time variations of the fundamental constants. This text is the original research proposal written eight years ago. We have added a series of notes to revisit it in the light of what has been since realized in the field.

Keywords:

• Cold molecular ions
• tests of fundamental physics
• quantum logic spectroscopy
• ultra-high resolution molecular spectroscopy
• parity violation
• variations in the fundamental constants

Acknowledgements

The authors thank Hélène Perrin, Anne Amy-Klein, Olivier Dulieu, Trond Saue, Jeanne Crassous and the French ion trapping community – in particular the members of the Quantum Information and Technologies group from the Laboratoire Matériaux et Phénomànes Quantiques, Université Paris-Diderot; the members of the Trapped Ions group from the Laboratoire Kastler Brossel, Université Pierre et Marie Curie; and the members of Confinement d’Ions et Manipulation Laser group from the Physique des Interactions Ioniques et Moléculaires laboratory, Aix-Marseille Université – for fruitful discussions. We would also like to thank the referees and editors for having very positively considered and criticized this unconventional manuscript.

Notes

No potential conflict of interest was reported by the authors.

1 Since 2009, the research into the electron EDM has seen remarkable advances. Molecules have made a sizeable impact here, as the best limits on the size of the electron EDM are now set using cold YbF [31] and ThO [32] molecules, outperforming the limit set by measurements on atoms [4]. The present proposal argues that, compared to atoms and neutral species, molecular ions have the potential to improve on precision tests of fundamental physics. Thus, in this context, the recent demonstration, in the group of Eric Cornell, of the first measurement of the electron EDM using trapped molecular HfH${}^{+}$ ions [33] is of particular pertinence. The resulting electron EDM upper bound is only 1.4 times larger than the current record using neutral species [32], and offers the potential to improve on this limit in the near future.

2 Since then, the search for varying fundamental constants, or for putting constraints on their variation, has become a very active part of experimental science. Recently, laboratory constraints on a drift rate of both the fine structure constant, $\mathit{\alpha }$, and the electron-to-proton mass ratio, $\mathit{\mu }$, in the present epoch have been determined by measuring two optical transitions in ${}^{171}$Yb${}^{+}$ ions [34,35]. Assuming a linear drift rate, intertwined constraints of $\dot{\mathit{\mu }}/\mathit{\mu }<{10}^{-16}$ yr${}^{-1}$ and $\dot{\mathit{\alpha }}/\mathit{\alpha }<{10}^{-17}$ yr${}^{-1}$ were derived. The LPL 2008 measurement that resulted in $\dot{\mathit{\mu }}/\mathit{\mu }=(-3.8\pm 5.6)\times {10}^{-14}$ yr${}^{-1}$ [6] remains the only current epoch direct $\mathit{\mu }$ constraint derived from a molecular study. As such, although less constraining, it is less model dependent. Complementary astrophysical measurements have also led to stringent constraints on the rate of change of $\mathit{\mu }$ on a cosmological timescale. The most stringent current constraints are derived from methanol absorption lines at redshift $z=0.89$ [36,37] and translate into $\dot{\mathit{\mu }}/\mathit{\mu }=(1.4\pm 1.4)\times {10}^{-17}$ yr${}^{-1}$, if a linear rate of change is assumed.

3 The supersonic beam approach has shown limitations since. Suitable chiral molecules for a parity violation measurement are solids with little to no vapour pressure [38,39]. They are thus poorly suited to a continuous supersonic beam setup which requires significant vapour pressure. Buffer-gas-cooled molecular beams formed using laser ablation of solid-state molecules in a cryogenic cell exhibit some of the highest beam fluxes to date, and are thus now considered [40]. They also exhibit lower velocities, allowing for yet longer interaction times.

4 With the exception of a few dimers formed by the photo-association or magneto-association of pre-cooled atoms, the ultra-cold world was until recently confined to atomic systems. The extension of laser cooling to neutral molecules has recently begun, with the demonstration of magneto-optical traps of diatomic molecules [41–43] and Sysiphus (optoelectrical [44] or laser [45]) cooling of polyatomic species, producing molecular samples at temperature down to 50 $\mathit{\mu }$K [42]. In the last two decades several methods to control beams of gas-phase molecules (in particular decelerators of various kinds [46]) have been developed, leading to the first molecular fountain, producing ammonia molecules in free-fall for up to 266 ms [47], or to the trapping of samples of CO molecules on a microchip, at temperatures as low as 5 mK [48]. We finally note that increasingly complex molecules have been cooled to 1 K using buffer-gas cooling, exploiting collisions with cryogenically cooled noble gas atoms (see [40] and references therein). We however stress again that the range of neutral species amenable to trapping and cooling is limited.

5 Small ion ensembles can nowadays be controlled to form a truly programmable 5-qubit quantum computer [49].

6 We note that, recently, a Yb${}^{+}$ single ion clock achieved an unprecedented relative frequency uncertainty of $3\times {10}^{-18}$ [50].

