The increasing ability to manipulate physical systems at the most fundamental quantum level is currently leading to a wave of new technologies that have superior performance and capabilities for many applications in metrology, sensing, communication, simulation and computing. In this context, trapped and laser-cooled atomic ions have proven to be an outstanding system. Their exploitation, is however, typically limited by their coupling to time-varying stray magnetic fields which shortens the time available to perform high precision measurements, quantum simulations or to process quantum information. In this perspective, molecular ions are very promising because they can be made almost insensitive to magnetic field fluctuations. Their complex internal structure, however, makes quantum control of molecular ions very challenging. The action COMAMOC aimed at achieving full deterministic coherent control over the quantum states of a single molecular ion by demonstrating, on a test molecule MgH⁺, frequency comb driven manipulation of its rotational states. This innovative approach is today made possible by the development of frequency comb laser technologies and by the invention of a refined non-destructive state detection technique named “quantum logic spectroscopy”.

To achieve this goal, the scientific objectives of this Marie Skłodowska Curie Action (MSCA) have been to 1) achieve fast manipulation of both the electronic and motional quantum states of a single atomic ion with a frequency comb laser, 2) to implement photon recoil spectroscopy and 3) to combine the two techniques to perform frequency comb manipulation of pure quantum states of a molecular ion. A parallel goal of the MSCA Individual Fellowship was 4) to foster the development of the individual researcher.

 

Figure 1: CCD images of two Ca+ ions trapped and laser cooled simultaneously (top). At the bottom, an image of one Ca+ ion and of one MgH+ molecular ion. The MgH+ ion appears dark because it cannot be detected and cooled directly by laser. However, thanks to its Coulomb interaction, it can be detected and cooled via the laser-cooled and co-trapped Ca+ ion. Besides, the Ca+ ion can be used to detect the absorption or emission of photons by the molecular ion. This method is called Photon Recoil Spectroscopy (PRS) and is a more general form of Quantum Logic Spectroscopy.

During the time-frame of the project (01/05/2018-30/04/2020), objective 2 has been reached; objective 1 was almost completed, while important steps have been taken towards the final objective 3. As for objective 4, the action has without any doubts greatly enhanced the development and the career prospects of the individual researcher.

1. Fast frequency comb excitation of single Ca+ ions.

 

The main target within WP1 is to achieve faster manipulation of the quantum states of a single Ca⁺ ion when compared to previous experiments realized in the group using a fiber-based frequency comb laser. To that end, a solid-state Ti:sapphire frequency comb laser was set-up. This laser was demonstrated to fulfill all the requested requirements in terms of optical power, spectrum and stability to reach fast and coherent quantum state manipulation of ions. We are currently testing this laser on a single Ca⁺.

In parallel, spurious heating of the ion’s motion by voltage noise from the trapping electric sources has been investigated and reduced. This allows for less stringent requirements on the speed for quantum state manipulation.

 

2. Photon Recoil Spectroscopy

The main objective within WP2 was to implement Photon Recoil Spectroscopy (PRS) which is necessary for state detection of the molecular ion. To do so, the strategy was to first implement it on a simple system made of a purely atomic-ions Coulomb crystal (Ca⁺ - Mg⁺), where the Ca⁺ ion is the same ion to be used within WP3 for reading out the spectroscopic signal for MgH⁺, and the Mg⁺ ion, which has essentially the same mass as MgH⁺, is the test ion.

The first milestone was to achieved efficient ground-state cooling of the two motional modes of the Coulomb crystal (the in-phase and out-of-phase modes). To that end, a carefully designed sequence including Doppler cooling followed by so-called sideband cooling has been implemented and allowed to achieve ground-state cooling of both motional modes with an efficiency better than 98%.

Implementation of QLS was demonstrated by driving the broad 3s ²S_1/2 - 3p ²P_3/2 electronic dipole transition in Mg⁺, adding many photon momentum kicks to the two-ion system and then detecting them by driving the so-called “red sidebands” on the Ca⁺ ion (f_L-f₀ = -f_IP,f_OP < 0 kHz. see Fig. 4). Because the red sidebands can be driven if and only if the two-ion system is NOT in its motional ground-state, this scheme allows for detecting that the transition occurred in Mg⁺. Until now, QLS was almost exclusively implemented in systems where the motional mode frequencies were larger than both the natural linewidth of the transition and the linewidth of the exciting laser source. Here, the motional mode frequencies (f_IP ~ 150 kHz, f_OP ~ 300 kHz) are smaller than the natural linewidth of the transition (~ 40 MHz). In this regime that we call Unresolved Sideband Photon Recoil Spectroscopy (unresolved PRS), a time-consuming task consisted in simulating the expected QLS signal. Based on Einstein rates equations, we could numerically solve the complete dynamics of the two-ions system and compare the simulation results to experimentally obtained data. We obtained a very good agreement between experiments and simulations (see Fig. 5). Apart from reaching the milestone M2.2, this lead us to better understand the physics at play and mainly to apprehend the very high potential of unresolved PRS, in particular in the search for poorly known molecular lines. These results are published in a preprint (arXiv:2004:02959).

3. Frequency comb coherent manipulation of pure quantum states in MgH+

The main objective within WP3 was to achieve coherent manipulation of pure quantum states in MgH⁺ using the Ti:sapphire frequency comb that was set-up within WP1 and the PRS method that was demonstrated in WP2. Although this objective could not be reached within the timeframe of the project, many important steps have been realized towards it. The first milestone (M3.1) was to find an efficient protocol for loading Ca⁺ - MgH⁺ coulomb crystals into the trap (see Fig.6 left). The main difficulty was to ensure that only one of each ion were trapped simultaneously. To do so, a careful experimental procedure involving about 20 steps was devised.

The second milestone (M3.2) was to perform rotational laser-cooling of the MgH⁺ molecular ion. To that end, a quantum cascade laser (wavelength λ = 6 µm) was set-up, characterized and aligned on the molecular ion. In order to find the molecular line, our strategy is to actively broaden the spectrum of the laser to a full width at half maximum (FWHM) of the order of few 100 MHz, thus reducing the number of frequency points necessary to span the ±1.5 GHz uncertainty on the transition frequency. More precise determination of the transition frequency will then be achieved by reducing the FWHM of the laser to hone in on the specific ro-vibrational line. To optimize the experimental parameters, simulations of the expected PRS spectra have been performed for different laser intensities, linewidth and spectroscopy time. In particular, we found that unresolved PRS is a very powerful tool for the search of molecular lines due to an additional broadening mechanism that depends on the spectroscopy time. The search for the ro-vibrational transition is currently ongoing.