7 Since this proposal has been written, Quantum Logic Spectroscopy has been extended to ionic molecules, demonstrating the ability to non destructively measure a given molecular state [51] and even manipulate it [52].

8 For a review of the various cooling techniques that can be applied to trapped ions we refer the reader to [53]. See also the recent demonstration of an electromagnetically-induced-transparency cooling method to cool to the ground state the radial motional modes of an 18-ion string [54].

9 The ion internal degrees of freedom manipulations described here have been introduced in the context of quantum information processing (QIP), see for example [55]. QIP is still a very active field and nowadays, the trend is to perform those operations – except for detection – using direct microwave addressing of the qubit transition [56–58], which is less prone to scattered photons. Very recently the same microwave-based techniques were successfully applied to trapped molecular ions [52].

10 Internal state cooling via optical pumping using schemes related to those in [14,15] (in particular using broadband and incoherent optical sources) has been demonstrated for a variety of bialkali dimers as well as for a number of diatomic molecular ions (for a very good recent review, see [59]). The first implementation for a polyatomic molecule, methyl fluoride (CH${}_3$F), has been reported recently [60]. We also note that non optical internal state cooling has recently been demonstrated for BaCl${}^{+}$ [61] and MgH${}^{+}$ [62] molecular ions, through sympathetic cooling with respectively ultra-cold calcium atoms (see also footnote 11) or helium buffer-gas.

11 Sympathetic cooling relying on the Coulomb interaction between dissimilar ions is very efficient. For instance small ion crystals including molecular ions have been cooled to the motional ground state [63]. Using an astute selective photo-ionization scheme combined with sympathetic cooling it has been possible to produce samples of rotationally and vibrationally state-selected, translationally cold molecular ions [64]. We also note that alternative strategies are promising: the reader will find a recent review of sympathetic cooling of molecular ions by ultra-cold neutral atoms in [65].

12 Precise spectroscopic measurements with molecules have indeed increasingly been used in the last decade to test fundamental symmetries (parity [66,67], or parity and time-reversal, a signature of which would be the existence of a non-zero electron EDM, see footnote 1) and postulates of quantum mechanics [68], to measure either absolute values of fundamental constants (such as the Boltzmann constant $k_{\mathrm{B}}$ [69,70], or the proton-to-electron mass ratio $\mathit{\mu }$, with recently the first determination of $\mathit{\mu }$ from a molecular system [71]), or their variation in time (fine structure constant $\mathit{\alpha }$ [72], proton-to-electron mass ratio $\mathit{\mu }$, see foornote 2).

13 Over the last few years, several techniques for the production of molecular ions have emerged and are reviewed in [65]. The technique pioneered by the Drewsen group consists in first trapping an atomic ion of interest, usually produced by ionization of a neutral atomic gas, and then leaking in neutral molecular gas to react with the atomic ions and produce the desired molecular ions [22]. Recent examples are implementations by the Brown and Chapman groups to produce CaH${}^{+}$ [73] and Ba containing molecular ions [74] respectively. Another method for producing molecular ions is via laser ablation of a solid target [65]. In a third method reviewed in [75], a low-density neutral gas containing a parent molecule is leaked into the vacuum chamber and an electron beam or lasers are used to ionize the neutral molecules producing the desired molecular ion inside the trap volume.

14 Since then an ever increasing number of groups has mastered those techniques that are now part of the ‘toolbox’ to manipulate trapped ions. Dissemination of this know-how is particularly important in the context of experiments on cold molecular ions. For instance the European Commission (FP7) supports since 2013 a Marie Curie initial training network called ‘Cold Molecular Ions at the Quantum limit’ dedicated to this task (see http://itn-comiq.eu).

15 Recently, SrH${}^{+}$ has attracted much interest in fields ranging from precision measurements to cold chemistry or astrophysics and several theoretical studies [76–79] were reported for the calculation of the potential energy curves, permanent and transition dipole moments, static dipole polarizabilities of electronic states of SrH${}^{+}$.

16 Since then, the MMTF group has gained experience in frequency stabilizing QCLs at unprecedented levels and has used them to perform precise spectroscopic measurements [40,67,80,81]. The use of QCLs allows the study of any species showing absorption between 10 and 100 THz, paving the way for precise measurements on a considerably larger number of species.

17 Recently, the ability to operate micro-fabricated planar silicon-based ion traps in a cryogenic environment was demonstrated [82], thus combining a scalable trap design with a low heating environment.

18 See for instance the work by M. Kajita et al. who show that ultra-precise vibrational spectroscopy of SrH${}^{+}$ ions is possible at the ${10}^{-16}$ level and can thus be used to probe the temporal stability of $\mathit{\mu }$ in the present epoch [83,84], or could even be exploited in new generation molecular clocks [85].

Additional information

Funding

This work was supported by the Université Paris 13 through the Invited Professor Programme; Agence Nationale de la Recherche [grant number ANR-15-CE30-0005-01]; and Région Île-de-France through DIM Nano-K.